Long-lasting insecticidal net (LLIN) distribution campaigns have played an important role in recent successes in malaria control
. LLINs protect against mosquito bites that mostly occur indoors during sleeping hours, coinciding with times when people are using LLINs. Furthermore, the nets have a protective ‘community effect’ by killing mosquitoes
, thereby reducing the probability that the infected mosquito will survive the extrinsic incubation period and become infectious.
Resistance to pyrethroids in mosquito populations is increasing
, threatening the effectiveness of pyrethroid-based interventions such as LLINs
. LLIN effectiveness is also threatened by shifts in biting behaviour, from nocturnal towards crepuscular, with mosquitoes actively host searching during the early morning and/or evening, when many LLIN users are not under their nets
[5–7]. For example, Russell and colleagues
 observed increased outdoor feeding after exposure to insecticide treated nets (ITNs) in Tanzania. Such a shift could occur simply ifmosquitoes are unsuccessful in finding a blood meal during their normal active host-searching period and if mosquitoes learn
[9, 10] and repeat behaviour that resulted in a blood meal The above causes of these shifts can be described as phenotypic plasticity
. It could occur if mosquitoes that search for hosts indoors during sleeping hours have a higher risk of being killed (by LLINs). If there is a genetic basis for the behaviour
, pressure from LLINs could select for alleles that are associated with crepuscular biting behaviour, resulting in decreased exposure of mosquitoes to LLINs, and decreased effectiveness of LLINs over time. If these alleles are associated with certain (sub) species, this could lead to differential suppression of (sub) species
In this paper, ‘behavioural resistance’ is defined as the behaviour-related ability to be unaffected by something. Such ability can, but does not need to be, acquired (or evolved) in response to pressure. Mosquitoes that tend to bite during times that LLIN users are not under their nets are less affected by LLINs than nocturnal host-searching mosquitoes, and thus have some ‘behavioural resistance’ against LLINs. However, mosquitoes that avoid contact with LLINs are not necessarily more behaviourally resistant than mosquitoes that do not if the contact-avoiding mosquitoes subsequently fail to find a blood meal or have a lower survival rate associated with crepuscular activity.
If host-searching behaviour varies in the vector population, this has implications for LLIN effectiveness. Molineaux and colleagues
 show that with the assumption of non-uniform exposure to insecticides, vector control tools are much less effective than under the usual implicit assumption of uniform exposure. If all female mosquitoes in a population have the same stochastic probability of behaving a certain way each gonotrophic cycle, then mosquito potential exposure to LLINs is uniform. If, at the other extreme, each female always repeats her behaviour each gonotrophic cycle, her behaviour being determined before (genetically or phenotypically) or during the first gonotrophic cycle (through learning from experience), behaviour is fully determined and potential exposure is non-uniform. In the former fully ‘probabilistic’ case, each mosquito has a priori the same chance of surviving each gonotrophic cycle. In the latter, fully ‘determined’ case, those mosquitoes that never search for human hosts indoors during human sleeping hours are never exposed to LLINs, and thus their survival is not affected by LLINs. While behaviour is unlikely to be fully probabilistic, it is also unlikely to be fully determined. In reality, the degree of determinedness will lie somewhere in between these two extremes.
The proportion of mosquito-host encounters that occur indoors during sleeping hours in the absence of bed nets gives an indication of how strongly the mosquito population can be affected by LLINs. The more crepuscular and exophagic the vector population, the lower this proportion. This proportion, also called the ‘πi value’
 or ‘πs value’
, can also be defined as “…the proportion of normal exposure of unprotected humans lacking nets that occurs at times and places when net users would be protected by sleeping under them”
. If host-searching behaviour is fully determined, LLINs cannot reduce exposure to bites beyond the level that occurred during human sleeping hours prior to invention. In such a case, and if mosquitoes are killed by LLINs, the πi value will be lower during intervention than prior to intervention. However, if there is some stochasticity in the behaviour, LLINs can potentially reduce exposure beyond the level occurring during human sleeping hours prior to intervention, because all mosquitoes are at risk of being killed by LLINs.
A previous modelling study
 quantified the sensitivity of the effectiveness of a mass distributed LLIN batch to insecticide resistance, as measured in experimental hut studiesa. In that study, the pre-intervention πi was kept constant at a value of 0.75, and host-searching behaviour was assumed to be fully determined. This paper extends that previous study by incorporating sensitivity to assumptions about host-searching behaviour into the analysis.