Optimal Control of Vaccination and Quarantine for the SIIQR Model with Asymptomatic Individuals and Reinfection

The COVID-19 pandemic in 2020 has characteristics such as asymptomatic infections and reinfection, and the characteristics have not seen in previous SARS. An SIIR model was proposed as the mathematical model that considered such characteristics, but the control strategies, for example, vaccination and quarantine, was not considered in the model. Therefore, in this paper, we propose an SIIQR model that employs vaccination and quarantine as control inputs to the SIIR model. We also obtain optimal control using Pontryagin's maximum principle in order to suppress infectious people as well as minimizing the costs of vaccination and quarantine. Finally, the validity of the proposed method is confirmed through numerical simulation.