Mathematical model of economic dynamics in an epidemic

The paper proposes a model of economic growth in an epidemic. It takes into account the dependence of the labor force on the parameters of the epidemic and the contacts restrictions, built on the base of the stable equilibrium in the corresponding SIR model, which evolves in a faster time compared to the main model. The model is formalized as an optimal control problem on an infinite horizon. The verification theorem is proved and the turnpike for the growth model without the epidemic is found. The study of a non-trivial stationary regime in a growth model during an epidemic makes it possible to analyze the dependence of the main macroeconomic indicators on the model parameters. Examples of calculations are presented that confirm the adequacy of the developed model.