In this paper, an approach to the disease transmission dynamic of a coronavirus pandemic is presented. Compared to models commonly known from the literature, new classes that describe this dynamic to our model were added, which are a class representing costs of the pandemic and a class of the individuals being vaccinated but without antibodies. Parameters which at most of them depend on time were used. Sufficient conditions for a dual $\varepsilon$-closed-loop Nash equilibrium in the form of the verification theorem are formulated. A numerical algorithm and numerical example are constructed.

• Received 30 September 2022
• Revised 19 February 2023
• Accepted 15 March 2023

DOI:https://doi.org/10.1103/PhysRevE.107.044202