A spatial epidemic model with contact and mobility restrictions (Q6577759)

The goal of this paper is to study policy strategies for the epidemics control considering the geographical dynamics of infectious disease transmission. Timely implementation of appropriate regional policy measures can significantly mitigate the impact of a disease outbreak. In this paper, the authors propose and analyze a model that integrates both geographical factors and policy measures optimization aimed at controlling the spread of the disease while balancing the associated economic and social impacts.\N\NThe model is build on existing SIR-type models on graphs and incorporates preventive policy measures -- contact rate reduction, lock-downs, and testing. It also considers optimal policies taking into account the number of deaths, economic consequences, and social disutility. For a multi-city SIR type model with proportional random mixing of the population, the following control policies are included: the first focuses on the effects of contact restrictions at a specific location, \(x,\) which do not disrupt business continuity; the second examines mobility restrictions, such as limiting travel from one location, \(x\), to another, \(y\), which may have implications for business activity. It is established that the disease-free equilibrium is stable and the formula for the basic reproduction number is derived. The optimization of policy measures aimed at minimizing the number of deaths, accounting for the socioeconomic costs associated with these interventions is proposed. The analysis of the dependence of the optimal policy on some basic model parameters is provided using the numerical results obtained with help of a software based on the gradient projection method in the control space.