Stability Analysis of a Mathematical Model for the Use of Wolbachia to Stop the Spread of Zika Virus Disease

The use of wolbachia-infected mosquitoes to stop the spread of zika virus disease is modeled and analyzed. The model consists of a system of 10 ordinary differential equations which describes the dynamics of the disease in the human population, a wolbachia-free Aedes aegypti population, and a wolbachia-infected Aedes aegypti population used for disease control. A stability analysis of the disease-free equilibrium is conducted, which shows that it is both locally and globally asymptotically stable when the reproduction number is less than one. The result of the stability analysis shows that the spread of zika virus disease can be stopped, irrespective of the initial sizes of the infected human and mosquito populations, when wolbachia-infected Aedes aegypti are introduced in the area where the disease is endemic.