A periodic Ross-Macdonald model in a patchy environment

Daozhou Gao, Yijun Lou, Shigui Ruan

Research output: Contribution to journalArticle

12 Scopus citations

Abstract

Based on the classical Ross-Macdonald model, in this paper we propose a periodic malaria model to incorporate the effects of temporal and spatial heterogeneity on disease transmission. The temporal heterogeneity is described by assuming that some model coefficients are time-periodic, while the spatial heterogeneity is modeled by using a multi-patch structure and assuming that individuals travel among patches. We calculate the basic reproduction number ℛ0 and show that either the disease-free periodic solution is globally asymptotically stable if ℛ0 ≤ 1 or the positive periodic solution is globally asymptotically stable if R0 > 1. Numerical simulations are conducted to confirm the analytical results and explore the effect of travel control on the disease prevalence.

Original languageEnglish (US)
Pages (from-to)3133-3145
Number of pages13
JournalDiscrete and Continuous Dynamical Systems - Series B
Volume19
Issue number10
DOIs
StatePublished - Dec 1 2014

Keywords

  • Basic reproduction number
  • Malaria
  • Patch model
  • Seasonality
  • Threshold dynamics

ASJC Scopus subject areas

  • Discrete Mathematics and Combinatorics
  • Applied Mathematics

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