Bifurcation analysis of a wild and sterile mosquito model

The bifurcation of an ordinary differential equation model describing interaction of the wild and the released sterile mosquitoes is analyzed. It is shown that the model undergoes a sequence of bifurcations including saddle-node bifurcation, supercritical Hopf bifurcation, subcritical Hopf bifurcation, homoclinic bifurcation and Bogdanov-Takens bifurcation. We also find that the model displays monostable, bistable or tristable dynamics. This analysis suggests that the densities of the initial wild mosquitoes and the released sterile ones determine the asymptotic states of both populations. This study may give an insight into the estimation number of the released sterile mosquitoes.