Optimal Control on Model of SARS Disease Spread with Vaccination and Treatment

Ririt Andria Sari, Ummu Habibah, Agus Widodo

Abstract


The spread of SARS (Severe Acute Respiratory Syndrome) disease in a human population is one of the phenomena that can be mathematically modeled. The exposed period of SARS disease underlies the formation of the SVEIR epidemic model which is a modification of the SVIR epidemic model by adding subpopulation E (exposed). In the SVEIR model, there are two control variables in the form of vaccination and treatment which aimed to minimize exposed subpopulation, infected subpopulation, and control implementation cost. The Pontryagin’s minimum principle is used to obtain optimal control and system, thus minimizing objective functional as the objective to be achieved. Furthermore, the forward-backward sweep method is used for numerical simulation in order to determine the most appropriate control strategy in a finite time. The simulation results show that implementation of both vaccination and treatment is the most effective decision making to control the spread of SARS disease.

Keywords: optimal control, Pontryagin’s minimum principle, SARS.


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