DYNAMICS OF A PERIODIC WEST NILE VIRUS MODEL WITH MOSQUITO DEMOGRAPHICS

In this paper, we propose a time-delayed model of West Nile virus with periodic extrinsic incubation period (EIP) and mosquito demographics including stage-structure, pair formation and intraspecific competition. We define two quantities R-min and R-max for mosquito population and the basic reproduction number R-0 for our model. It is shown that the threshold dynamics are determined by these three parameters: (i) if R-max <= 1, the mosquito population will not survive; (ii) if R-min > 1 and R-0 < 1, then WNv disease will go extinct; (iii) if R-min > 1 and R-0 > 1, then the disease will persist. Numerically, we simulate the long-term behaviors of solutions and reveal the influences of key model parameters on the disease transmission. A new finding is that R-0 is non-monotone with respect to the fraction of the aquatic mosquitoes maturing into adult male mosquitoes, which can help us implement more effective control strategies. Besides we observe that using the time-averaged EIP has the possibility of underestimating the infection risk.