Fig 1.
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).
Table 1.
All parameters were set to their typical values unless explicitly mentioned.
Fig 2.
The effect of bed net coverage (ϕ) and repellency (r) on malaria prevalence.
Panel (a) shows a situation with highly anthropophilic mosquitoes (Q = 0.95; panel (b) with zoophilic mosquitoes (Q = 0.3). Other parameters are given in Table 1.
Fig 3.
The effect of coverage on malaria prevalence at the epidemiological equilibrium.
Prevalence in unprotected people is shown by the dashed line, in protected people by the dotted line, and the population as a whole is represented by the solid line. In panel (a) repellency is r = 0.3, in panel (b) r = 0.9. Other parameters are given in Table 1.
Fig 4.
The effect of repellency on malaria prevalence at the epidemiological equilibrium.
Unprotected people are represented by the dashed line, protected people by the dotted line, and the population as a whole by the solid line. In panel (a) coverage is ϕ = 0.2, in panel (b) ϕ = 0.7. Other parameters are given in Table 1.
Fig 5.
The effects of repellency and probability of surviving the exposure to the insecticide on malaria prevalence.
The epidemiological equilibrium prevalence is shown for low ITN coverage (ϕ = 0.2) and high ITN coverage (ϕ = 0.7). Other parameters are given in Table 1.