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# The impact of releasing sterile mosquitoes on malaria transmission

• * Corresponding author: Cuihong Yang
• The sterile mosquitoes technique in which sterile mosquitoes are released to reduce or eradicate the wild mosquito population has been used in preventing the malaria transmission. To study the impact of releasing sterile mosquitoes on the malaria transmission, we first formulate a simple SEIR (susceptible-exposed-infected-recovered) malaria transmission model as our baseline model, derive a formula for the reproductive number of infection, and determine the existence of endemic equilibria. We then include sterile mosquitoes in the baseline model and consider the case of constant releases of sterile mosquitoes. We examine how the releases affect the reproductive numbers and endemic equilibria for the model with interactive mosquitoes and investigate the impact of releasing sterile mosquitoes on the malaria transmission.

Mathematics Subject Classification: Primary: 92D25, 92D30; Secondary: 34C60.

 Citation: • • Figure 1.  With the parameters given in (25), the threshold values are $\bar b = 5.3960$ and $b_c = 8.0033$. By using $b$ as an independent variable, the horizontal axis is for $b$ and the vertical axis is for $R_0^c$. The curve in this figure represents the reproductive number $R_0^c(b)$ for $0\le b \le b_c$. The reproductive number $R_0^c(0) = R_0 = 1.1284 >1$ at $b = 0$. At $b = \bar b$, the curve for $R_0^c(b)$ crosses the horizontal line $R_0^c = 1$ so that $R_0^c(b) < 1$ for $\bar b < b \le b_c$

Figure 2.  With the parameters given in (25), the threshold values are $\bar b = 5.3960$ and $b_c = 8.0033$, respectively. The curve on the left figure is for $\lambda_h(b)$ at the endemic equilibrium for each $b$. The upper and lower curves are for $I_h(b)$ and $I_v(b)$, respectively, at the endemic equilibrium for each $b$ as well in the right figure. Clearly, $\lambda_h(b)$, $I_h(b)$, and $I_v(b)$ all become negative for $b > \bar b$ which implies that no endemic equilibrium exists for $b \ge \bar b$ although positive $N_{vb}^\pm(b)$ exist for $\bar b < b < b_c$

Figure 3.  With the parameters given in (25), the reproductive number for system (1) and (6) is $R_{0} = 1.1284>1$ and hence the infection spreads when there are no sterile mosquitoes released as shown in the left figure. After the sterile mosquitoes are introduced, for $b = 6>\bar b = 5.3960$, the reproduction number becomes $R_{0}^{c} = 0.9773 < 1$ and hence the infection goes extinct as shown in the right figure.

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