Optimal control on a mathematical model to pattern the progression of coronavirus disease 2019 (COVID-19) in Indonesia

Abstract Background Understanding the pattern of COVID-19 infection progression is critical for health policymakers. Reaching the exponential peak of cases, flattening the curve, and treating all of the active cases are the keys to success in reducing outbreak transmission. The objective of this study was to determine the most effective model for predicting the peak of COVID-19 in Indonesia, using a deterministic model. Methods The SEI2RS model considers five strategies for control, namely: large-scale social restriction (u 1 ), contact tracing (u 2 ), mass testing (u 3 ), case detection and treatment (u 4 ), and the wearing of face masks (u 5 ). Three scenarios were developed, each differentiated by the controls. The model used April 10, 2020, and December 31, 2020, as the initial and final times. Results The simulation results indicated that the peak of COVID-19 cases for scenarios 1, 2, and 3 occur on the 59th day with 33,151 cases, on the 38th day with 37,908 cases, and on the 40th day with 39,305 cases. For all of the scenarios, the decline phase shows a slow downward slope and about 8000 cases of COVID-19 still active by the end of 2020. Conclusion The study concludes that scenario 2, which consists of large-scale social restriction (u 1), contact tracing (u 2), case detection and treatment (u 4), and the wearing of face masks (u 5), is the most rational scenario to control COVID-19 spreading in Indonesia.