The impact of human activity on the risk index and spatial spreading of dengue fever

To understand how human diffusion and media coverage affect the dynamics of dengue fever epidemiology, we propose a SIR v.s. SI dengue model with a nonlinear contact transmission rate. The free boundaries are also introduced to describe the expanding fronts of the contaminated area caused by the dengue virus. With the help of the basic reproduction number for a relevant problem, we establish the spatio-temporal risk index associated with the diffusive coefficient and media index for our model. Furthermore, some sufficient conditions are obtained to guarantee dengue fever to vanish or to spread, and the asymptotic behavior of the solution for a special system is also discussed when spreading happens. Our results indicate that the degrees of human diffusion and mass media propaganda play an essential role in dengue fever control and prevention. Some numerical simulations, which illustrate the impacts of human activity, are carried out to confirm our analytical findings.