| Abstract: |
| We present a general problem of optimally controlling of an epidemic outbreak of a disease structured by age since exposure, with the aid of two types of control instruments, namely social distancing and vaccination. We prove the existence of at least one optimal control pair, derive the first-order necessary conditions for optimality and prove some useful properties of such optimal solutions. This general model can be specialized to include a number of subcases relevant for epidemics (e.g., like COVID-19), such as, the arrival of vaccines in a second stage of the epidemic, and vaccine rationing, making social distancing the only optimizable instrument in the first stage. The control problem takes also into account the indirect epidemic cost, namely the broader societal and economic cost due to the impact of social distancing on overall social and relational activities.
The presentation is based on a joint paper with Alberto D`Onofrio, Mimmo Iannelli and Piero Manfredi. |
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