Global dynamics of a mathematical model for the propagation of Wolbachia bacteria in mosquito populations.

Mosquito-borne diseases are infectious diseases transmitted by mosquitoes, including dengue fever, Zika and malaria. A new way to control and prevent mosquito-borne infectious diseases is to use the endosymbiotic bacterium Wolbachia to interrupt the transmission of the pathogen. A new ordinary differential equation model is established to study the transmission of Wolbachia in mosquito population. By using the qualitative theory of ordinary differential equations, the nonnegativity and boundedness of solutions of the model are proved, and the existence condition of the equilibrium points is given. The globally asymptotic stability of the equilibrium is obtained in different situations. The conditions of Wolbachia successfully invading wild mosquito population are discussed. In special case for parameters, the threshold for initial values of Wolbachia invasion is given, which provides a new strategy for releasing mosquitoes carrying Wolbachia. Finally, main conclusions are verified by numerical simulation. [ABSTRACT FROM AUTHOR]