A dengue fever model with free boundary incorporating the time-periodicity and spatial-heterogeneity

Propagation of dengue fever is characterized by periodicity and seasonality and further influenced by geographic heterogeneity. To account for these characteristics, we formulate a dengue model in a spatial-heterogeneous and time-periodic environment. Moreover, the free boundary is additionally incorporated into our model to reflect the boundary change of region where dengue virus spreads. Employing the properties of the contagion risk threshold, that is the spatial-temporal basic reproduction ratio, we derive some sufficient conditions regarding the vanishing and spreading of virus. Importantly, the long-time asymptotic behavior of solution is studied in depth when spreading happens. Our findings manifest that as time goes on, dengue virus will behave periodically when spreading. Finally, these phenomena are numerically simulated and epidemiologically explained.