Wavefront propagation in a hyperbolic model of hantavirus infection

This paper focuses on the study of hantavirus infection in a mouse population. In particular, starting from a 1D two-compartment reaction–diffusion model, in order to depict the evolution of susceptible and infected mice, its hyperbolic extension is deduced to characterize the inertial effects. Moreover, the emergence of smooth and sharp wavefronts between two equilibria is investigated to analyse the system’s response to any abrupt or gradual phenomena that strongly affect the disease and are not directly included in the model parameters. Finally, the effect of the spatio-temporal dependence of the resource availability, which includes both seasonality effects and spatial distribution, is considered to better mimic the combined role of refugia and inertia in hantavirus dynamics. Results lead to the occurrence of both retracting and invading fronts, depending on the excited migration speed, which are characterized by the propagation or the extinction of the disease. Numerical simulations are also conducted to corroborate the analytical one and extract additional insights on the disease evolution in response to any change of external conditions.