Fig. 2

Schematics for mosquito feeding model. a The deterministic mosquito feeding cycle according to the model described in [25]. (Model is reproduced here with permission [25]; notations are provided in Table 2). Mosquitoes emerge from breeding sites and survive to the host-seeking state (A) at rate \(N_{v0}\). From among all mosquitoes in the host-seeking state (A), a proportion \(P_{A^{i}}\) encounter a host of type i (\(B_{i}\)). For all available host types indexed with i, a proportion \(P_{A}\) stay in state A and a proportion \(P_{A\mu }\) die. Depending on the host type encountered, the mosquitoes follow distinct cycles until they reach state A again or die. Of all mosquitoes in state \(B_{i}\), a proportion \(P_{B_{i}}\) successfully feed on a host of type i (\(C_{i}\)) and a proportion \(P_{B_{i}\mu }\) die (\(P_{B_{i}\mu } = 1 - P_{B_{i}}\)). Of all mosquitoes in state \(C_{i}\), a proportion \(P_{C_{i}}\) move to the ‘resting state after having fed on a host of type i’ (\(D_{i}\)) and a proportion \(P_{C_{i}\mu }\) die (\(P_{C_{i}\mu } = 1 - P_{C_{i}}\) ). Of all mosquitoes in state \(D_{i}\), a proportion \(P_{D_{i}}\) move to the ‘ovipositing state after having fed on a host of type i’ (\(E_{i}\)) and a proportion \(P_{D_{i}\mu }\) die (\(P_{D_{i}\mu } = 1 - P_{D_{i}}\) ). Of all mosquitoes in state \(E_{i}\), a proportion \(P_{D_{i}}\) find a ovipositing site, lay eggs and return to the host-seeking state (A) and a proportion \(P_{E_{i}\mu }\) die (\(P_{E_{i}\mu } = 1 - P_{E_{i}}\) ). b Continuous-time Markov model for the behaviour of an individual mosquito in the host-seeking state (A) of a feeding cycle with three host types. A, H, T and M represent the states of host seeking, HLC, trap catch and death, respectively. \(P_{\text {A}}(t), P_{\text {H}}(t), P_{\text {T}}(t)\) and \(P_{\text {M}}(t)\) represent the probabilities to move within a time window of duration t from state A to state A, H, T and M, respectively. It is assumed that these probabilities are independent of how long the mosquito has already stayed in state A before the given time window (Markov property)