Stability Analysis of Deterministic Cholera Model

DIMI Jean Luc; BISSILA BISSILA; Theophile MAVOUNGOU

DIMI Jean Luc Departement de Mathematiques, University Marien Ngouabi Congo, Faculte des Sciences, Congo
BISSILA BISSILA Institut National de la Recherche en Sciences Exactes et Naturelles Avenue de l'Auberge de Gascogne BP 2400 Brazzaville, Congo
Theophile MAVOUNGOU Universite des Sciences et Techniques de Masuku Franceville (Gabon), Congo

Keywords: Nonlinear epidemic model, Lyapounov function, asymptotic stability.

Abstract

In this paper, we study two models models for the dynamics spread and transmission of cholera.For these models Lyapounov functions are used to show that when the basic reproduction number is less than or equal to one, the disease free equilibrium is globally stable , and when it is greater than one there is an endemic equilibrium which is also globally asymptotically stable.

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