Mathematical model of mosquito populations dynamics with logistic growth in a periodic environment

In this paper, we analyze the effect of climate change on the dynamics of mosquito population. The model is formulated as a nonautonomous system of ordinary differential equations with Verhulst-Pearl logistic growth. We show that the global dynamics of the model is determined by the vectorial reproduction ratio, Rv which is defined through the spectral radius of a linear integral. Indeed, we show that if the threshold Rv is greater than 1, then the mosquito-free equilibrium is globally asymptotically stable; but if it is smaller than 1, then the mosquitoes persist and the system admits at least one positive periodic solution. Finally, we perform some numerical simulations in order to illustrate our mathematical results.