The effectiveness of travel restriction and vaccination for multi-region discrete-time SIRI epidemic model: optimal control approach

Abstract

In this paper, we develop a multi-region discrete-time SIRI epidemic model, which describes the spatial-temporal spread of an infectious disease in a geographical domain divided into p regions and assumed to be connected and allow their people’s mobility. We introduce two control variables into our model to study the effectiveness of travel restriction and vaccination in limiting the spread of epidemic. We aim to reduce the number of infected individuals in all regions and minimize the cost of administering travel ban and vaccination. In addition, we propose an optimal control approach using the definition of a supplementary function that identifies the activation of travel restriction and vaccination in every region according to health authority decisions. Numerical results are presented where we test the spread of epidemic without any intervention, when travel restriction only is applied, and when vaccination is added.