Optimal reduced-mixing for an SIS infectious-disease model

Which reduced-mixing strategy maximizes economic output during a disease outbreak? To answer this question, we formulate an optimal-control problem that maximizes the difference between revenue, due to healthy individuals, and medical costs, associated with infective individuals, for SIS disease dynamics. The control variable is the level of mixing in the population, which influences both revenue and the spread of the disease. Using Pontryagin's maximum principle, we find a closed-form solution for our problem. We explore an example of our problem with parameters for the transmission of <i>Staphylococcus aureus</i> in dairy cows, and we perform sensitivity analyses to determine how model parameters affect optimal strategies. We find that less mixing is preferable when the transmission rate is high, the per-capita recovery rate is low, or when the revenue parameter is much smaller than the cost parameter.