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.
Highlights
Infectious diseases are caused by pathogens or biological agents such as virus, bacteria, fungi, and other microorganisms
Susceptible individual can be infected with the SARS virus as a result of making contact with infected individual so that it can lead to new infection that will spread the disease to other susceptible individual
Vaccination is used to control the spread of SARS disease, where susceptible individual is given anti-SARS vaccine to build up immunity against SARS virus [10], and apply control policies in the form of treatment given to individuals infected with SARS
Summary
Infectious diseases are caused by pathogens or biological agents such as virus, bacteria, fungi, and other microorganisms. The impact of infectious diseases are very harmful in a country or population, it is important to understand the dynamics of disease progression and develop the control of disease spread and consider the costs associated with control implementation. In 2017, Kumar and Srivastava added control variables to the SVIR (Susceptible Vaccinated Infected Recovered) epidemic model in order to control the spread of the disease. Vaccination is used to control the spread of SARS disease, where susceptible individual is given anti-SARS vaccine to build up immunity against SARS virus [10], and apply control policies in the form of treatment given to individuals infected with SARS. The existence of control function in this study aims to minimize exposed subpopulation and infected subpopulation so that the spread of SARS disease is not widespread and minimize the costs associated with the implementation of control. The simulation results are analyzed to determine the most effective control strategies in controlling the spread of SARS disease
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