Global dynamics and optimal control of an influenza model with physiological age structure

The spread and control of influenza are inevitably influenced by the age heterogeneity of the population. This paper investigates an age-structured SVEIQHR influenza model with physiological age structure, which includes the self-healing ability of latent individuals and the choice of home care or going to the hospital for infected individuals. First, the existence and uniqueness of the solution are proved using the operator semigroup theory. The expression of the basic reproduction number [Formula: see text] is derived through the characteristic equation. Then, we prove that the disease-free steady state is globally asymptotically stable if [Formula: see text]. There exists a unique endemic steady state, which is locally asymptotically stable when [Formula: see text]. Additionally, in order to minimize the number of infections at the lowest cost, we explored the optimal control measures for influenza by selecting strengthened vaccination and antiviral treatment as control variables. Finally, numerical simulations are conducted based on actual data. Our results show that it is essential to consider self-healing and home care for the prevention and control of influenza. Furthermore, vaccination and antiviral treatment can effectively prevent influenza infection and reduce the spread of influenza in the population.