Threshold dynamics of a periodic reaction–diffusion model for dengue fever

This paper proposes a periodic reaction–diffusion model for dengue fever that incorporates environmental virus transmission, a two-stage mosquito life cycle, and saturating infection rates. Since the environmental virus and infected larva components do not involve spatial diffusion, the model is partially degenerate. We define the basic reproduction number R₀ and establish clear threshold dynamics: under the assumption that the disease-free mosquito subsystem admits a strictly positive, globally attracting T-periodic solution, the infection-free periodic solution is globally asymptotically stable when R₀<1, while at least one positive periodic solution exists when R₀>1. In addition, we analyze the asymptotic behavior of R₀ as the diffusion coefficients tend to zero. Numerical simulations not only quantify the sensitivity of R₀ to key parameters but also confirm the correctness of the preceding conclusions.