Global Stability of a Two Patch Cholera Model with Fast and Slow Transmission

Authors

  • Jean Lubuma Professor & DST/NRF SARChI Chair: Mathematical Models and Methods in Bioengineering and Bioscience, University of Pretoria, South Africa
  • Berge Tsanou* Postdoc fellow, University of Pretoria, South Africa

DOI:

https://doi.org/10.11145/282

Abstract

Global stability of epidemic patch models is always a challenging mathematical issue. For a waterborne disease such as Cholera, we extend aВ model originated from [1] in three ways: we consider a two patches environment, add disease induced mortality and migration of humansВ В between the patches. We give the conditions under which the modelexhibit four different equilibria and show that their existence is based on the local basic reproduction numbers and the type-reproduction numbers of the two patches.В Using technical Lyapunov functions that combine quadractic, Volterra-type and linear functions, we prove the global asymptotic stability of both theВ disease free equilibrium and the two boundrary equilibria in the positiveВ orthant. As for the endemic equilibrium, we use a Volterra-type LyapunovВ function to prove its global stability in the positive orthant under В biologicalВ reasonable conditions on model parameters.

Author Biography

Berge Tsanou*, Postdoc fellow, University of Pretoria, South Africa

Postdoc fellow, University of Pretoria

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Published

2014-04-16

Issue

Vol. 1 No. 1 (2014)

Section

Conference Contributions

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