The role of delay in vaccination rate on Covid-19

Mohammed Salman; Sanjay Kumar Mohanty; Chittaranjan Nayak; Sachin Kumar

doi:10.1016/j.heliyon.2023.e20688

The role of delay in vaccination rate on Covid-19

Heliyon. 2023 Oct 10;9(10):e20688. doi: 10.1016/j.heliyon.2023.e20688. eCollection 2023 Oct.

Authors

Mohammed Salman¹, Sanjay Kumar Mohanty¹, Chittaranjan Nayak², Sachin Kumar³

Affiliations

¹ Department of Mathematics, SAS, Vellore Institute of Technology, Vellore, 632014, Tamil Nadu, India.
² Department of Communication Engineering, School of Electronics Engineering, Vellore Institute of Technology, Vellore, 632014, Tamil Nadu, India.
³ Department of Electronics and Communication Engineering, SRM Institute of Science and Technology, Kattankulathur, 603203, Tamil Nadu, India.

Abstract

The role of vaccination in tackling Covid-19 and the potential consequences of a time delay in vaccination rate are discussed. This study presents a mathematical model that incorporates the rate of vaccination and parameters related to the presence and absence of time delay in the context of Covid-19. We conducted a study on the global dynamics of a Covid-19 outbreak model, which incorporates a vaccinated population and a time delay parameter. Our findings demonstrate the global stability of these models. Our observation indicates that lower vaccination rates are associated with an increase in the overall number of infected individuals. The stability of the corresponding time delay model is determined by the value of the time delay parameter. If the time delay parameter is less than the critical value at which the Hopf bifurcation occurs, the model is stable. The results are supported by numerical illustrations that have epidemiological relevance.

Keywords: R 0 ; Covid-19; Lyapunov stability; Time delay; Vaccination.