Traveling Wave Solutions in a Nonlocal Dispersal SIR Epidemic Model with General Nonlinear Incidence

In this paper, for a class of nonlocal dispersal SIR epidemic models with nonlinear incidence, we study the existence of traveling waves connecting the disease-free equilibrium with endemic equilibrium. We obtain that the existence of traveling waves depends on the minimal wave speed c* and basic reproduction number R-0. That is, if R-0 > 1 and c > c* then the model has a traveling wave connecting the disease-free equilibrium with endemic equilibrium. Otherwise, if R-0 > 1 and 0 < c < c*, then there does not exist the traveling wave connecting the disease-free equilibrium with endemic equilibrium. The numerical simulations verify the theoretical results. Our results improve and generalize some known results.

Automated summary

This paper investigates the existence of traveling waves in a class of nonlocal dispersal SIR epidemic models with nonlinear incidence, showing that the presence of traveling waves depends on the minimal wave speed c* and basic reproduction number R-0. Numerical simulations confirm the theoretical findings, which improve and generalize existing results.