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. [ABSTRACT FROM AUTHOR]