Dynamic analysis and optimal control of influenza model with discrete age structure

Abstract

Age heterogeneity in influenza transmission leads to significant differences in infection risk among different age groups. In this paper, an influenza model with vaccination and discrete age structure is constructed. First, we obtain the basic reproduction number and prove that the disease‐free equilibrium is globally stable at . When , the disease will persist uniformly, and there is a unique positive equilibrium, which is globally asymptotically stable under certain conditions. The model is used to analyze influenza data from 2016 to 2017 in China. By comparing various prevention and control measures, it can be found that by wearing masks to reduce contact between different age groups, while increasing vaccine coverage and reducing vaccine failure rates, the prevention and control goals can be achieved in the shortest time. However, if only the vaccine coverage rate is increased and the vaccine protection rate is strengthened, the time to reach the control target is 8 months later than the above case, and the cost is the lowest.