Vaccination control of an epidemic model with time delay and its application to COVID-19

Shidong Zhai; Guoqiang Luo; Tao Huang; Xin Wang; Junli Tao; Ping Zhou

doi:10.1007/s11071-021-06533-w

Vaccination control of an epidemic model with time delay and its application to COVID-19

Nonlinear Dyn. 2021;106(2):1279-1292. doi: 10.1007/s11071-021-06533-w. Epub 2021 May 28.

Authors

Shidong Zhai¹, Guoqiang Luo¹, Tao Huang¹, Xin Wang¹, Junli Tao², Ping Zhou³

Affiliations

¹ School of Automation, Chongqing University of Posts and Telecommunications, Chongqing, 400065 China.
² Chongqing University Cancer Hospital, Chongqing, 400030 China.
³ School of Science, Chongqing University of Posts and Telecommunications, Chongqing, 400065 China.

Abstract

This paper studies an SEIR-type epidemic model with time delay and vaccination control. The vaccination control is applied when the basic reproduction number $R_{0} > 1$ . The vaccination strategy is expressed as a state delayed feedback which is related to the current and previous state of the epidemic model, and makes the model become a linear system in new coordinates. For the presence and absence of vaccination control, we investigate the nonnegativity and boundedness of the model, respectively. We obtain some sufficient conditions for the eigenvalues of the linear system such that the nonnegativity of the epidemic model can be guaranteed when the vaccination strategy is applied. In addition, we study the stability of disease-free equilibrium when $R_{0} < 1$ and the persistent of disease when $R_{0} > 1$ . Finally, we use the obtained theoretical results to simulate the vaccination strategy to control the spread of COVID-19.

Keywords: Epidemic model; State delayed feedback; Time delay; Vaccination.