Figure 1.
Diagram showing the model structure.
Grey-shaded boxes represent mosquito stages infected with Wolbachia. Females have fecundity , larval development time is TL days, and adult mosquitoes experience mortality at a rate
which depends on adult age a. Subscripts W and U denote mosquitoes infected and uninfected with Wolbachia. Infected females fail to transmit Wolbachia to their offspring with probability
.
Figure 2.
The Wolbachia infection frequency in male and female adults following the introduction of infected mosquitoes.
Solid lines show the frequency in males and dashed lines show the frequency in females. Introduction is assumed to occur at a constant rate and the rate of female introduction is 1% of the rate of male introduction. Lines A show introduction at the minimum rate required for Wolbachia to spread (IM = 0.39 day−1) and lines B show an introduction rate twice as high as the minimum rate. The dotted line shows the unstable equilibrium male infection frequency. Other parameters are as in Table 1.
Figure 3.
The number of released mosquitoes required for Wolbachia to spread at different release times.
Solid lines show the mosquito abundance and dashed lines with crosses show the minimum total number of released mosquitoes required for Wolbachia to spread. The sex-ratio of the releases is 95% male and 30 equal-sized daily releases are made. Panels A and B show the seasonal mosquito abundance patterns described in the text. Panel A also shows the minimum total number of introduced insects required to cause spread for equal sex-ratio releases (dashed lines, open squares), and the number of females introduced for the 95% male strategy (dotted lines, crosses) and for the equal sex-ratio strategy (dotted lines, open squares). Other parameters are as in Table 1.
Table 1.
The parameters used in the model and their default values.
Figure 4.
The daily EIR (dashed line) and female population size (dotted line) following male-biased Wolbachia releases.
A strategy of 30 daily 95% male releases of the minimum number of Wolbachia-infected mosquitoes required for spread is shown. Releases begin in the second year in the second month of the high-abundance season. Seasonal dynamics follow pattern A. The solid line shows the male infection frequency and the shaded area shows the period during which releases occur. Other parameters are as in Table 1.
Figure 5.
Daily EIR (dashed line) and female population size (dotted line) following extended Wolbachia releases.
A strategy of 90 daily releases of 95% male, Wolbachia-infected mosquitoes is shown. The solid line shows the male infection frequency and the shaded area shows the period during which releases occur. Panels show different effects of Wolbachia on adult longevity: A. a 16% reduction in average adult lifespan (sg = 0.16), B. a 5% reduction in average adult lifespan (sg = 0.05, rw = 0.03). Insets show the same results for the third year only, and also include lines showing the EIR for different effects of Wolbachia on pathogen development; lines labelled 1,2 and 3 show cw = 0, cw = 0.5 and cw = 0.8 respectively. Other parameters are as in Table 1.