Optimal isolation strategies of emerging infectious diseases with limited resources - Yinggao Zhou; Jianhong Wu; Min Wu (Mathematical Biosciences and Engineering)
A classical deterministic SIR model is modified to take into accountof limited resources for diagnostic confirmation/medical isolation. We show that this modificationleads to four different scenarios (instead of three scenarios in comparison with the SIR model) for optimal isolation strategies, and obtainanalytic solutions for the optimal control problem that minimize the outbreak size under the assumptionof limited resources for isolation. These solutions and their corresponding optimal control policies arederived explicitly in terms of initial conditions, model parameters and resources for isolation (such as the number of intensive care units).With sufficient resources, the optimal control strategy is the normal Bang-Bangcontrol. However, with limited resources the optimal control strategy requires to switch totime-variant isolation at an optimal rate proportional to the ratio of isolated cases over the entire infected population once the maximum capacityis reached.