Dynamics of a non-autonomous delay mosquito population suppression model with <i>Wolbachia</i> -infected male mosquitoes

In this paper, we develop a non-autonomous delay differential equation model for mosquito population suppression. After establishing the positiveness and boundedness of the solutions, we study the dynamical behaviours of the model with or without <i>Wolbachia</i>-infected male mosquitoes. More specifically, for the model without infected male mosquitoes, we analyse the asymptotic stability of the equilibria and demonstrate that the model undergo Hopf bifurcations under certain conditions. For the model incorporating infected male mosquitoes, we derive sufficient conditions for the global asymptotic stability of the origin. Numerical examples are provided to illustrate and support our theoretical findings.