Propagation phenomena of a vector-host disease model

Abstract

This paper is devoted to the study of spreading properties and traveling wave solutions for a vector-host disease system, which models the invasion of vectors and hosts to a new habitat. Combining the uniform persistence idea from dynamical systems with the properties of the corresponding entire solutions, we investigate the propagation phenomena in two different cases: (1) fast susceptible vector; (2) slow susceptible vector when the disease spreads. It turns out that in the former case, the susceptible vector may spread faster than the infected vector and host under appropriate conditions, which leads to multi-front spreading with different speeds; while in the latter case, the infected vector and host always catch up with the susceptible vector, and they spread at the same speed. We further obtain the existence and nonexistence of traveling wave solutions connecting zero to the endemic equilibrium. We also conduct numerical simulations to illustrate our analytic results.