Abstract
In this work, we assess the impact of the phage-bacteria infection and optimal control on the indirectly transmitted cholera disease. The phage-bacteria interactions are described by predator-prey system using the Smith functional response, which takes into account the number of bacteria binding sites. The study is done in two steps, namely the model without control and the model with control. For the first scenario, we explicitly compute the basic reproduction number R0 which serves as stability threshold and bifurcation parameter. The proposed model exhibits a bi-stability phenomenon via the existence of backward bifurcation, which implies that the classical requirement of bringing the reproduction number under unity, while necessary, is no longer sufficient for cholera elimination from the population. We intuitively introduce a new threshold number N0 needed for the global stability of the disease free equilibrium point which is achieved when R0⩽1 and N0⩽1. It is further shown that the phage absorption is a possible cause of bi-stability, since in its absence, the condition R0⩽1 is sufficient for cholera to die out. The existence of endemic equilibrium points depends on the range of both R0 and N0. Regarding the model extend...Continue Reading
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