Optimal Lockdown Timing during an Epidemic: An Extended Model

Abstract

During the COVID-19 pandemic, the rapid spread of the virus posed a serious challenge for decision makers. Decision makers must implement timely, feasible, and effective interventions to control disease transmission. The COVID-19 outbreak led to a significant growth in epidemic modeling and research, resulting in the development of frameworks that evaluate the trade-off between the health cost associated with disease spread and the economic cost of interventions such as lockdowns. To reduce mortality and limit the spread of the virus, many research studies have been conducted. These studies have explored several directions, including optimal vaccination strategies, the timing of lockdown implementation, the impact of testing on infection spread, and forecasting the number of new cases. The rapid spread of the virus led many countries to resort to lockdowns to reduce transmission. However, the timing of such lockdowns is critical, as acting at the right moment can significantly limit the outbreak. The model used in this paper relies on a pre-established framework proposed by El Hassan et al. (2024). In our work, we focus on enhancing the computational time of the Markov Decision Process (MDP) proposed by El Hassan et al. (2024) to support rapid and well informed decision-making. The proposed model is based on the well-known Susceptible-Infected-Susceptible (SIS) epidemic process. Our work focuses on handling large populations, starting from 100 individuals up to 5 million, by improving the CPU time of the algorithm. This enhancement allows testing large populations within a feasible time frame, given the complexity of the problem. In addition, our model extends the framework of El Hassan et al. (2024) by integrating uncertainty in the number of infections and a time-dependent transmission rate, making the model more realistic.