A mathematical model of the impact of present and future malaria vaccines
© Wenger and Eckhoff; licensee BioMed Central Ltd. 2013
Received: 13 December 2012
Accepted: 20 March 2013
Published: 15 April 2013
With the encouraging advent of new malaria vaccine candidates, mathematical modelling of expected impacts of present and future vaccines as part of multi-intervention strategies is especially relevant.
The impact of potential malaria vaccines is presented utilizing the EMOD model, a comprehensive model of the vector life cycle coupled to a detailed mechanistic representation of intra-host parasite and immune dynamics. Values of baseline transmission and vector feeding behaviour parameters are identified, for which local elimination is enabled by layering pre-erythrocytic vaccines of various efficacies on top of high and sustained insecticide-treated net coverage. The expected reduction in clinical cases is further explored in a scenario that targets children by adding a pre-erythrocytic vaccine to the EPI programme for newborns.
At high transmission, there is a minimal reduction in clinical disease cases, as the time to infection is only slightly delayed. At lower transmission, there is an accelerating community-level protection that has subtle dependences on heterogeneities in vector behaviour, ecology, and intervention coverage. At very low transmission, the trend reverses as many children are vaccinated to prevent few cases.
The maximum-impact setting is one in which the impact of increasing bed net coverage has saturated, vector feeding is primarily outdoors, and transmission is just above the threshold where small perturbations from a vaccine intervention result in large community benefits.
In recent years, dramatic progress has been made in reducing the burden of malaria through the scale-up of insecticide-treated net (ITN) coverage and the increasing use of artemisinin combination therapy (ACT) as first-line treatment[1–4]. Nonetheless, as of the 2010 WHO report there were still over 200 million cases of malaria per year with 800 thousand attributed deaths, mostly young sub-Saharan African children. Further reductions in burden and large-scale clearance of the disease will increasingly depend on combinations of interventions. In the face of potential drug resistance[5, 6], insecticide resistance, and vector behaviour changes[8, 9] an effective vaccine could become an increasingly important tool.
Malaria vaccine development is particularly challenging given the complexity of the parasite life cycle and the variation in its antigenic presentation[10–12]. In spite of the early potential demonstrated in studies of irradiated sporozoites, it has only been in the last few years that vaccine trials have shown sufficiently high and durable efficacies to consider widespread deployment. The RTS,S subunit vaccine targeting the circumsporozoite protein (CSP) in the pre-erythrocytic phase has advanced the furthest along the clinical trial pathway among current vaccine candidates. In Phase IIb and Phase III field trials to date, the following protective efficacies have been observed: 34% against infection in Gambian adults waning rapidly over 15 weeks; 30% against clinical episodes and 45% against infection in Mozambican children over 6 months and persisting at similar levels out to 21 months; 49–56% against clinical episodes over a year in children from Kenyan and Tanzanian children and from seven African countries[18, 19]. These trials are consistent with a ‘leaky’ vaccine that provides partial protection to most vaccinated individuals[20, 21] by reducing the number of successful sporozoites and the size of the liver-to-blood inoculum. Beyond RTS,S, there are additional pre-erythrocytic vaccine candidates, as well as blood-stage vaccines to reduce morbidity and gametocyte-blocking vaccines to limit human-to-vector transmission. While this latter class of ‘sexual-stage’ vaccines does not provide direct individual protection against infection, it may be a potent tool in bringing down malaria transmission. Recent Phase I trials targeting the sexual stage of the parasite, in particular the ookinete surface proteins Pfs25 and Pfs28, have demonstrated persistent high antibody levels that are effective in blocking oocyst formation in the mosquito[23–26].
The objective of the present modelling study is to quantify the potential impact of first-generation vaccine candidates as components in multi-intervention elimination strategies, to elucidate which geographical settings in a wide range of transmission intensities and entomological behaviours enable the greatest impact, and to estimate efficacy targets for future vaccines as a function of desired impact. Among the many malaria vaccine scenarios to which mathematical modelling may be applied, the focus of the present effort is limited to simulating pre-erythrocytic and sexual-stage vaccines, which are distributed either by mass campaign or by routine vaccination. Their effects will be quantified in terms or reduced inoculation rates, prevalence, clinical incidents, and interruption of transmission. Mathematical modelling is especially relevant today as some countries are looking for evaluations to inform decisions and potential plans regarding incorporating RTS,S into their national Expanded Programme on Immunization (EPI).
The present work builds upon a substantial body of work by the malaria modelling community to understand the potential impact of malaria vaccines. Early malaria models from Ross and Macdonald[27, 28] were used to focus on vector control. The modelling work to support The Garki Project represented a major advance in modelling capabilities; evolutions of this model were used in early models of vaccine action. The clinical trials of RTS,S and its potential rollout have helped to drive forward a new generation of mathematical models with new features, new capabilities, and more detailed representations of parasites and immunity[31–35]. The community is benefiting from the array of independent modelling efforts to understand vaccine rollouts, and more benefits will accrue as ensemble modelling becomes the standard in the field.
The present study utilizes the Disease Transmission Kernel (DTK) model developed by the Epidemiological Modelling (EMOD) group at Intellectual Ventures. This individual-based model couples a detailed description of the vector life cycle with a comprehensive, mechanistic representation of the intra-host parasite and immune dynamics. The model additionally includes a flexible and powerful framework for configuring and distributing arbitrarily specified campaign interventions to targeted groups of individuals.
Multiple species of Anopheles mosquitoes may be simulated simultaneously, each population separately configured according to its ecological and behavioural preferences. For example, the female Anophelesarabiensis deposits eggs primarily in temporary, rainfall-driven habitat and has a higher propensity to feed outdoors or on livestock. Vector populations are tracked as cohorts throughout the full mosquito life cycle: from eggs to larvae with a temperature-dependent development period preceding emergence; a brief immature phase including sugar-feeding and mating; repeating multi-day gonotrophic cycles during which mosquitoes may be exposed to infection by gametocytes; and a temperature-dependent latency for sporogony. This closed-loop feeding cycle ensures that only successful blood meals, which avoid potentially multiple modes of vector control, result in viable eggs.
Critical to modelling multiple simultaneous interventions accurately, the various feeding cycle outcomes – death before, during, or after feeding; host unavailable; successful human feed; etc. – are calculated from branching trees of conditional probabilities, the nodes of which can be influenced by individual interventions. For example, in the case of indoor-host-seeking mosquitoes encountering both indoor residual spraying (IRS) and an ITN, feeding outcomes will branch first at pre-feed IRS killing and repellency from the house. The fraction surviving these fates can be blocked by the ITN, which may additionally kill a subset of the blocked fraction. The unblocked fraction makes a feeding attempt, during which some may be killed. Those surviving the feeding attempt may at last be killed by IRS post-feed. Thus, the deterrent and toxic effects of multiple interventions can be represented simultaneously. The allocation of mosquitoes to feeding-cycle outcomes is done based on end-state probabilities that have been aggregated over the individual humans in the simulation. The presented simulations do not examine interventions targeting other phases of the vector life cycle (e.g. larvicides, larval habitat management) or those targeting outdoor or animal feeds, as these are not common components in vaccine rollout scenarios. Nonetheless, the vector transmission model supports such interventions.
Malaria infection and immune model
Within-host parasite dynamics are simulated by a microsolver for each individual in the simulation. Within the framework of this microsolver, each new Plasmodiumfalciparum infection begins with a fixed-duration, liver-stage latency that is susceptible to drugs such as primaquine. The latent period ends with a configurable burst of merozoites that commences the repeating two-day cycles of the asexual blood-phase infection. The model accounts for several antigenic components, to which the immune system may develop immunity: the merozoite surface protein (MSP) variant, the P.falciparum erythrocyte membrane protein (PfEMP-1) presented on the surface of the infected red-blood cell (IRBC), and less immunogenic minor surface epitopes. A single clonal infection is modelled with an antigenic repertoire of 50 unique PfEMP-1 variants, each associated with one of five repeating minor epitopes. In the first asexual cycle, the first five variants are expressed in equal numbers. The blood-stage infection is updated in hourly time steps, during which the immune system is stimulated by the IRBC count of each antigenic variant, and concomitantly the IRBC counts are decremented on account of immune and drug killing effects.
At the end of each asexual cycle, the model calculates the fraction of merozoites (16 for each previous IRBC) that are killed by specific recognition of the MSP variant. It also calculates the fraction that is differentiated into male and female gametocytes. To capture the dynamics of the parasite’s immune evasion strategy, the model imposes a constant per-parasite switching rate on the remaining merozoites for advancing to subsequent antigenic variants in the repertoire. Super-infection is allowed for up to five simultaneous infections. The full set of population-level antigenic variants, out of which a single infection’s repertoire is randomly drawn, consists of 100 MSP variants, 20 sets of five minor epitopes, and 1000 PfEMP-1 variants. The number of population-level variants affects the age-pattern of natural immunity acquisition. The former two parameters drive the asymptotic levels of adult detected parasitaemia; the latter parameter primarily governs the transition between child and adult detected prevalence rates, provided the number of PfEMP-1 variants is substantially more than an individual would experience in a year. As in a previous study on the acquisition of immunity through the mechanism of parasite population diversity, the numbers of antigenic variants in this study were chosen to resemble age-prevalence curves from Namawala, Tanzania. A ‘burn-in’ period allows simulated individuals to build antibody responses to a broad repertoire of parasite antigens appropriate for their age, before perturbing the system with campaign interventions. The simulations presented here used a ten-year burn-in – a trade-off that allows population-level transmission to approach asymptotic dynamics while making appropriate use of available computing resources.
The immune response to infection is characterized by innate inflammatory and specific antibody components. The cytokine-driven inflammatory response is modelled to depend on a temporary contribution from rupturing schizonts at the end of each asexual cycle, as well as the concentration of IRBC surface antigens to which an antibody response has not yet been developed. The innate response – suppressed by the presence of specific antibodies – is responsible for driving febrile symptoms and broad-spectrum parasite suppression. The capacity to generate specific antibodies grows in response to the concentration of each novel antigen. Above a threshold level on the capacity, antibodies are produced in increasing concentration until the corresponding antigenic variant is cleared, at which time the capacity will decay to a non-zero memory level. This mechanism captures the delayed onset of specific antibody response that is reduced on re-infection.
The model advances gametocytes through five stages of development, characterized by different drug susceptibilities, reaching maturity after ten days. Infectiousness of individuals to mosquitoes is proportional to the number of mature gametocytes taken up in a blood meal, but modulated by a factor that inactivates gametocytes at high cytokine densities[44–49]. Peak infectiousness typically follows peak parasitaemia by about ten days. The contribution of different age groups to transmission is dependent on the more pronounced innate inflammatory response in malaria-naïve individuals, as well as the different durations of infection. The transmission-blocking effect of sexual-stage vaccines is also applied at this stage to directly reduce the probability of a viable human-to-vector infection.
In the present study, the probability of a sporozoite-positive mosquito feed infecting an individual is based on a single random draw with 50% average transmission rate. In the model, the generic pre-erythrocytic vaccine takes an input efficacy parameter that defines the fractional reduction in the probability of an infectious bite causing an infection. In a time step (Δ t) with a daily infectious biting rate (R), the probability of an individual with vaccine efficacy (E) acquiring a new infection is: 1−e x p(−R·(1−E)·Δ t). For the sake of simplicity, several additional model features related to vector-to-human transmission have not been exercised in this analysis. These include the potential to assign heterogeneous susceptibility, biting rates, and CSP-specific antibody production in response to repeated challenges.
Simulated population and geography
Simulations have been run on the scale of a single village with an initial population of 1,000 individuals, distributed exponentially in age with a mean of 23.2 years. The annual birth rate of 36.5 per 1,000 individuals and the age-dependent non-disease mortality rate result in a population doubling time of roughly 20 years. The age structure of individual immune systems is initialized through a 10-year ‘burn-in’ period, after which various interventions – insecticide-treated bed nets, pre-erythrocytic vaccines (PEV), and sexual-stage vaccines – are distributed to a subset of the population.
The climate and vector parameters were modelled on the well-instrumented study site of Namawala, Tanzania. The rainfall data for January 1990 through December 1999 were obtained from the Global Precipitation Climatology Centre (GPCC), and the temperature data from the Swiss Tropical and Public Health Institute (TPH). The simulation includes distinct populations for each of the three dominant species: Anophelesgambiaes.s., Anophelesfunestus, and An.arabiensis, which account for around 10%, 20%, and 70% of annual infectious bites, respectively. The scale factors governing the available habitat for each species have been set as in by fitting basic vector-model simulations with the seasonality and species-mix of the Namawala series; the overall magnitude is varied over a range of values of the entomological inoculation rate (EIR) that are all below those historically seen in Namawala. The baseline transmission has a pronounced rainy season, during which individuals in the high-transmission scenarios average more than one infectious bite per day. During the dry season, though, the An.funestus component plays a disproportionately significant role, when for several months it accounts for the majority of infectious bites. In order to present results on vaccine impact that are more broadly applicable to diverse geographic settings, simulations were configured over a range of values for the annual EIR (0 - 150) and the fraction of An.arabiensis feeds that occur indoors (0 - 1).
Results and discussion
The simulated outputs presented in this paper address two distinct deployment scenarios. The first section explores the effect of adding a pre-erythrocytic or sexual-stage mass-vaccination event to a large-scale distribution of ITNs. This is not necessarily how first-generation vaccines are initially conceived to be deployed, but it is an instructive exercise to understand what can or cannot be achieved towards a goal of local disease elimination with these tools alone. This scenario also explores the potential further reduction in burden once ITN campaigns have saturated in their possible local impact. The second section explores the effect of an EPI-like deployment of pre-erythrocytic vaccines on the number of clinical disease cases in various age groups. These results should be directly relevant to current and future vaccine deployment plans, especially in pointing out the settings where the greatest impact may be realized.
Mass-vaccination towards eradication
The right panel of Figure4 shows the marginal impact of the additional vaccine intervention and how it depends on vaccine efficacy ranging from 0% to 90%. Each isocline corresponds to the location of the 50% elimination probability isocline inferred as in the left panel. For example, moving along a vertical slice at 50% An.arabiensis indoor-feeding, a 50% effective vaccine increases the baseline transmission intensity where elimination is achievable from an EIR of 75 to an EIR of 80. However, a 90% effective vaccine would allow disease elimination for a pre-intervention baseline transmission up to an EIR of 110 when combined with a high-coverage ITN campaign. Note that this range of intermediate EIR values corresponds to relatively large swaths of sub-Saharan Africa as estimated by the Malaria Atlas Project. Alternatively, consider a horizontal slice at a baseline EIR of 20. A 50% effective vaccine reduces the lower limit of the elimination regime from an indoor-feeding fraction of about 18% down to 10%; a 90% effective vaccine ensures that elimination is achieved even for exclusively outdoor-feeding An.arabiensis. The ITN campaign completely stops transmission due to the other species, and the vaccine efficacy is high enough to drive residual transmission into stochastic fadeout.
The very significant reduction in transmission (i.e. local elimination) that is shown here for 80% ITN coverage at high endophily is comparable to previous modelling work that has shown dramatic reductions at high population-wide coverage. Similar large-scale reductions in transmission have also been noted in village-scale trials with mass ITN coverage where the dominant vectors were highly endophilic[56, 57]. However, several important confounding factors should be noted before attempting to relate these simulations to operational discussions of disease elimination. First, distributed bed nets do not necessarily translate to protected individuals – they may fall into disrepair; they may not cover all residents in a covered household; potentially-protected individuals may not use them every night. The latter effect is especially notable, as individual usage is typically substantially lower than household ownership[1, 58–60]. As such, it is important to clarify that the simulations in this paper correspond to consistent ITN usage in 80% of simulated individuals. Second, the sustained efficacy of ITNs relies on the persistence of susceptible feeding behaviour in the mosquito. While in many cases the indoor fraction of human exposure remains high[61, 62], in some settings significant shifts in feeding time and location have been observed. Finally, while the present work focuses on single-village dynamics, the interruption of transmission at larger spatial scales is likely to be significantly more challenging, due to heterogeneity in transmission intensity, spatial structure in ITN coverage, and re-introduction from human migration[64, 65]. While the present analysis can show generically the magnitude of the potential added-value from layering pre-erythrocytic vaccines on top of mass-distributed ITNs, it will be valuable to address the above considerations in the future in a site-specific fashion.
Clinical incident reduction with child-targeted campaign
Because of the personal protection provided by even a partially protective pre-erythrocytic vaccine, there are several reasons why it is natural to consider a targeted intervention to minimize cases in young children. This group bears most of the current burden of disease, and children have less acquired immunity than older individuals in the same geographic settings[66, 67]. Furthermore, EPI represents the most logical existing vaccination infrastructure within which to deploy a new vaccine. To this end, scenarios are constructed that represent an “EPI-plus” rollout of a pre-erythrocytic vaccine (50% efficacy and 5-year decay profile) and a potential future vaccine (90% efficacy) as part of a one-time mass vaccination of under-5 year olds followed by vaccination of new births over the following decade. Both the initial campaign and the ongoing routine vaccination coverage is 80% of targeted individuals.
At the highest residual transmission levels (EIR=150 with 0% ITN coverage), despite protection from 50% or even 90% of infectious bites, most individuals still spend the majority of the year infected with one or more infections (see Figure1). It can be easily understood, then, why the total number of clinical cases in a year is only slightly reduced as even vaccinated individuals inevitably become infected. However, the fractional reduction in incidence accelerates at lower residual transmission (i.e. higher ITN coverage or lower baseline EIR as in Figure2). This transition is also characterized by significant numbers of cases averted in unvaccinated individuals. At very low residual incidence, there are diminishing marginal benefits from vaccinating a whole population to avert the last few cases. The exception to this trend is the realization of continuing dividends upon achieving local elimination. If vaccination could be targeted at identifiable hot-spots[69, 70] the cost-effectiveness of the campaign would be extended to lower transmission levels.
It is instructive to look more closely at why the accelerated reduction in clinical cases is more correlated with the level of dry-season transmission than the annually averaged parasite prevalence. The right panels of Figure6 compare two parameter combinations, for which the annually averaged parasite prevalence in the ITN-only baseline scenario is around 28% and the annual number of clinical cases is around 80. The two scenarios in the right panels correspond to the no-vaccine baselines for the points indicated by (a) and (b) in the left panel. For the first set of parameters (baseline EIR = 100, exclusive indoor-feeding An.arabiensis, 40% ITN coverage) shown in the upper-right panel, all vectors are very susceptible to bed nets. This is evident in the pronounced separation in incidence between protected and unprotected individuals. The latter group is responsible for maintaining the moderate level of dry-season transmission. However, for the second set of parameters (baseline EIR = 15, exclusive outdoor-feeding An.arabiensis, 60% ITN coverage) shown in the lower-right panel, the An.arabiensis component is unaffected by ITNs while the components of transmission due to An.funestus and An.gambiae s.s. are essentially wiped out. This situation is evident in the homogeneous risk of protected and unprotected individuals to the remaining transmission that is almost exclusively exophagic. The very low transmission during the dry season makes the system sensitive to a relatively modest vaccine rollout. For these reasons, the latter scenario results in 46 cases averted annually, compared to 16 cases averted for the first set of parameters (see the 90% PEV efficacy points indicated in left panel of Figure6).
At this point, it is worthwhile to note that the predictions of previous modelling efforts are largely consistent with what has been presented in the this paper. It has been noted previously that pre-erythrocytic vaccines should be more effective when deployed in low-transmission environments and more cost-effective when combined with transmission-blocking elements. Similarly, it has been shown in an individual-participant pooled analysis of phase II RTS,S data that vaccine efficacy against clinical episodes drops quickly from 60% at low transmission to 4% at high transmisison. While substantial positive effects of mass-vaccination near the elimination threshold (EIR=2) have been predicted, at higher transmission (EIR=20) EPI should be more cost-effective, especially if it can be targeted at low-transmission areas. Finally, heterogeneity in biting exposure (as e.g. in Figure6) has also been shown to affect the apparent efficacy of vaccine trial data if the effect is ignored.
Towards the long-term eradication of malaria, the history of other vector-borne diseases, such as yellow fever, suggests that an effective, long-lasting vaccine will be an invaluable tool. Looking at the current generation of vaccines, a goal of global eradication is certainly daunting. However, pushing to higher efficacy (as shown in Figure4) provides a potentially complementary way of ‘shrinking the map’ of malaria endemic regions beyond what is achievable with high sustained ITN coverage — especially in areas with plentiful exophagic vectors. A few features of the presently constructed mass-vaccination campaign will warrant future studies. In order to maximize the waning vaccine effectiveness at transmission chokepoints, it would appear preferable to engage in mass-vaccinations at least a year following the initial drop in incidence from ramping up ITN coverage. Furthermore, investigations including boosting doses and newborn vaccination would be expected to benefit from sustaining high efficacy over several years before elimination. In this study, vaccine doses and ITNs have been distributed independently. However, while this is an assumption that may be justified under certain circumstances, the modes of distribution may be such that the interventions are more correlated (e.g. ITN distributions at ante-natal clinics or accompanying the vaccination campaign). Finally, the potential to combine pre-erythrocytic and sexual-stage vaccines in a single dosing schedule would likewise provide complementary increased impact.
A broad survey of how a ‘catch-up + EPI’ rollout of an RTS,S-like vaccine can effect a reduction in clinical disease cases has been presented. Over the many scenarios considered, a rough scaling emerges in the magnitude of the clinical case reduction versus the dry-season incidence, revealing subtle thresholds that depend on heterogeneous vector behaviour and intervention coverage. Figure6 reminds us that for the same average transmission levels, homogeneous populations (e.g. the dark-coloured 0% ITN coverage points) are an easier target than populations with heterogeneous baseline intervention coverage. The unprotected sub-population represents a pocket of more persistent transmission, and the protected sub-population already has some potential infections blocked by ITNs, which need not be perfectly complementary to the addition of vaccines. Especially relevant to the question of where vaccines would have the most impact, it has been shown that regions with similar parasite prevalence levels can have significantly different responses to vaccine interventions. One characteristic pattern is where ITN coverage is low and vector behaviour is conducive to ITN control. In this case, a small ramp-up in ITN coverage would not only have a greater effect than introducing a vaccination campaign, but would also make a potential vaccination campaign much more effective. On the other hand, there are settings with negligible marginal benefit of additional ITNs, since only a strongly exophagic residual vector population remains. Especially when the ITN-susceptible vectors were responsible for a large fraction of dry-season transmission (as for the Namawala ecology), this type of setting makes a good candidate for introducing vaccines.
In this paper, ITNs and vaccines have been compared in their combined effectiveness at preventing clinical cases. That is to say, at 80% coverage of the 218 children under age 5 in year-0 and the 62.7 new births per year in the following decade, 680 vaccinations are being dispensed to prevent up to 200 or 450 clinical cases with a 50% or 90% effective vaccine, respectively. These and related models and simulations can thus provide a bridge from vaccine efficacies measured in single-patient challenge studies to the efficaciousness at preventing clinical disease in community rollouts in different settings. Meriting future efforts will be an extension of this study to compare to a metric that is weighted even more to the younger ages who disproportionately experience the most severe symptoms and deaths, and to judge the cost of potential vaccine interventions not simply against the absence of additional benefit from more ITNs, but also against other interventions that can provide personal protection against outdoor feeding vectors[76–78].
Artemisinin combination therapy
Disease transmission kernel
Entomological inoculation rate
Expanded programme on immunization
Infected red-blood cell
Indoor residual spraying
Merozoite surface protein
Plasmodium falciparum erythrocyte membrane protein
The authors would like to thank Bill and Melinda Gates for their active support of this work and their sponsorship through the Global Good Fund. Productive discussions with colleagues at Intellectual Ventures Laboratory, PATH Malaria Vaccine Initiative, and the malaria programme of the Bill and Melinda Gates Foundation are likewise greatly appreciated.
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