ZHANG Zhiwen, BAI Zhenguo
Acta Mathematicae Applicatae Sinica.
2023, 46(6):
895-911.
To study the effects of periodic incubation period in infected mosquito and human diffusion on malaria transmission, we formulate a partially degenerate reactiondiffusion model with periodic delay. In view of only considering the diffusion of human but ignoring that of mosquito, the solution maps of our model are not compact, which brings some difficulties in our analysis. We obtain the existence of a global attractor by proving that the Poincaré map is α-contracting, point dissipative, and the positive orbits of bounded subsets are bounded. We then establish the threshold dynamics concerning the basic reproduction number $\mathcal{R}$0 with the help of the persistence theory. That is, if $\mathcal{R}$0 < 1, the disease will go extinct; and if $\mathcal{R}$0 > 1, then the disease will persist. Numerically, we examine the influences of heterogeneity, seasonality and diffusion on $\mathcal{R}$0, and further show that ignoring the periodic change in incubation period may underestimate the risk of disease outbreak.