Optimal Control Problem of Mathematical Model with Fuzzy Parameter for the COVID-19 Epidemic with Symptomatic and Asymptomatic cases in Indonesia

Abstract

The COVID-19 pandemic first emerged in late 2019 in Wuhan, China. This pandemic has had a significant impact on life, especially in Indonesia. In this study, we analyze the optimal control model for the COVID-19 epidemic in Indonesia, considering both symptomatic and asymptomatic cases, and considering government policies. We used three control parameters: policies to prevent the spread of the disease among vulnerable people, quarantine with treatment for symptomatic patients, and infection testing followed by isolation for asymptomatic patients. To obtain the optimal solution, the Pontryagin Maximum Principle and cost-effectiveness analysis methods were used. Based on the cost-effectiveness analysis, it was concluded that implementing the three control measures simultaneously at each temperature was significantly more cost-effective in preventing the spread of infection than when only one or two controls were implemented. Another interesting finding was the emergence of symptomatic patients again if preventive controls were reduced, while asymptomatic patients still existed.