A nonlocal spatial model for Lyme disease (Q272251)

This article continues the consideration started in the work of \textit{W. Wang} and the second author [SIAM J. Appl. Math. 75, No. 3, 1142--1170 (2015; Zbl 1335.35129)]. The new feature is an incorporation of the self-regulation mechanism for the tick population, i.e., density-dependent death terms and intra-competition into the system. Although the biological interpretation of model parameters is provided, the rest of the paper is devoted to pure mathematical study. In particular, a threshold type result on the global dynamics of the considered reaction-diffusion system is proven and the global dynamics of the process, which is associated with the Lyme disease invasion, is analyzed.