THRESHOLD DYNAMICS OF A DENGUE FEVER MODEL WITH SEASONALITY AND MULTIPLE PATCHES

In this paper, we formulate a periodic dengue fever model for the population living in a multipatch environment. Firstly, we establish the well-posedness of the model. Secondly, we overcome the difficulty that the mosquito system cannot be linearized at the zero equilibrium point, thereby introducing the mosquito basic reproduction number R_M and the disease basic reproduction number R₀: if R_M < 1, then mosquito populations will become extinct; if R_M > 1 and R₀ < 1, then the disease will die out; if R_M > 1 and R₀ > 1, then both the disease and mosquito populations are persistent. Numerically, we verify the theoretical results and explore the effects of mosquito migration rates, human migration rates, mosquito natural mortality rates, and seasonality on disease transmission.