Wave features of a hyperbolic model for the within-season dynamics of insect pathogens

Hyperbolic models are suitable for describing invasive phenomena with a well-defined boundary. In fact, for a class of hyperbolic reaction–diffusion models derived in the context of extended thermodynamics (ET), the non-existence of smooth travelling waves has been proved under suitable assumptions on the wave speed. In this paper a hyperbolic model for the within-season dynamics of insect pathogens is derived and smooth and discontinuous travelling wave solutions are investigated. Validation of the model in point is also accomplished by searching for numerical solutions of the system of PDEs.