The impact of vaccination and social distancing on COVID-19: A compartmental model and an evolutionary game theory approach

Abstract

The spread of COVID-19 disease is a worldwide issue that has impacted many countries. Mathematical modeling can help us better understand this disease and predict how different interventions and behavioral changes will affect disease progression. This study presents a compartmental model that corresponds to the COVID-19 trend in some countries. The compartments are: susceptible–exposed–unvaccinated infectious-partially vaccinated infectious–hospitalized–recovered–death–vaccinated (with at least three doses of vaccine). In this model, we have compartments such as individuals who have recovered but may re-infect if they come into contact with infection after completing the post-recovery immunity course, and individuals who have received one or two doses of vaccine are assumed to be partially immune and may infect. Individuals who have received at least three doses of vaccine are considered fully immune and will no longer be infected. The results show this model fits the data from the World Health Organization (WHO) for Finland, Denmark, the Netherlands, the United Kingdom, Italy, and Canada. Furthermore, the basic reproduction number of the proposed model is calculated, and we can compare it to the one released by the WHO to analyze the relative risk of infection based on the amount of investment in social distancing. People in Denmark, according to the study’s findings, invested less in social distancing than people in the other five countries. Finally, we use evolutionary game theory to examine the impact of changing strategy from not-vaccinated to partially vaccinated (with one or two doses of vaccine) in a population that is not fully immune.