Complex Dynamics of a host–parasite model with both horizontal and vertical transmissions in a spatial heterogeneous environment. (April 2018) - Cai, Yongli; Kang, Yun; Banerjee, Malay; Wang, Weiming
Abstract: In this paper, we investigate the dynamical outcomes of a host–parasite model incorporating both horizontal and vertical transmissions in a spatial heterogeneous environment analytically and numerically. Our study provides valuable insights in two aspects: Mathematically, we propose three threshold parameters, the demographic reproduction number R d, the horizontal transmission reproduction number R 0 h and the vertical transmission reproduction number R 0 v, to identify the conditions that lead to disease-free dynamics, or susceptible-free dynamics, or endemic dynamics. Epidemiologically, we find that both host population movements and spatial heterogeneity strongly affect the disease dynamics of our proposed epidemic model: (1) the larger random mobility can result in 100 % infection prevalence; and (2) the heterogeneity tends to enhance the persistence of the infected hosts with uninfected ones. As a consequence, our work suggests that, in order to control the invasion of the parasite, different preventive measures can be implemented in different regions.