Game Theory and Dual Approach to the Dynamic Programming on the Example of the COVID‐19 Pandemic in Poland Described by Mathematical Model With Three‐Dose Vaccinated.

In this paper, a new approach to the disease transmission dynamics of the COVID‐19 pandemic is presented, involving the use of game theory and dual dynamic programming. A new compartmental model that describes these dynamics is introduced. New classes have been added to this model to account for the portion of the population vaccinated with one dose, two doses, or three doses. Pandemic costs are also included. Time‐dependent parameters (strategies) are employed, allowing for the consideration of different behavior variants and decisions made by policymakers. Sufficient conditions for a dual ε$$ \varepsilon $$‐closed‐loop Nash equilibrium, are formulated in the form of a verification theorem. A numerical algorithm is constructed, and numerical simulations are performed. A comparison between real pandemic data for Poland and the data obtained from the model is made. [ABSTRACT FROM AUTHOR]