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

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 R-0, 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 L-1 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. (C) 2021 The Authors. Publishing services by Elsevier B.V. on behalf of KeAi Communications Co. Ltd.