Control theory has proven to be a successful tool in understanding ways to curtail the spread of infectious diseases. The theory determines the best strategy for implementing containment measures by finding a solution to the optimal control problem, which is a control of a dynamic system that optimizes the target cost functional. Pontryagin's maximum principle is considered indispensable when it comes to solving the problem of optimal control. The principle is regarded as a triumph of mathematical control theory since it transforms the infinite dimensional optimal control problem into a point optimization. Building on an extended SEIR model adapted to the COVID-19 disease a control system incorporating various possible interventions is formulated. The system models interventions which include transmission reduction, testing and isolation of the exposed, symptomatic, asymptomatic individuals and increasing healthcare capacity. Optimal strategies for the implementation of various interventions are derived by considering the country's capacity. Results show that, if all the controls are to be used, the more able the country is, the more it should implement measures to reduce transmission, increase health capacities and test symptomatically infected individuals. However, if the country finds it very difficult to implement the controls, the best approach is to test asymptomatic individuals.
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