Necessity of Social Distancing in Pandemic Control: A Dynamic Game Theory Approach

We model a society with two types of citizens: healthy and vulnerable individuals. While both types can be exposed to the virus and contribute to its spread, the vulnerable people tend to be more cautious as being exposed to the virus can be fatal for them due to their conditions, e.g., advanced age or prior medical conditions. We assume that both types would like to participate in in-person social activities as freely as possible and they make this decision based on the total number of infected people in the society. In this model, we assume that a local governmental authority imposes and administers social distancing regulations based on the infection status of the society and revises it accordingly in each time period. We model and solve for the steady state in four scenarios: (i) non-cooperative (Nash), (ii) cooperative, (iii) egoistic, and (iv) altruistic. The results show that the Altruistic scenario is the best among the four, i.e., the healthy citizens put the vulnerable citizens' needs first and self-isolate more strictly which results in more flexibility for the vulnerable citizens. We use a numerical example to illustrate that the Altruistic scenario will assist with pandemic control for both healthy and vulnerable citizens in the long run. The objective of this research is not to find a way to resolve the pandemic but to optimally live in a society which has been impacted by pandemic restrictions, similar to what was experienced in 2020 with the spread of COVID-19.