Dynamical analysis of an age-structured COVID-19 transmission model with voluntary vaccination strategies and evolutionary game

COVID-19 infection exhibits significant age-related differences. In this paper, we consider an infectious disease model with age-structure in susceptibility and evolutionary game and analyze the impact of mandatory and voluntary vaccination strategies on disease progression. We derive the conditions for the existence of equilibria and confirm that the basic reproduction number <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msub><mml:mi>R</mml:mi><mml:mn>0</mml:mn></mml:msub></mml:math> serves as a threshold parameter that fully determines the dynamical properties of the model. Theoretical analyses indicate that the persistence of COVID-19 is contingent upon the value of the basic reproduction number. By conducting numerical simulations, we investigate the impacts of various factors, including relative vaccine cost and vaccine effectiveness, on disease dynamics under a voluntary vaccination policy. Our analysis reveals that enhancing vaccine effectiveness does not reduce disease transmission when vaccination rates are extremely low. Under voluntary vaccination policies, it is crucial to keep relative vaccine costs below a certain threshold to promote higher vaccination uptake.