Host searching cycle of a mosquito.

A mosquito bites indoors with probability ϵ (for night-active and highly anthropophilic mosquitoes, this happens mainly at night) and takes a bite outdoors with probability 1 − ϵ. A mosquito then bites humans with a probability Q. If biting indoors, it will enter a house where a person sleeps under a bed net with a probability ϕ (the ITN coverage) or a house with an unprotected person with a probability 1 − ϕ. If the person is protected, the mosquito is repelled by the insecticide (or mechanically blocked by the net) with a probability r; if it is not repelled, it takes its bite and escapes with probability s or it is killed by the insecticide on the net with probability (1 − s). If a mosquito is repelled by a bed net, it leaves the house and continues to search for a host. There is a mortality cost μr associated with each repellency event. We assume that a mosquito will always land a successful bite on unprotected people and and on animals, whereas the feeding success on protected people depends on r and s. The host search happens once per mosquito gonotrophic cycle, i.e. once every three days (see Table 1).