Exploring the contributions of bed nets, cattle, insecticides and excitorepellency to malaria control: a deterministic model of mosquito host-seeking behaviour and mortality

Abstract

Domestic and personal protection measures against malaria exposure either divert host-seeking vectors to other hosts or kill those attempting to feed. Here, we explicitly model mosquito host-seeking processes in the context of local host availability and elucidate the impacts and mechanisms of pyrethroid-treated bed nets in Africa. It has been suggested that excitorepellent insecticides could increase exposure of unprotected humans by concentrating mosquito biting activity on this vulnerable group. This worst-case scenario is confirmed as a possibility where vector populations lack alternative hosts, but an approximate 'break-even' scenario, with users experiencing little overall change in exposure, is more likely because of increased mosquito mortality while foraging for resources. Insecticidal nets are predicted to have epidemiologically significant impacts on transmission experienced by users and non-users at levels of coverage that can be achieved by sustainable net distribution systems, regardless of excitorepellency or the ecological setting. The results are consistent with the outcome of several randomised controlled trials, predicting enormous reductions in transmission at individual and community levels. As financial support, technology and distribution systems for insecticide-treated nets improve, massive reductions in malaria transmission could be realised.

Figure 1

Diagrammatic representation of the model for the mosquito feeding cycle, outlining the rate at which mosquitoes encounter hosts (ɛ) and the probabilities that they will attack (γ), be diverted from (Δ), successfully feed upon (φ) or die (μ) while attempting to feed upon cattle (c) or unprotected humans (h,u). Also depicted are the changes to these probabilities for humans brought about by personal protection with bed nets (p), resulting in overall probabilities of these events for vectors encountering protected humans (h,p).

Figure 2

Predicted effects upon malaria transmission intensity of insecticide-treated nets that both divert and kill mosquitoes. The diversionary and insecticidal properties of the nets are as described in experimental hut trials (Lines et al., 1987) and are summarised in Section 2.4. The outcome variables plotted on the y-axes are the survival probability per feeding cycle (P_f; Eq. (9)), the human blood index (Q_h; Eq. (11); human bites per bite), the feeding cycle length (f; Eq. (A.1); nights), the biting rate experienced by unprotected humans (B_h,u; Eq. (A.5); bites per person per night), the sporozoite prevalence (S; Eq. (A.4); infectious bites per bite), the entomological inoculation rate of an unprotected human (EIR_u; Eq. (12); infectious bites per person per year) and the relative exposure of unprotected community members (EIR_c,u/EIR_0,u; Eq. (12)) as well as protected members using nets (EIR_c,p/EIR_0,u; Eqs (12) and (13)). These outcomes are plotted as a function of increasing levels of coverage with effectively treated nets (C, expressed in terms of net use) for Anopheles gambiae and A. arabiensis vector populations in the presence and absence of one head of cattle per person: A. arabiensis without cattle (□), A. arabiensis with cattle (▵), A. gambiae s.s. without cattle (○) and A. gambiae s.s. with cattle (◇).

Figure 3

Impacts of insecticide-treated nets on malaria transmission as a function of their ability to divert and kill host-seeking mosquitoes. Malaria transmission intensity (entomological inoculation rate) for individuals with (EIR_h,p; Eq. (13)) and without (EIR_h,u; Eq. (12)) nets is plotted as a function of their ability to divert (Δ_p) and kill (μ_p) mosquitoes attacking protected humans. The results presented represent simulations assuming 75% usage of nets in two distinctive scenarios: Anopheles gambiae s.l. in the absence of cattle (results for both sibling species are identical) and A. arabiensis in the presence of one head of cattle per person.

Figure 4

Influence of reduced mosquito survival during foraging (P_ov; Eq. (17)) on the protection of non-users (Eq. (12)) by nets that divert (□), kill (▵) or divert and kill (○) mosquitoes. We assume 75% coverage with nets (C = 0.75; Killeen et al., unpublished data) that cause 40% diversion (Δ_p = 0.4) and/or mortality (μ_p = 0.4) of mosquitoes in two scenarios: Anopheles gambiae s.l. in the absence of alternative hosts and A. arabiensis in the presence of cattle. Protection is expressed in terms of reduction in the entomological inoculation rate (EIR) relative to conditions without any nets (C = 0) in the community at the same value of survival during foraging (P_ov).

Figure 5

Impact of nets that divert, kill, or divert and kill mosquitoes on transmission intensity experienced by users and non-users (Eqs (12) and (13)). We assume 75% coverage with nets (Killeen et al., unpublished data) that cause 40% diversion (Δ_p = 0.4) and/or mortality (μ_p = 0.4) in two distinct scenarios: Anopheles gambiae s.l. in the absence of alternative hosts and A. arabiensis in the presence of cattle. Impact is expressed in terms of reduction in the entomological inoculation rate (EIR) relative to conditions without any nets (C = 0) elsewhere in the community. Mosquito survival while foraging (P_ov; Eq. (17)) was set to a median plausible value of 0.80 per day.