A delay differential equation model depicting mosquito suppression paradox

An environmentally benign approach for the control of mosquito-borne diseases is to sterilize female mosquitoes by releasing the males carrying the bacterium Wolbachia. It is well known that a wild mosquito population can be nearly eradicated if a sufficient number of Wolbachia-infected males are released in the field. However, the scenario under insufficient male release is not well-characterized. By analyzing a new model of delay differential equations, we identify a threshold release intensity, below which the male release would not reduce but instead increase the stable adult population level, a phenomenon called suppression paradox. It is largely caused by the reduction in the density-dependent larval competition and the subsequent increase in the larval survival rate. For Aedes albopictusmosquitoes in Guangzhou, our extensive simulations predict that paradox would occur if the ratio of the released males over wild males is below $3.69~:~1$, and a ratio $1.448~:~1$ would induce the strongest paradox. Several release strategies are proposed to avoid the paradox and to optimize the suppression process.