Optimal Quarantine Programmes for Controlling an Epidemic Spread

An optimal control problem is formulated with a simple epidemic model in which the control of the epidemic is effected by varying the scale of the quarantine program in a way which minimizes a discounted linear cost over an infinite horizon. An important function of the problem parameters is identified. It is shown that if this function has a value of less than or equal to one, then the optimal policy is not to quarantine at all. While if this functions assume a value in excess of one, then the optimal policy is not to quarantine at all if the initial fraction of infectives is sufficiently high; otherwise, it is optimal to have a full scale quarantine program. Slight modification in these policies are required for the finite horizon version of the problem.