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

Yongli Cai, Yun Kang, Malay Banerjee, Weiming Wang

Research output: Contribution to journalArticlepeer-review

44 Scopus citations

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 Rd, the horizontal transmission reproduction number R0h and the vertical transmission reproduction number R0v, 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.

Original languageEnglish (US)
Pages (from-to)444-465
Number of pages22
JournalNonlinear Analysis: Real World Applications
Volume40
DOIs
StatePublished - Apr 2018

Keywords

  • Endemic
  • Heterogeneity
  • Parasite-free
  • Susceptible-free
  • Vertical transmission

ASJC Scopus subject areas

  • Analysis
  • Engineering(all)
  • Economics, Econometrics and Finance(all)
  • Computational Mathematics
  • Applied Mathematics

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