Complex Dynamics of a host –parasite model with both horizontal and vertical transmissions in a spatial heterogeneous environment

Publication date: April 2018 Source:Nonlinear Analysis: Real World Applications, Volume 40 Author(s): Yongli Cai, Yun Kang, Malay Banerjee, Weiming Wang 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.
Source: Nonlinear Analysis: Real World Applications - Category: Research Source Type: research