Modelling entomological-climatic interactions of Plasmodium falciparum malaria transmission in two Colombian endemic-regions: contributions to a National Malaria Early Warning System

Background Malaria has recently re-emerged as a public health burden in Colombia. Although the problem seems to be climate-driven, there remain significant gaps of knowledge in the understanding of the complexity of malaria transmission, which have motivated attempts to develop a comprehensive model. Methods The mathematical tool was applied to represent Plasmodium falciparum malaria transmission in two endemic-areas. Entomological exogenous variables were estimated through field campaigns and laboratory experiments. Availability of breeding places was included towards representing fluctuations in vector densities. Diverse scenarios, sensitivity analyses and instabilities cases were considered during experimentation-validation process. Results Correlation coefficients and mean square errors between observed and modelled incidences reached 0.897–0.668 (P > 0.95) and 0.0002–0.0005, respectively. Temperature became the most relevant climatic parameter driving the final incidence. Accordingly, malaria outbreaks are possible during the favourable epochs following the onset of El Niño warm events. Sporogonic and gonotrophic cycles showed to be the entomological key-variables controlling the transmission potential of mosquitoes' population. Simulation results also showed that seasonality of vector density becomes an important factor towards understanding disease transmission. Conclusion The model constitutes a promising tool to deepen the understanding of the multiple interactions related to malaria transmission conducive to outbreaks. In the foreseeable future it could be implemented as a tool to diagnose possible dynamical patterns of malaria incidence under several scenarios, as well as a decision-making tool for the early detection and control of outbreaks. The model will be also able to be merged with forecasts of El Niño events to provide a National Malaria Early Warning System.


Background
The World Health Organization estimates that malaria parasites infect from 200 to 300 million persons and kill more than 1 million people each year, primarily children under the age of five [1]. The efficacy of control measures has decreased over the past decades because mosquitoes and parasites are becoming more resistant to the commonly used insecticides and anti-malarial drugs [2]. As a result, malaria kills more people today than three decades ago. To further complicate matters, the international community suggests that diseases relayed by mosquitoes, such as malaria, are among those infectious diseases most likely to spread dramatically as global temperatures head upward [3,4]. Forecasts from different models suggest that by the end of the 21st century ongoing warming will have enlarged the zone of potential malaria transmission from an area containing 45 percent of the world's population to an area containing about 60 percent [4]. Although this expansion certainly fits the predictions, the cause of that growth may not be attributed convincingly to global warming. Other factors (maybe the dominant contributors) may have been involved as well, for instance: disruption of the environment in ways that favour the mosquitoes' proliferation, declines in vector-control and in other public health programs, and rises in drug and insecticide resistance [4]. To make matters worse, there are a number of 'macro-factors' such as economic inequalities, continuous human migratory patterns and vegetation patterns that may increase or decrease vulnerability and exposure to vector-borne infections and play an important role in regional morbidity and mortality profiles. Clearly, it is impossible to treat climate isolated from the other biological, socioeconomic and demographic contributors if the determination of the potential impact of climate change on malaria incidence is urgently need to be made. However, the hypothesis for a climatic contribution becomes stronger: even though malaria is a highly complex multi-factorial disease, previous studies have identified environmental factors and climate variability as going a considerable way in helping to explain the fluctuations of disease incidence [5][6][7].
In Colombia, currently, the population exceeds 44 million people; more than five million live in endemic-prone regions. Malaria has recently re-emerged as a significant public health burden in the country: incidence during epidemic years (total positive cases for both Plasmodium falciparum and Plasmodium vivax malaria scaled by the total population at risk per 1,000 inhabitants) increased from less than 2.5 in 1963 to 6 in 1983 and almost 10 in 1998. During 1996, disease transmission reached 42 cases per 1,000 inhabitants in high-risk areas. In the Chocó Department, on the Colombian Pacific Coast, more than 80,000 cases were reported during 1998, when the population at risk was 380,000 people [8]. During the year 2000 malaria cases were reported in 69% of the 125 towns of the Department of Antioquia, in the Andean region. Besides the aforementioned strongly increasing trend, the Annual Parasite Index also exhibited a significant association between the increase in the number of malaria cases and the occurrence of the El Niño warm event, which is considered the main forcing mechanism of Colombia's hydroclimatology at inter-annual timescales [8]. There is strong evidence that the El Niño event intensifies the annual cycle of malaria cases in endemic rural areas as a consequence of concomitant anomalies in the normal annual cycle of temperature and precipitation. During 'normal' years, endemic malaria exhibits a clear-cut 'normal' annual cycle, which is associated with prevalent climatic conditions. During El Niño events, characterized by increasing temperatures and decreasing monthly rainfalls, river flows and soil moistures, malaria outbreaks were found to be enhanced by climate anomalies. The annual cycle of malaria seems to be affected in its amplitude (increase in the number of cases), although the phase (or timing) remains unaltered in most malaria prone-regions of the country [8].
As recent scientific and technological advances have permitted much better predictions of the El Niño event, there is an evident opportunity to incorporate this climate forecasting capability into programs, campaigns, control measures and mitigation plans to reduce the human health impact of malaria outbreaks in Colombian proneregions. Nevertheless, there remain significant gaps of knowledge in the understanding of the interactions between climatic factors and the dynamics of malaria transmission, which have motivated attempts to explore and develop mathematical comprehensive models.
Detailed dynamic models of malaria epidemiology have been developed extensively and have made important contributions to understanding the transmission of malaria and other diseases [3,[9][10][11][12][13][14][15][16][17][18][19][20][21]. There are limitations, however. Although these models can provide adequate approximations to some biological and epidemiological characteristics, most of them have not been able to describe the overall transmission dynamics [21]. Even though mosquitoes and vertebrate host dynamics are generally included, most models do not include changes in environmental and climatic patterns that could affect disease incidence in both spatial and temporal scales, nor do they include the social, economical and demographical conditions prevailing in the communities that were studied. In this article experiences in developing and implementing a vector-borne disease model, which is based on previously proposed differential-equation 'compartment' models, are reported. The aim was to validate the mathematical tool by comparing its results under conditions of intense transmission in two specific malaria prone-regions of Colombia. To do so, malaria prevalence changes were monitored in these areas and model predictions were tested to assess their consistency with field observations.
In developing the mathematical model, three major steps were followed: (i) First, the parasite transmission cycle was studied to define those endogenous variables strongly affected by climatic conditions. (ii) The vector ecology, behavioural patterns of mosquitoes and entomological parameters were analysed in order to determine those exogenous variables (and their relationships with climatic anomalies) that might be relevant for representing malaria transmission. Analyses were focused on the necessity to represent the observed fluctuations in vector density. (iii) The vector population dynamics during preimago stages was represented, including the availability of adequate breeding sites and the predator-prey interactions during larval stage.
In applying and validating the mathematical tool, five major steps were followed: (a) homogeneity analysis of hydrological time series, to detect possible changes in mean and variance, as well as significant trends in historical series of both temperature and precipitation. (b) Analysis of total positive malaria cases, to determine the behaviour of epidemiological time series, to establish the initial values of state variables, and for fine-tuning the parameters. (c) Correlation analysis, to determine the contribution of climate factors on the temporal variance of malaria transmission. (d) Simulation-base scenario, to analyse the behaviour of the proposed differential-equation model and its preliminary results. And (e) simulation-alternate scenarios, to analyse several simulation results of the set of non-linear differential equations when perturbations of several exogenous variables, changes in control parameters and changing climate scenarios were considered.
The mathematical tool allowed improving the understanding of the linkages between climate patterns and malaria outbreaks, mainly during the onset of ENSO warm events. Experiences suggest that forecasts of future El Niño events will be able to be merged with mathematical models to provide a Malaria Early Warning System (MEWS) to enhance disease surveillance, control and response to epidemics, and facilitate early, coupled and environmentally sound public health interventions [8]. Figure 1 depicts the schematic diagram of the proposed overall malaria model. The comprehensive tool has three linking components that can be simulated separately, if desired, except in the case of vector-host interactions.

Main module
These components are the human host population, the mosquito population (vector ecology), and the weather patterns. Climate strongly affects the corresponding interaction between populations during a blood meal, as well as the vector ecology and the availability of breeding sites.
By ignoring the secondary exo-erythrocytic schizogony, that takes place in the parenchymal cells of the liver, simulation was limited to representing P. falciparum malaria transmission. Based upon the widely known biological and epidemiological aspects of malaria transmission, a susceptible person may become a member of the infected class if the individual is inoculated with sporozoites during an adult female Anopheles mosquito infective bite. The exo-erythrocytic schizogony and the erythrocytic schizogony take place in the infected vertebrate host. During this stage, sexually differentiated forms (gametocytes) are present in the host's blood circulation and can be taken by a susceptible female mosquito during a new blood meal. Parasites can then be transmitted from this mosquito to a susceptible person in some latter human-vector interaction. The progressive increase of parasitaemia in the infectious host as a result of multiple erythrocytic cycles may be slowed down by the immune response of the human. Finally, the immune individual loses immunity and returns to the reservoir of susceptible hosts.
In the vector ecology, a susceptible adult female Anopheles mosquito becomes a member of the infected class when it takes a blood meal from an infectious host and ingests the gametocytes present in the individual's blood stream. The vector finally enters the reservoir of infectious mosquitoes after the completion of the sporogonic cycle.
Since vector density is commonly assumed to be constant by most researchers, this variable has played a minor role in the construction of their mathematical infectious disease models. It is generally accepted that it is very difficult to arrive at a reliable estimate of the changes in vector density over large areas as a result of changes in temperature, precipitation and humidity. The effort of this research is aimed at fully representing the vector density in humanmosquito interactions, by considering three additional stages (virtual compartments) in the mosquito ecology: the pre-imago stages eggs, larvae, and pupae. Interests included the analysis of average development periods from eggs to adult mosquitoes, expressed as time delays and the related survival probabilities, expressed as successes in hatching, larval development, and adult emergence. All these entomological variables seem to be strongly dependent on the ambient temperature or water temperature of the breeding site. Figure 1 Schematic diagram. The main blocks represent linking components: mosquito population (vector ecology), vertebrate host (human) population, and weather patterns. Level variables are represented by small rectangles: egg, larva and pupa (virtual compartments), susceptible vector, infected vector and infectious vector (top), and susceptible, infected, infectious, and immune host (bottom). Mosquito and host populations are linked by the transmission of parasites through mosquito blood meals (vertical). The non-continuous arrows represent time delays. The ovals on top represent: (left) table functions affecting the main module and denoting the availability of adequate breeding sites, and (right) predator-prey interactions during preimago stages. On non-continuous arrows, the circles represent hatching, larva development and emergence success. Variables DT, RH, DP, WP and SM represent mean daily temperatures, mean daily relative humidity values, total daily rainfall records, wind patterns, and soil moistures, respectively. DT and HR affect the vector ecology and the blood meal. DP and SM affect the availability of adequate larval habitats. At the first approximation, wind patterns, which may affect mosquito densities, are not considered. The 'virtual' compartments representing pre-imago stages are only used when vector densities obtained by simulation are required for estimating the Vectorial Capacity.

Breeding places availability model
The availability of larval habitats ( Figure 1) has been based on level fluctuations of the quantity of water in breeding places of varying capacities. Table functions affecting the egg laying (oviposition) of a vector population -into the main module-have been estimated through Fuzzy Logic. This methodology was used to generalize the discrete events 'larval habitat completely available-completely full' and 'larval habitat not available-completely dry' to a continuous (fuzzy) form or partial truth. We considered the collections of water as 'reservoirs' ranging from 10 to 60 mm in depth opened to observed rainfall, estimated actual evaporation, and assumed constant infiltration. Daily evapotranspiration was estimated using the models introduced by: Turc (1945), assuming a homogeneous distribution of evapotranspiration throughout the year; Coutagne (1974) using Budyko's equation (1974); Cenicafé (1997), a specific evaporation model suited for Colombia; and Thornthwaite (1948), assuming a relation between actual and potential evapotranspiration of about 0.70 and a homogeneous distribution throughout each month [22].
As ovipositing anopheline females often prefer standing fresh water with low organic contents [23], this model determine the number of successive days that a breeding site remained between 90 and 100% of its capacity. This period of time is needed to complete all stages including egg batching, growth and metamorphosis in aquatic existence, and adult (imago) emergence. A 'favourable' condition is given when this period exceeds 12-15 successive days [2], and is normally affected by the water temperature of the breeding site. Finally, as anopheline eggs cannot survive prolonged desiccation, we assumed that a breeding site is 'not favourable' for the development of the species during pre-imago stages if it remains dry for more than two successive days. For the sake of simplicity, other relevant factors such as exposure to sunlight, emergent vegetation, temperature, salinity, and organic content [23], were not included in the model.

Predator-prey interaction models
This module allowed us to represent the interaction between the pre-imago stages of the mosquito population (mainly during larvae stage) and natural predators ( Figure  1). As a first effort, the Lotka-Volterra predator-prey type model [24][25][26] has been introduced into the differentialequation system to analyse the dynamics of both the prey and predator populations. Parameters for other types of models that were included in the model, but are not currently used, including Henize predator-prey model [27,9], Kaibab III prey-food model [10], Ecological System with External Forcing [9], and Autonomous Ecological System [9], are being calibrated through laboratory experiments.

System of coupled non-linear differential equations
The mathematical model represents the feedback mechanisms and interactions depicted in Figure 1. The comprehensive tool is based on a system of coupled non-linear differential equations, which is solved through a fourth order Runge-Kutta numerical algorithm. Simulations are being run using the computer software Powersim Constructor Version 2.51. The system of differential equations for the human population component and hence, the dynamics of malaria transmission in human hosts, is the following: The variables HUS, HUI, HUF, and HUM denote the total number of susceptible, malaria-infected, infectious, and immune human hosts at a given time t, respectively. In this component, Martens' equations [3] were followed, although considering the infective stage of the human hosts.
For the vector ecology component, the model uses the following system of coupled non-linear differential equations to describe the dynamics of the pre-imago stages of the vector population: The dynamic variables E, L, and PU denote the total number of eggs, larvae, and pupae at a given time t, respectively. The table functions T 1 , T 2 , T 3 , and T 4 represent the multiplier factors affecting oviposition (competition during egg-laying), and eggs, larvae and pupae mortalities, respectively.
To describe the dynamics of the imago stages of the vector population and hence, the dynamics of malaria transmission in adult female mosquitoes, the model uses a second set of differential equations:  The dynamic variables VS, VI, and VF represent the susceptible or non-infectious, malaria-infected, and malaria infectious mosquito (adult females) population sizes at a given time t, respectively.
To represent the dynamics of natural predators, the following equation is initially considered in the overall malaria model: The exogenous and endogenous variables considered above are described in Tables 1 and 2 for the mosquito  population, Tables 3 and 4 for the human population, and Tables 5 and 6 for the represented infectious disease models (Vectorial Capacity [28], Entomological Inoculation Rate [29], and Basic Reproduction Rate [3]). Five assumptions on vector density, denoted by m, have been used for calibration (see parameter K1 in Table 6): (a) a Human Biting Rate observed during field campaigns for both indoor and outdoor landing captures (HBD); (b) a vector density obtained through simulation and considering the dynamics of mosquito ecology (DC); (c) a critical density threshold necessary to maintain parasite transmission [15] (DCR); (d) an assumed constant density (D_0); and (e) a variable vector density considering seasonal fluctuations (D_1).
The function represents the net oviposition that occur every FI pulse (see feeding interval in Table 2). That is, it is assumed that the interval between blood meals (i.e. the length of the gonotrophic cycle) is equivalent to the time interval between successive ovipositions. In the predator-prey interactions module, PD represents the predator population, aS the predation rate coefficient, bp the reproduction rate of predators per 1 prey eaten, and mp the predator mortality rate. In the breeding places availability model, fL and fL_S represent, respectively, the water availability and the level of desiccation (    Figure 10B. The actual average temperature T must range between T min, bd and the maximum temperature of about 40°C (this relationship was estimated for An. maculipennis and is used because it agrees with the observations of other Anopheles species [36,17,37,30,38]).
Finally, the carrying capacity of the mosquito population was defined assuming a maximum vector-human ratio of 30:1.

Study sites and demographic data
Previous diagnostic studies of the relationship between climate and malaria in Colombia focused on a nationwide level at yearly timescales [6][7][8], and on regional and local levels at inter-annual, annual and seasonal timescales [5]. Previous modelling efforts by the research group were applied to understand malaria transmission in an endemic site on the Pacific coast of Colombia (the Nuqui Region) [30][31][32]. For this application, the simulation period of the mentioned study site was extended and a new specific area located in the Department of Antioquia, in north-western Colombia ( Figure 2) was chosen. This area, or the so-called 'El Bagre' Region, is located in the 'Bajo Cauca' Programmatic Area along the floodplains of the Cauca and Nechi Rivers ( Figure 2C). The current total populations in Nuqui and El Bagre localities reach, according to demographic census, 5,324 and 65,342 individuals, respectively, with 2,565 (48,2%) and 24,470 inhabitants (37,4%) living in rural areas. Demographic analysis indicated that the growth rates for these municipalities reached -0,72% (decrease) and 3,09% (increase), respectively. In the study sites, several climatic, epidemiological and entomological data sets were gathered, and malaria incidences were simulated under conditions of intense transmission on a daily timescale.  The incubation period of the parasite in the malaria transmission vector n (also called the Extrinsic Incubation Period EIP, Sporogony, Exogenous Sexual Phase, or Single Sexual Multiplication in the mosquito host) represents the length of the interval between infection (gametocyte ingestion) and the onset of infectivity (sporozoite migration) in the vector host. This parameter is strongly dependent on actual air average temperature. It may range from 8 days at 31°C to 22 days at 20°C (the mean value commonly used reaches 15 days). The frequency with which human blood meals are taken (a) could also be a function of the representative risks of malaria transmission: for a community under a low risk of malaria (RISK = 0), a = 0.07; for a community under an intermediate risk of malaria (RISK = 1), a= 0.25; and for a community which is under a high-risk of malaria (RISK = 2), a= 0.90 [21].   Figure 3 illustrates the time series of these historical hydroclimatic records on a monthly timescale. Detailed information of available and missing periods for the weather stations is presented in Table 7.

HBI FI
As mentioned above, homogeneity analyses were conducted to detect changes in the mean, variance, as well as significant trends in the climatic data sets. To detect the point of change in the mean and/or the variance in each single hydrological time series the Bayesian Analysis (BA) and the Abbe' Criterion for Homogeneity Test were used, both at a 0.05 significance level. The BA allowed deter-mining the mean and the mode of the strongest point of change (NC point) and the mean of the total amount of change. The Abbe test allowed determining whether the hypothesis of homogeneity of each historical time series could be accepted or rejected.
To detect changes in the variance of each single hydrological time series (using the point of change estimated by the BA), the Simple F Test, the Simple F Test with corrections of dependence, the Modified F Test using both Chisquare and F distributions, the Ansari-Bradley Test, the Bartlett Test, and the Levene Test were conducted, all at a 0.05 significance level.
To detect changes in the mean of each single hydrological time series (using the point of change estimated by the BA), the Mann-Whitney/Wilcoxon Rank Sum Test, the Simple T Test assuming change and no change in the variance, the Modified T Test assuming change and no (*) In the system of differential equations, the sum (k in +k er ) represents the length of the interval between infection (sporozoite inoculation) and the onset of infectivity (gametocyte maturation) in a vertebrate host. It may range from 15 to 19 days (for a mean value commonly used of 17 days), according to good, deteriorating or intermediate social and economic conditions (SEC) prevailing in the community [21]. The average immune and infectious periods (1/V and 1/γ, respectively) were estimated following the Martens assumptions [3]. (**) In simulation results the variable 'Prevalence' considers only the proportion of infectious individuals, expressed by the total number of infectious human hosts at a given time t scaled by the total human population at risk. Some authors define this endogenous variable as the overall malaria prevalence, therefore including both the infected and infectious stages.  The hypotheses tests for detecting non-homogeneities in time series recorded in the Nuqui Region showed that the historical records are homogeneous for the entire available period (results not shown). Both time series of mean monthly temperatures and mean monthly relative humidity values registered in the El Bagre region exhibit, on the other hand, strong non-stationarities in the mean and variance in May, 1992 ( Figure 3B). As the shift showed not to  Finally, all daily missing records for both temperature and relative humidity were substituted by an estimated value based on observed monthly records. Missing daily precipitation records were reconstructed assuming no rain on each day.

Epidemiological data, statistical and correlation analyses
Unfortunately, in Colombia several health agencies have been in charge of monitoring malaria disease. The Malaria Eradication Service, a NGO operating on a nationwide level and working for the Ministry of Health, collected data on positive malaria cases from 1984 through 1993. Regional Health Services, public agencies operating at the regional level, were in charge of storing and processing information for each municipality in each Department from 1993 through 1998. In this case, regional authorities split the calendar year, for operational purposes, into 13 epidemiological periods (EP) of 4 weeks each. Roughly speaking, it can be assumed that the first EP corresponds to the month of January and the thirteenth EP corresponds to the month of December. More recently the National Public Health Surveillance System, an operative Department of the Colombian National Institute of Health, has been collecting data on positive malaria cases on the local level for each epidemiological week from 1998 onwards. Figure 4 illustrates the time series of these historical epidemiological records on monthly or per EP timescales.
Even though historical time series seem to be homogeneous in the Nuqui region, the continuous changes in the responsibilities of the local authorities have lead, on the contrary, to several non-homogeneities in epidemiological time series of the El Bagre region ( Figure 4B). In this case, strong changes in the mean were detected in the epidemiological records. Although the errors or omissions appear to be important in such historical time series, datasets were only checked for accuracy, logic and range of values.
In These data sets were collected according to the type of infection (P. falciparum, P. vivax, and mixed malaria) and age groups (<1, 1-4, 5-14, 15-44, 45-59, and >60 years), and were used to develop different types of statistical analyses for understanding the linear and no-linear degree of correlation between climatic variables and malaria transmission indexes. Statistical and correlation analyses were conducted using both the Microsoft Excel Data Analysis Tool and the SPSS version 11.5. The central tendency and variability of all these data sets were examined using descriptive statistics. Finally, the relationship between climatic variables and malaria cases (or incidences) was explored using linear regression and cross correlation with various time lags.
Time series regarding epidemiological data showed to be statistically associated with ambient temperatures and precipitation records during the continuous and homogenous climatic data sets, which comprised the periods from November, 1997 to May, 2002 and from May, 1992 to November, 2000 for the Nuqui and El Bagre regions, respectively. Historical time series for both positive P. vivax and P. falciparum malaria incidences registered in the first locality exhibited a significant degree of correlation with mean monthly ambient temperature time series, for a 1-month time lag (see Table 8). Correlation coefficients reached, respectively, positive values of 0.833 and 0.827 (P > 0.95). Time series also exhibited a significant degree Finally, correlation analyses show that epidemiological time series seem to be strongly associated with mean temperatures, particularly during the onset of the El Niño warm event, as shown in Figure 4. Noteworthy, similar increments in the number of malaria cases during the El Niño event have been found throughout Colombia [5,6,33,34].  Finally, and as mentioned above, the El Niño event seems to intensify the annual cycle of malaria cases in both regions as a consequence of the anomalies in the normal patterns of temperature and precipitation. The average monthly incidence of P. falciparum malaria in the Nuqui region shows that, under 'normal' conditions, malaria incidence reaches a peak in transmission of about 2% of the total population at risk during the months of May and June. During the El Niño events, the annual cycle of malaria incidence remains with one peak, around the month of April (the timing almost remains unaltered), although the number of cases (amplitude of the malaria outbreak) increases significantly. Based on the available epidemiological period, it can be argued that malaria incidence in the Nuqui region during the extreme weather event can increase to an average value of about 8% of the total population at risk, with maximum values reaching 12%. In the El Bagre region malaria incidence reaches a peak in transmission under 'normal' conditions of 3 to 5% of the total population at risk, and also during the months of May and June. During the El Niño events, a sharp rise in the number of cases was commonly observed in the locality, which led to malaria incidences affecting between 5 to 8% of the total population at risk ( Figure 6).

Base scenarios
Roughly speaking, it is generally accepted that there are two scenarios during which malaria transmission could be possible in Colombian endemic-regions: (1) High levels of disease transmission could be expected during periods of 'excellent' conditions following long rainy seasons, when mosquito densities are generally high and temperatures are not low enough to inhibit a successful parasite development within the mosquito host. This scenario is primarily controlled by vector density and suggests that temperature and precipitation variables might have syner- gistic effects on malaria transmission. Temperature affects those entomological variables relevant to the biology of the mosquito host mainly during its aquatic stages; precipitation controls the availability (and, in turn productivity) of adequate breeding sites. This scenario requires linking and simulating the dynamics of vector ecology and malaria transmission in adult mosquitoes and human hosts. (2) High levels of disease transmission could be also expected during periods of 'good' conditions following warm dry seasons, periods when vector densities tend to be extraordinarily low. Although this scenario is 'good' in terms of temperature for the development of parasites in the mosquito host, it seems not to be particularly favourable for disease transmission in terms of low vector densities. Under this scenario, transmission is primarily controlled by those entomological variables (sporogonic cycle and feeding interval) that are strongly affected by temperature. High temperatures could lead to a shortening of the duration of both the extrinsic incubation period and the gonotrophic cycle. The simulation of the dynamics of malaria transmission could be then simplified by estimating a constant vector density (or a smooth seasonal fluctuation of vector density) and separately simulating the disease transmission in human hosts.
As the analysis of annual cycles of rainfall, temperature and malaria incidence patterns shows peaks in malaria transmission following the periods of high temperatures (and when rainy seasons starts to occur), as shown in Fig Annual cycles of rainfall, temperature and malaria incidences under 'normal' and El Niño conditions   Figure 7A). The initial total human population at risk was assumed to be equal to 2,835 people, the population of the locality living in rural areas at the end of 1997. No human migration was assumed to have taken place during the simulation period. The initial number of total infectious individuals HUF(0) was assumed to be equal to 377 people, equivalent to the total number of positive cases reported during October, 1997. The initial number of total infected individuals HUI(0) was assumed to be equal to 234 people, equivalent to the total number of positive cases reported during November, 1997. The initial number of total immune individuals HUM(0) was assumed to be equal to 326 people, equivalent to the total number of positive cases reported during September, 1997. In this case it was proposed that individuals remained in the infectious stage during a short period of time (greater, but close to the duration of treatment) and experienced a re-exposure to malaria parasites. Finally, the initial number of total susceptible individuals HUS(0) was estimated to be the difference between the total population at risk and the total initial number of people in the infectious, infective and immune stages.
Based on the continuous and homogeneous periods of climatic and epidemiological data sets available in the El Bagre region, the observed P. falciparum malaria incidence in the study site was modelled for the period from January 3 rd , 1994 to December 28 th , 2002 (first epidemiological period 1994 -13th EP 2002). This period corresponds to a simulation exercise of about 3,282 days or 108 months, or 9 years (Figures 7B and 7C). The initial total human population at risk was assumed to be equal to 15,862 people, the population of rural areas at the end of 1994. The initial number of total infectious, infected and immune individuals was assumed to be equal to HUF(0) = 326, HUI(0) = 261, and HUM(0) = 453 people, equivalent to the total number of positive cases reported during the 13 th EP 1993, 1 st EP 1994, and 12 th EP 1993, respectively. Accordingly, the total number of susceptible individuals HUS(0) was assumed to be equal to 14,822 individuals. In the endemic area, malaria incidence was simulated assuming temperature values equal to either mean daily indoor temperatures or a constant value of 27.7°C, equivalent to the mean annual temperature of this malaria prone-region.
The system of coupled differential equations was solved by using a fourth order Runge-Kutta numerical algorithm for a 1-day time step at both study sites. Values of exogenous variables are shown in Tables 1, 3 and 5.

Preliminary analysis of instability cases
Based upon the aforementioned scenario and following the experimentation-validation processes, small changes in some exogenous variables were assumed in the analysis of instability cases. Simulations included changes in vector density (Figure 8), Human Blood Index, number of degree-days required for parasite development, human average infected period, and Primary Exo-erythrocytic Schizogony time delay. Analysis of instability cases were only conducted for the 3,282-day simulation period considered for the El Bagre region.

Sensitivity to initial conditions
Several parameters that might cause sensitivity to initial conditions in simulation results were also investigated ( Figure 9). Only three scenarios were analysed in these preliminary simulations: (1) Scenario 1 set the daily survival probability of the mosquito host to a constant value and considered both the gonotrophic and sporogonic cycles to be functions of mean daily temperatures. (2) Scenario 2 set the feeding interval of the mosquito host to a constant value and considered both the daily survival probability and the sporogonic cycle to be functions of mean daily temperatures. Finally, (3) scenario 3 set the sporogonic cycle to a constant value and considered both the daily survival probability and the feeding interval to be functions of mean daily temperatures. Analyses were only conducted for the El Bagre region and the 3282-day simulation period.
To simulate the base scenario and conduct the analysis of instability cases and sensitivity to initial conditions, the values reported in literature for the daily survival probability (longevity), the sporogonic period and the feeding interval were compared with either field-based approximations or values estimated under controlled laboratory conditions ( Figure 10). The daily survival probability was contrasted with the nulliparous-to-parous ratio estimated from collections of adult female mosquitoes captured through the Human Landing method [2]. Field campaigns were conducted during at least three consecutive evenings per month, both indoors and outdoors around houses located at the study sites. Primary vectors of malaria transmission captured in these areas were Anopheles albimanus on the Colombian Pacific Coast, and Anopheles darlingi on the floodplains of Cauca and Nechi rivers. The reported Time series of climatic and epidemiological data observed during the simulation periods  Figure 10. The research group is currently estimating the duration of the sporogonic period.

Vector densities
During a 1,800-day period assumed for the El Bagre region (January 3rd 1994 -December 7th 1998) mean daily temperatures ranged from 24.0 to 32.5°C, and at least 83% of the observed values were in the interval (27-30°C]. Within these temperature ranges, the critical density necessary to maintain parasite transmission ranged from 16.9 to 6.6, and from 8.9 to 6.7 mosquitoes per human host, respectively. The assumed simulation period also showed five wet seasons, which are generally associated with peaks in vector densities, and four dry seasons, which commonly lead to low levels in this entomological variable.    Figure 11 for a daily timescale in simulated incidence). In the first endemic area, modelling results show that seasonality, observed prevalence and time of occurrence of recorded malaria outbreaks were 'well' simulated.
Although the observed sharp rise in malaria incidence during the El Niño 1997-1998 was well represented (time steps 1-501), the model shows that outbreaks recorded during the period 1,601-2,252 were overestimated (Figure 11A). In the El Bagre region modelling results for Parameters and scenarios considered for sensitivity analysis

T [°C] FI (T) [Days] , GC [Days]
FI An. maculipennis FI An. culicifacies FI An. stephensi GC An. albimanus  mean daily temperatures show that seasonal fluctuations of disease transmission and incidence rates were 'well' represented, except for the time steps 2,801-3,282 when prevalence was overestimated ( Figure 11B). Nevertheless, simulated prevalence exhibits peaks in transmission two and three epidemiological periods before recorded outbreaks. That is, prevalence rates and observed incidences were delayed in this study site ( Figure 11B). For a constant value of 27.7°C, equivalent to the mean annual temperature of the El Bagre region, modelling results (not included) show that prevalence oscillates during the first 100 days of the simulation period, increases almost linearly from 0.8% to 1.4% during the time steps 100-1,000, and reaches an equilibrium point of 1.43% of total population at risk. Modelling results in both endemic areas showed that, as expected, temperature became the most relevant climatic variable strongly affecting those entomological variables considered relevant for disease transmission and incidence.
Under the base scenario, the Vectorial Capacity (VC) and the Basic Reproduction Rate (R o ) estimated for El Bagre showed values ranging from 0.6 to 1.8 potential infective bites per day, and from 0.5 to 1.8 arising secondary cases, respectively, for mean daily outdoor temperatures and the assumed vector density. For the interval 27-30°C, VC ranged from 1.0 up to 1.8 daily potential infective bites. In Nuqui, VC and R o reached values in the ranges 0.5-1.9 and 0.5-2.1, respectively.
The estimated R o for the El Bagre region showed a broad range of values although all of them remained at lower levels. For temperatures below 27°C, R o showed values below the transmission threshold (R o = 1) meaning that the disease cannot develop in this community. For temperatures above 27°C, most of R o values ranged between 1.0 and 2.0, suggesting that the disease can develop in the population at risk but at low endemic levels. In Nuqui, R o reached values below the transmission threshold for temperatures below 25°C. For temperatures above this threshold, R o values ranged linearly between 1.0 and 2.0.

Instability cases
In El Bagre, simulation results for changes in vector density show low correlation coefficients (less than 0.351) and high mean square errors (above 0.0030) for densities greater than 11 mosquitoes per human host (Figure 8). For instance, if vector density is set to a constant value of 12 mosquitoes per host, the model significantly overestimates observed malaria incidence (R = 0.293 and MSE = 0.0055; see solid line 1). For values of this entomological variable lower than 7-8 (below the critical density threshold necessary to maintain parasite transmission), the model shows, as expected, that malaria disease recedes and dies out due to the low values of the Basic Reproduc-tion Rate. If vector density is set to 9 mosquitoes per human host, the model represents (R = 0.662 and MSE = 0.0001, see solid line 3) the observed malaria incidence but mainly for the period from January 1994 to July 1999. If vector density is set to 10 mosquitoes per human host (base scenario, see solid line 2), the correlation coefficient drops to 0.455 and the mean square error reaches 0.0010. In this case, the model adequately represents the malaria incidence for the period from January 1994 to November 2000. Modelling results suggest that a density of about 9-10 mosquitoes per human host are required for the development of malaria in the community at risk of the El Bagre region.
Simulation results (not included) for changes in Human Blood Index (HBI) show correlation coefficients and mean square errors reaching 0.455-0.395 and 0.0010-0.0019, respectively, for values of HBI in the range 0.41-0.42. For values above 0.44, the model considerably overestimates observed malaria incidences. In this case, simulation results show low correlation coefficients (less than 0.318) and high mean square errors (greater than 0.0042). If HBI is set to 0.38, the model is not able to reproduce either the observed malaria incidence or the recorded outbreaks. Modelling results suggest that a Human Blood Index of about 0.40-0.41 is required for the development of malaria in the community at risk. If this exogenous variable is set to these values, the model adequately represents malaria incidence but mainly for the period from January 1994 to November 2000.
Simulation results (not included) for changes in the number of Degree Days for Parasite Development (DD) in the mosquito host show high correlation coefficients (0.455-0.529) and low mean square errors (0.0010-0.0005) for values of DD in the range 111-115°C-days. If DD is set to 111°C-days, the Extrinsic Incubation Period (EIP) or sporogonic cycle decreases from 13.9 days at 24°C to 7.0 days at 32°C. If this exogenous variable is set to 115°C-days, the EIP is shortened from 14.4 days at 24°C to 7.2 days at 32°C. If DD is set to 120°C-days (EIP ranging between 15 and 7.5 days) the correlation coefficient increases to 0.675 and the mean square error decreases to 0.0001. If DD is set to 105°C-days (EIP ranging between13.1 and 6.6 days), R drops to 0.383 and MSE increases to 0.0021. In this case, the mathematical model considerably overestimates observed malaria incidences.
Simulation results (not included) for changes in the Human Average Infected Period (ν) show correlation coefficients and mean square errors reaching 0.455-0.315 and 0.0010-0.0059, respectively, for values of ν in the range 0.95-1.10 years. If ν is set to 1.50 years, the correlation coefficient drops to 0.199 and the mean square error significantly increases to 0.0403. In this case, the model overestimates the recorded malaria incidence. If this exogenous variable is set to 0.80 years, the model shows that malaria disease recedes and dies out due to low values of R o .
Finally, simulation results (not included) for changes in the time lag regarding the primary Exo-erythrocytic Schizogony (k in ) show high correlation coefficients and low mean square errors for values of k in in the range 8-10 days. For values above or below this threshold, correlation coefficients and mean square errors do not change significantly. Under the assumed second scenario and for a feeding interval (FI) of 2.0 days, simulation results show that the mathematical model is not able (R = 0.196 and MSE = 0.0011) to represent seasonality, prevalence and time of occurrence of recorded outbreaks. The model briefly simulates the observed values for the period from January 1994 to June 1999 but significantly overestimates malaria incidence from July 1999 onward. If FI is set to 2.1 days, when temperatures are in the favourable range for vector survivorship (Figure 9), the model adequately represents the observed incidence (R increases to 0.472 and MSE decreases to 0.0001). For values of FI below 2.0 days, i.e. 1.7 days, R dramatically drops to 0.008 and MSE increases to 0.0115. As expected, malaria incidence and outbreaks are significantly overestimated.

Sensitivity to initial conditions
Finally, simulation results for the assumed third scenario show that the mathematical model is not able (R = 0.151 and MSE = 0.0042) to represent seasonality, prevalence and time of occurrence of recorded outbreaks. For a constant sporogonic cycle (n) of 8.0 days, the model significantly overestimates malaria incidence throughout the entire simulation period. If n is set to 10 days, when temperatures are in the favourable range for vector survivorship (Figure 9), the model adequately represents the observed disease incidence (R increases to 0.576 and MSE decreases to 0.0001). Finally, for values of n below 8 days, i.e. n = 7 days, R decreases to 0.113 and MSE increases to 0.0082. As expected, malaria incidence and outbreaks are significantly overestimated. Figure 12 depicts the time series of model results for the Nuqui region when a final simulation scenario is considered. In this case, the entomological variables involved in the estimation of the Vectorial Capacity of An. albimanus were replaced by field-based approximations and/or values observed under controlled laboratory conditions (see Figure 12B)   Figure 12C), in which (a) a crude seasonality of mosquito density (values between 9-11 mosquitoes per human host) is assumed, according to the availability of adequate breeding sites; (b) the HBI exogenous variable is set to a constant value of 0.41; (c) the DD exogenous variable is set to 114°C-days; (d) the ν exogenous variable is set to 0.95 years; (e) the k in endogenous variable is set to 8 days; (f) the daily survival probability of the mosquito host is set to a constant value of 0.890; and (g) the endogenous variables FI and n are assumed to be function of mean daily temperatures.

Final simulation scenarios
Under this final scenario, the proposed mathematical model adequately reproduced (R = 0.628 and MSE = 0.0005) both seasonality and prevalence of P. falciparum malaria recorded in the area during the period from January 3 rd , 1994 (first EP 1994) to December 28 th , 2002(13th EP 2002. Noteworthy, is that the system of differential equations was able to replicate malaria outbreaks that were recorded in this endemic prone-region as a result of climatic and environmental anomalies associated with the occurrence of the El Niño in the Tropical Pacific (Figure 12C). The period from January 1994 to December 1996, which comprised the event of the El Niño 1994-1995, was better simulated. Nevertheless, modelling results still exhibit peaks in transmission two epidemiological periods before recorded outbreaks (see solid line 1 in Figure 12C).
Finally, Figure 12C    El Bagre region, in which the Vectorial Capacity was delayed one epidemiological period (see solid line 2 in Figure 12C). In this case, the correlation coefficient between observed and simulated malaria incidence rates increased to 0.668, whereas the mean square error remained constant. Figure 13 presents the results for the simulation period from January 3 rd , 1994 (first EP 1994) to December 28 th , 2002(13th EP 2002 under the scenarios (S +1.0 ), (S +1.6 , not shown), (S +1.9 ) and (S +2.8 ). For a changing climate scenario (S +1.0 , see solid line 1 in Figure 13), the model indicates that for an increase of +1.0°C in mean daily temperatures and a constant vector density D 0 , malaria reaches an average prevalence of about 7% of the total population at risk. Moreover, peaks in P. falciparum malaria prevalence during the El Niño warm events could reach 12.6, 15.1 and even 15.7% of the total number of people living in rural areas (Figure 13). For a S +1.9 scenario (an increase of +1.9°C in mean daily outdoor temperatures and a constant vector density D 0 ; solid line 2 in Figure 13), model results suggest that malaria prevalence might reach an average value of about 11% of the total population at risk. In this case, peaks in transmission could increase to almost 17.7%. Finally, under the S +2.8 scenario, modelling results show an average prevalence of 14% and peaks in transmission during the periods of expected outbreaks reaching 19.2% of the total population (see solid line 3 in Figure 13).  For the El Bagre region it was found that a constant density of about 9-10 mosquitoes per human host are required for the development of malaria in the community. The results of the analysis of instability cases seem to suggest that, in order to counteract malaria in the selected region, it is not necessary to eliminate Anopheles mosquitoes from there entirely: field campaigns aimed at the control and eradication of the disease must reduce the number of vectors to values below 9 mosquitoes per human host. The model also suggests that if environmental conditions favour the development of the mosquito population (letting vector densities reach values above 11 mosquitoes per human host), malaria disease will propagate in the community and reach endemic levels of 9% of the total population at risk. In this case, malaria outbreaks could affect almost 15% of the total number of people living in the area.

Discussion
The results of the analysis of changes in Human Blood Index seem to suggest that An. darlingi, the common primary vector found in El Bagre, is basically zoophilic in its feeding behaviour. It is of interest to note that, if this characteristic of the vector population drastically increases to 60% of total bites on humans, malaria disease could propagate in the community at high endemic levels and reach 20% of the total population at risk.
Based on modelling results it can therefore be argued that if an infection of P. falciparum lasts for a period of time greater than 1.1-1.2 years in humans (when left untreated), malaria could propagate rapidly in the population at risk and reach high-endemic levels. If the average infected period is shortened to periods below 0.9 years, the model suggests that the disease could be controlled through the ecosystems themselves and minor efforts can lead to its eradication. The Human Average Infected Period might be considered one of the critical variables for understanding the malaria cycle in the vertebrate host. Under our conditions in the field (research is still ongoing), most patients are treated immediately or within one month after the detection of malaria parasites in their blood streams.
Simulation results also suggest, as expected, that changes in the time lag representing the Primary Exo-erythrocytic Schizogony do not appreciably affect malaria transmission. In fact, the duration of the parasite cycle in human hosts is more dependent on host characteristics than on external ecological factors.
So far, the mathematical model suggests those entomological variables more strongly affected by climatic conditions and that in turn finally impact transmission potential of mosquito population. These parameters include the sporogonic cycle of the malaria parasite, the daily rate of vector biting, the daily rate of vector natality and the daily survival probability of the mosquito host. Field research must be undertaken in order to estimate how changes in microclimatic and environmental conditions of breeding and resting sites affect these relevant entomological variables. Other variables such as hatching, larval developing, and adult emerging time delays, which seem also to be affected by ambient temperatures, must be included as well.
However, simulation results show that the degree days required for digestion of a portion of ingested blood and for parasite development, which in turn influence the feeding interval and the sporogonic cycle inside vectors, respectively, might be the key variables that cause sensitivity to initial conditions and affect or control malaria transmission. According to these results, vector survivorship is NOT the most important element in the Basic Reproduction Rate of malaria. This conclusion is contrary to Macdonald's statement: 'the formula for the Basic Reproduction Rate holds that the influence of vector survivorship is greater than the influence of the average number of men bitten by one mosquito in one day or the sporogonic cycle, which are in turn greater than the influence of the proportion of anophelines with sporozoites in their salivary glands which are actually infective, or the proportion of affected people, who have received one infective inoculum only, who revert to the unaffected state in one day' [19]. Nevertheless, it has to be said that research is still ongoing.
According to the model and based on the simulated scenarios, malaria outbreaks in the selected regions are possible during the favourable periods following the onset of the El Niño warm event. This epidemiological scenario is primarily controlled by the sporogonic cycle and the feeding interval, which are strongly affected by ambient temperatures. Hence, under the conditions in the field, it appears that temperature becomes the most relevant parameter driving the final malaria incidence and must be considered an essential variable for an adequate representation of malaria transmission in the selected endemic areas. It has to be argued that precipitation, which controls the availability of adequate breeding sites, is responsible for representing observed fluctuations in vector density. Even though mosquito's density is not the key variable for understanding the patterns of malaria outbreaks in the selected region, the model results show that a crude seasonality of vector density is also needed for understanding disease transmission. The model suggests that between periods of high temperatures, malaria disease is maintained at low endemic levels due to the role of vector density. Field research is currently under way in order to consider possible synergistic effects of temperature and precipitation on malaria transmission.
Simulation results suggest that assessing the impact of climate on malaria transmission not only requires consideration of the changes in annual mean temperatures, but also, and more importantly, the extent of inter-annual variability in both temperature and rainfall.
Most of the mathematical models used to derive the standard formulae in malaria epidemiology assume a homogeneous mosquito population, random and uniform vector bites on humans, and a constant adult mosquito population size. Although the first two useful approximations were followed, simple differential equations and basic entomological exogenous variables were included for representing seasonal fluctuations of mosquito density. Thus, the intrinsic differences in mortality rates, the mosquito biting preferences, and the proximity to larval habitats were deliberately ignored. But the dynamics of vectors during pre-imago stages, the predator-prey-food interactions during larval stage, and the relationships between environmental factors and survivorship-behaviour of vectors were purposely included. In fact, the analysis of human biting rates available from field campaigns conducted up to this point shows that, as expected, population densities might be significantly associated with observed rainfall patterns. These vector dynamics, following the preliminary analyses, are being clearly captured by the mathematical model.
New analysis will focus on more detailed examination of key variables that control the dynamic response of malaria transmission in the study sites. Particular interests include testing the model for parsimony and simplicity. A thorough dissection of all the components is currently being conducted in order to capture the most basic interactions between climatic and entomological variables. The mathematical tool will be improved by the inclusion of new subroutines for predator-prey interactions, as well as new field and laboratory data for the entomological parameters.
New analysis will focus also on additional stage variables (following Yang's equations [20,21]) that will be used to describe different levels of protection or anti-malarial immunity, which are commonly observed among people exposed to continuous and intense disease transmission. Migratory patterns and exogenous introduction of infected individuals at certain times are to be included in the model.

Conclusion
The observed monthly values of malaria incidence are characterized by seasonal oscillations alternating irregularly with high incidence periods. Modelling results must show at least such fluctuations of disease transmission. Simulations using only mean annual temperatures do not represent this characteristic. In contrast, simulations using mean monthly/daily temperatures adequately represent the seasonality of malaria prevalence. Apparently, results seem to suggest that the intra-annual cycle of mean temperatures is good enough to represent the seasonal oscillations of monthly malaria incidence rates in the selected study sites. However, simulation results show that seasonality of vector density also becomes an important factor towards understanding disease transmission, thus suggesting that seasonal and inter-annual variability of both temperature and rainfall are required to assess the impact of climate on malaria dynamics. In the applied model described here, attempts were made to include the seasonality of vector density. The module representing the availability of breeding sites was intentionally used to estimate the seasonal fluctuations of such an important entomological variable. Modelling the preimago cohorts for different larval habitats resulted in an estimation of the availability of reservoirs. The BPAM model simulations suggested that (a) oviposition and the development of mosquitoes during pre-imago stages are significantly slower during dry periods, and (b) egg-laying by the mosquito population is appreciably enhanced during periods of notable availability of adequate larval habitats. The system of differential equations also included the simulation of vector dynamics in the field on a daily time scale. In addition to climate data, biological information was required to incorporate species-specific values for each of the parameters of the mathematical model. As a result, seasonal fluctuations in vector density were predicted, with values in the range of the estimated critical densities necessary to maintain parasite transmission.
Malaria is a complex disease that cannot be studied in a uni-disciplinary and exclusively qualitative-descriptive manner. The research project has used an interdisciplinary approach for understanding malaria epidemiology by studying, concurrently, the mosquito vector ecology, the malaria parasite, the human population dynamics, and the characteristics of our heterogeneous environment. Thus, this effort summarizes the joint work of diverse disciplines including Mathematics, Hydrology, Climatology, Entomology, Epidemiology, Field Study and Public Health Medicine.
The mathematical model and the proposed simulation process constitute promising tools to deepen the understanding of the entomological, epidemiological, and climatic interactions related to malaria transmission conducive to disease outbreaks. Mathematical models could help in comprehending how climatic (and non-climatic) factors affect the dynamics of malaria transmission in order to evaluate its spatial and temporal risks in each endemic area. A profound understanding of all these linkages is required for basic research, and for important practical mitigation and human health control interventions.
In this context, biological models are significantly necessary to have a quantitative understanding of malaria transmission. As this model is still in its early stages of development, so far it has not been used for operational purposes. However, in the foreseeable future, biological/ eco-epidemiological models could be implemented as powerful tools to diagnose possible dynamic patterns of malaria incidence under several entomological, demographic and climatic scenarios, as well as decision-making tools, for the early detection and control of disease outbreaks.
Transmission models could permit (a) to estimate the time of occurrence of unexpected malaria outbreaks; (b) to evaluate the possible magnitude of the concomitant sharp rises in the incidence of the disease; and (c) to pose and answer "what if" questions for remote areas potentially vulnerable to changing scenarios, for which data is commonly sparse. Mathematical models could also identify those elements or appropriate components of the complex eco-epidemiological systems for which there exist proven and effective interventions, particularly in the areas of mosquito control, education in environmental health, and treatment. That is, comprehensive models could provide quantitative goals for effective interventions adapted to the specific ecological circumstances of each endemic area. Then, mathematical models will be able to determine the most appropriate preventative actions that have to be taken in order to reduce the vulnerability of populations to climate-induced epidemics and to prevent outbreaks before they begin. Finally, they are also able to identify 'when' these interventions need to be implemented in each area.
Although malaria is a highly complex multi-factorial disease related to diverse socio-economic and demographic factors, it has been demonstrated here that environmental factors and climate variability go a considerable way in explaining fluctuations of disease incidence in these particular endemic areas. Forecasts of relevant climatic variables (future ENSO events) can be merged with selected mathematical tools (statistical and biological/eco-epidemiological models), creating a Malaria Early Warning Sys-tem (MEWS) to facilitate early, coupled and environmentally sound public health interventions [8].
A complete MEWS framework will permit a continuous evaluation of the local risk of malaria transmission in the face of multiple changing scenarios. The MEWS could then be combined with several public health strategies in order to develop Integrated Malaria Surveillance and Control Systems. Other components should be included, such as: (a) epidemiological surveillance and control activities, (b) early diagnosis and treatment of primary cases, and (c) entomological surveillance and control activities.