Optimal control and cost-effective analysis of an age-structured emerging infectious disease model

Abstract

Emerging infectious diseases are one of the global public health problems which may lead to widespread epidemics and potentially life-threatening infection. Integrated vaccination and physical distancing interventions are two elementary methods for preventing infectious diseases transmission. In this paper, we construct a continuous age-structured model for investigating the transmission dynamics of an emerging infection disease during a short period. We derive the basic regeneration number R0, the spectral radius of the next generation operator K, which determines the disease outbreak or not. Furthermore, we propose an optimal control problem to take account for the cost-effectiveness of social distancing intervention and vaccination. We rigorously obtain sufficient conditions for a L1 control problem. Numerical simulations show that coupling integrated vaccination and physical distancing intervention could effectively eliminate the infection, and such control strategy is more sensitive for people aged 10–39 and over 60.

Keywords

• Age-structured model
• Admissible control
• Ekerland variational principle
• The basic reproduction number