Traveling wave of a reaction-diffusion vector-borne disease model with nonlocal effects and distributed delay

This paper is devoted to investigate the existence and nonexistence of traveling wave solution for a diffusive vector-borne disease model with nonlocal reaction and distributed delays. We demonstrate that the basic reproduction number R-0 of the corresponding ordinary differential equation system as a threshold determines whether the model admits traveling waves or not and there exists a critical wave speed c(m)* > 0 when R-0 > 1. Specifically, (i) As R-0 > 1 and the wave speed c > c(m)*, the existence of traveling waves for the system is established with the aid of a perturbed system; (ii) As R-0 > 1 and 0 < c < c(m)*, the nonexistence of traveling waves is proved via the two-sided Laplace transform; (iii) As R-0 <= 1 and c > 0, the nonexistence is obtained by utilizing the comparison principle. The theoretical results are applied to dengue fever epidemics. We study the effects of geographical movement, nonlocal interaction, incubation period and R-0 on the threshold speed c(m)* for dengue fever.

Automated summary

This paper investigates the existence and nonexistence of traveling wave solutions for a diffusive vector-borne disease model with nonlocal reaction and distributed delays, using the basic reproduction number R-0 as a threshold. It is found that the model admits traveling waves based on the value of R-0 and a critical wave speed c(m)* > 0. These theoretical results are then applied to dengue fever epidemics, studying the impact of various factors on the threshold speed c(m)*.