Backward Bifurcation in a Cholera Model: A Case Study of Outbreak in Zimbabwe and Haiti
Domaine:
healthcareType de record:
paper
Créateur:
SanNit
Éditeur:
Wor
Hôte:
In this paper, a nonlinear deterministic model is proposed with a saturated treatment function. The expression of the basic reproduction number for the proposed model was obtained. The global dynamics of the proposed model was studied using the basic reproduction number and theory of dynamical systems. It is observed that proposed model exhibits backward bifurcation as multiple endemic equilibrium points exist when [Formula: see text]. The existence of backward bifurcation implies that making [Formula: see text] is not enough for disease eradication. This, in turn, makes it difficult to control the spread of cholera in the community. We also obtain a unique endemic equilibria when [Formula: see text]. The global stability of unique endemic equilibria is performed using the geometric approach. An extensive numerical study is performed to support our analytical results. Finally, we investigate two major cholera outbreaks, Zimbabwe (2008–09) and Haiti (2010), with the help of the present study.
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