Optimal recruitment of Wolbachia-infected mosquitoes to control Zika virus disease

Povzetek

This paper presents optimal control of zika virus disease when wolbachia-infected Aedes ae-
gypti mosquito is used as bio-control. In using wolbachia-infected mosquitoes to ght the spread
of zika virus disease, the natural mosquitoes are infected with wolbachia in a laboratory and released in the wild at dierent times to mate with the uninfected ones. In this paper therefore, we model this control procedure using a system of non-linear ordinary dierential equations. The Pontryagin maximum principle is then applied to determine the levels of recruitment or release of the wolbachia-infected mosquitoes that would optimally reduce the population of susceptible wolbachia-free mosquitoes. With the help of forward-backward sweep numerical method, the resulting optimal control model is solved. The graphical solution shows that the population of wolbachia-free mosquitoes are reduced when the recruitment level of the wolbachia-free mosquitoes is optimal compared to when no control is applied.