Abstract:

Pine wilt disease, as a destructive forest disease, is mainly transmitted through the pine ink beetle.In order to investigale the impact of non-local dispersal and infection age of longhorn beetles on the transmission of the disease in a space heterogeneous environment. In this paper, we propose an age-space structured pine wilt model with nonlocal dispersal. Firstly, we investigate the well-posedness of the model. Secondly, by constructing the general renewal equation of the model, the next-generation operator$\mathcal{R}$is derived, and the basic reproduction number$\mathcal{R}_0$is obtain as the spectral radius of$\mathcal{R}$. As the dynamics threshold of the infectious disease model, $\mathcal{R}_0$ determines the extinction and outbreak of the disease. Finally, the existence of nontrivial solution for the system was proved by using Krasnoselskii fixed point theorem. Furthermore, the asymptotic profiles of the nontrivial solution was proved in spacial case.

Key words: pine wilt disease, nonlocal dispersal model, spatial heterogeneity, age-space structure, basic reproduction number, threshold dynamics