Dynamics analysis of a quarantine model in two patches

Mohammad A. Safi, Abba Gumel

Research output: Contribution to journalArticle

5 Citations (Scopus)

Abstract

A new deterministic model for assessing the impact of quarantine on the transmission dynamics of a communicable disease in a two-patch community is designed. Rigorous analysis of the model shows that the imperfect nature of quarantine (in the two patches) could induce the phenomenon of backward bifurcation when the associated reproduction number of the model is less than unity. For the case when quarantined susceptible individuals do not acquire infection during quarantine, the disease-free equilibrium of the model is shown to be globally asymptotically stable when the associated reproduction number is less than unity. Furthermore, themodel has a unique Patch i-only boundary equilibrium (i = 1, 2) whenever the associated reproduction number for Patch i is greater than unity. The unique Patch i-only boundary equilibrium is locally asymptotically stablewhenever the invasion reproduction number of Patch 3 - i is less than unity (and the associated reproduction number for Patch i exceeds unity). The model has at least one endemic equilibrium when its reproduction number exceeds unity (and the disease persists in both patches in this case). It is shown that adding multi-patch dynamics to a single-patch quarantine model (which allow the quarantine of susceptible individuals) in a single patch does not alter its quantitative dynamics (with respect to the existence and asymptotic stability of its associated equilibria as well as its backward bifurcation property).

Original languageEnglish (US)
Pages (from-to)349-364
Number of pages16
JournalMathematical Methods in the Applied Sciences
Volume38
Issue number2
DOIs
StatePublished - Jan 30 2015
Externally publishedYes

Fingerprint

Quarantine
Dynamic Analysis
Dynamic analysis
Patch
Reproduction number
Backward Bifurcation
Model
Asymptotic stability
Exceed
Endemic Equilibrium
Globally Asymptotically Stable
Invasion
Deterministic Model
Imperfect
Asymptotic Stability
Infection

Keywords

  • Equilibria
  • Quarantine
  • Reproduction number
  • Stability

ASJC Scopus subject areas

  • Mathematics(all)
  • Engineering(all)

Cite this

Dynamics analysis of a quarantine model in two patches. / Safi, Mohammad A.; Gumel, Abba.

In: Mathematical Methods in the Applied Sciences, Vol. 38, No. 2, 30.01.2015, p. 349-364.

Research output: Contribution to journalArticle

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