Abstract
In this paper, an extended SIR mathematical model (SAIQR) along with an optimal control strategy is proposed to investigate the prevalence of a hypothetical epidemic. By providing controls and examining suitable strategies for control, the cost of control has been minimized. This is while the infected people have been reduced to a minimum in order to control the epidemic. After the full introduction of the model, while explaining the controls used in it, we will check the dimensions of these controls on different compartments. The simulations performed with the MATLAB software show the effectiveness of the controls applied on the model in the significant reduction of infected people.
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