Multiple Strategies as Optimal Control of a Covid-19 Disease With Quarantine and Using Health Masks

Abstract

This research develops an optimal control as an effort to push down the widely of Covid-19 with a mathematical model. Where, the problem of optimal control is conducted by adding three control variables, i.e an effort to avoid direct contact between the susceptible populations without masks and the infected populations without masks, and the thoughtfulness of a mask-wearing policy. The primary goal of optimal control is to minimize the infected populations without and with masks, and minimize the cost of weight control. Furthermore, if it applies Pontryagin's principle and discovers the Hamiltonian function, then optimal control conditions for the COVID-19 approximation are determined. Finally, as an addition to the model analysis results, numerical simulations are conducted to represent the solutions behavior of each subpopulation before and after the control was designed.

Boundedness and Existence Analysis Solution of an Optimal Control Problems on Mathematical Covid-19 Model

“…We know that some noteworthy contributors to mathematical modeling include McKendrick (1927) The benefit and highlight of the current research is to strengthen the previously performed research by Hakim [12] regarding an optimal control of the spreading COVID-19 disease, which is only discussed numerically without demonstrating an analysis of the positivity and boundedness of the solution. As a result, it is important to conduct this research to give fundamental evidence that the following numerical results are suitable and feasible.…”

“…In the current research, we establish an optimal control COVID-19 transmission epidemic system by Hakim [12]. The model is divided into several classes with different criteria, namely people who are susceptible without masks (𝑆 1 ), people who are susceptible and using masks (𝑆 2 ), people who are infected without masks (𝐼 1 ), people who are infected and using masks (𝐼 2 ), people in quarantine (𝑄), and the total population denoted by 𝑁 = 𝑆 1 + 𝑆 2 + 𝐼 1 + 𝐼 2 + 𝑄.…”

“…The existence analysis of control variable is conducted to depict and support the expressed of control variables provide a beneficial and deeper meaning. We determine the theorem 5 below based on the research previously by Hakim [12]. Theorem 5.…”