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Optimal Control of a Cholera Disease Model with Vaccination

L. Hakim, Trisilowati, I. Darti

Abstract


In this paper, we investigate an optimal control model of the spread of cholera disease by vaccination. Optimal control is conducted by adding two control variables i.e. the effort of reducing direct contact between infected and susceptible population as well as the effort of exterminating the cause of cholera disease. The aim of optimal control is to minimize the infected population and the cost of the controls. By applying the Pontryagin Minimum Principle, it can be obtained optimal control condition. Furthermore, numerical solution is solved by using sweep forward backward method to show the effect of the controls. Finally, numerical simulations show that the control strategy is effective in reducing the infected population and the bacteria population.

Keywords


Cholera, Optimal Control, Vaccination, Pontryagin Minimum Principle, Numerical simulations.

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