Abstract
In this paper, we present several optimal control approaches which are designed to control and regulate the evolution of infection numbers in the COVID-19 disease. In our setting, the number of infected people at a certain location is modeled by a continuous-time stochastic process which can be affected by a related stochastic control process. We use mathematical tools from stochastic analysis and optimal control theory. In particular, we prove an innovative stochastic maximum principle for continuous-state branching processes with immigration (so-called CBI processes) and apply the result to a stochastic control problem stemming from epidemiology.
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