A multipatch malaria model with logistic growth populations

Daozhou Gao, Shigui Ruan

Research output: Contribution to journalArticle

47 Citations (Scopus)

Abstract

In this paper, we propose a multipatch model to study the effects of population dispersal on the spatial spread of malaria between patches. The basic reproduction number R 0 is derived, and it is shown that the disease-free equilibrium is locally asymptotically stable if R 0 < 1 and unstable if R 0 > 1. Bounds on the disease-free equilibrium and R 0 are given. A sufficient condition for the existence of an endemic equilibrium when R 0 > 1 is obtained. For the two-patch submodel, the dependence of R 0 on the movement of exposed, infectious, and recovered humans between the two patches is investigated. Numerical simulations indicate that travel can help the disease to become endemic in both patches, even though the disease dies out in each isolated patch. However, if travel rates are continuously increased, the disease may die out again in both patches.

Original languageEnglish (US)
Pages (from-to)819-841
Number of pages23
JournalSIAM Journal on Applied Mathematics
Volume72
Issue number3
DOIs
StatePublished - 2012

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Logistic Growth
Malaria
Patch
Logistics
Die
Model
Basic Reproduction number
Endemic Equilibrium
Asymptotically Stable
Computer simulation
Numerical Simulation
Sufficient Conditions

Keywords

  • Basic reproduction number
  • Disease-free equilibrium
  • Human movement
  • Malaria
  • Monotonicity
  • Patch model
  • Travel rate

ASJC Scopus subject areas

  • Applied Mathematics

Cite this

A multipatch malaria model with logistic growth populations. / Gao, Daozhou; Ruan, Shigui.

In: SIAM Journal on Applied Mathematics, Vol. 72, No. 3, 2012, p. 819-841.

Research output: Contribution to journalArticle

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