Time optimal control for an epidemic system with isolation and quadratic treatment

This paper aims to explore the use of the time-optimal control problem to eradicate infectious diseases. In the first part, an SIS-type epidemic system including isolation and quadratic treatment control is proposed. The dynamical characteristics of the system are studied, considering the control variable fixed. Next, in the second part, a time-optimal control problem is formulated to reach the disease-free state in the minimum possible time. The control problem is solved by employing Pontryagin's maximum principle, and the explicit expression of the optimal time is derived for the developed model system.