Optimal control in epidemiology

Mathematical modelling of infectious diseases has shown that combinations of isolation, quarantine, vaccine and treatment are often necessary in order to eliminate most infectious diseases. However, if they are not administered at the right time and in the right amount, the disease elimination will remain a difficult task. Optimal control theory has proven to be a successful tool in understanding ways to curtail the spread of infectious diseases by devising the optimal diseases intervention strategies. The method consists of minimizing the cost of infection or the cost of implementing the control, or both. This paper reviews the available literature on mathematical models that use optimal control theory to deduce the optimal strategies aimed at curtailing the spread of an infectious disease.