A NONLOCAL AND TIME-DELAYED REACTION-DIFFUSION MODEL OF DENGUE TRANSMISSION

A nonlocal and time-delayed reaction-diffusion model of dengue fever is first proposed that incorporates the aquatic stage, the winged stage, and the incubation periods of the dengue virus within mosquitos and hosts. Then the basic reproduction number R₀ is established for the model system, and an explicit formula of R₀ is obtained in the case of spatially homogeneous infections. It is shown that this R₀ gives the threshold dynamics in the sense that the disease-free equilibrium is asymptotically stable if R₀ < 1 and the disease is uniformly persistent if R₀ > 1. The influences of diffusion coefficients, time delays, and infection heterogeneity on the spread of the disease are also studied via numerical simulations. It turns out that the infection risk may be underestimated if the spatially averaged parameters are used to compute the basic reproduction number for spatially heterogeneous infections.