The impact of vaccination on the spread of COVID-19: Studying by a mathematical model

Bo Yang; Zhenhua Yu; Yuanli Cai

doi:10.1016/j.physa.2021.126717

The impact of vaccination on the spread of COVID-19: Studying by a mathematical model

Physica A. 2022 Mar 15:590:126717. doi: 10.1016/j.physa.2021.126717. Epub 2021 Dec 12.

Authors

Bo Yang¹, Zhenhua Yu², Yuanli Cai¹

Affiliations

¹ School of Automation Science and Engineering, Xi'an Jiaotong University, Xi'an, China.
² Institute of Systems Security and Control, College of Computer Science and Technology, Xi'an University of Science and Technology, Xi'an, China.

Abstract

The global spread of COVID-19 has not been effectively controlled, posing a huge threat to public health and the development of the global economy. Currently, a number of vaccines have been approved for use and vaccination campaigns have already started in several countries. This paper designs a mathematical model considering the impact of vaccination to study the spread dynamics of COVID-19. Some basic properties of the model are analyzed. The basic reproductive number $ℜ_{1}$ of the model is obtained, and the conditions for the existence of endemic equilibria are provided. There exist two endemic equilibria when $ℜ_{1} < 1$ under certain conditions, which will lead to backward bifurcation. The stability of equilibria are analyzed, and the condition for the backward bifurcation is given. Due to the existence of backward bifurcation, even if $ℜ_{1} < 1$ , COVID-19 may remain prevalent. Sensitivity analysis and simulations show that improving vaccine efficacy can control the spread of COVID-19 faster, while increasing the vaccination rate can reduce and postpone the peak of infection to a greater extent. However, in reality, the improvement of vaccine efficacy cannot be realized in a short time, and relying only on increasing the vaccination rate cannot quickly achieve the control of COVID-19. Therefore, relying only on vaccination may not completely and quickly control COVID-19. Some non-pharmaceutical interventions should continue to be enforced to combat the virus. According to the sensitivity analysis, we improve the model by including some non-pharmaceutical interventions. Combining the sensitivity analysis with the simulation of the improved model, we conclude that together with vaccination, reducing the contact rate of people and increasing the isolation rate of infected individuals will greatly reduce the number of infections and shorten the time of COVID-19 spread. The analysis and simulations in this paper can provide some useful suggestions for the prevention and control of COVID-19.

Keywords: 37C20; 37G10; Backward bifurcation; Basic reproductive number; COVID-19; Mathematical spread model; Stability.