• epidemic covid
• lockdown policy
• optimal control

The dramatic impact of COVID-19 pandemic has shown some flaws of global society handling the outbreak of an unknown infection disease. Implementation of an optimal policy capable of mitigate early phase of an epidemic, when pharmaceutical therapies are not available, can help to strengthen pandemic prevention measures.
The epidemiological approach extends common epidemic models such as SIR and SEIR models, including other factors such as stages of infection (e.g., asymptomatic, critical cases) and number of hospitalizations in order to monitor the status of a pandemic and evaluate whether a combination of Non-Pharmaceutical Interventions (NPIs) is effective or not. However, these models exclude the potential economic loss due to NPIs, disruption of public health and economic activities and societal damages.
Then, Economists integrate these considerations in their studies, seeking the optimal policy over time, which has the best trade-off between health and societal costs. However, this strategy tends to oversimplify the epidemiological standpoint, using simple epidemic models.
In this work, we join intuitions of both strategies, implementing an epidemic model which describe transmission dynamics of an epidemic in as much detail as possible and a cost functional that considers both direct damages due to infection and negative consequences of NPIs, with particular focus on general isolation and contact-tracing during the outbreak of an epidemic. The main objective of this Thesis is the creation of a detailed optimal control problem, which returns the most realistic and effective optimal policy.