Dynamics of Cholera Transmission with hyperinfactious State of Bacteria
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Cholera is an infection of the small intestine caused by the gram-negative bacterium, Vibrio cholerae. The mathematical models discussed in this study is a model of the cholera transmission with hyperinfectious state of bacteria. This study aims to modify the cholera model by involving hyperinfectious state of bacteria and taking into account the effect of vaccination, treatment and water sanitation. Then we performed the stability analysis around equilibrium point. There are two equilibria, namely disease free and endemic equilibrium. The results of model analysis shows that the number of each subpopulation of humans and bacteria is asymptotically stable around disease free equilibrium if the basic reproduction number is less than one, and asymptotically stable around the positive endemic equilibrium if the basic reproduction number is greater than one. Numerical analysis is given to justify the theorem from mathematical analysis and to see the effect of parameters variation (i.e. vaccination, treatment and water sanitation) to the number of infected humans.