A delay differential equation model on covid-19 with vaccination strategy

¹ Department of Mathematics, Shri P.N. Pandya Arts, M.P. Pandya Science & Smt. D.P. Pandya Commerce College Lunawada-389230, Shri Govind Guru University, Godhra 388713, Gujarat, India
² Department of Mathematics, Government Science College, Chhotaudepur 391165, Shri Govind Guru University, Godhra 388713, Gujarat, India

^* Corresponding author: gaurangsharma508@gmail.com

Received: 3 December 2023
Accepted: 14 July 2024

Abstract

In this paper, we have extended SEIR model of COVID-19. The model incorporates two vital aspects in the form of vaccine compartment and constant time delay. The vaccination and time delay provide the information about immune protection and actual existence of the infection among the individuals, respectively. The model is analysed numerically and numerical simulation are executed for three different initial histories and constant time delays which affirm the biological relevance of the system. The analysis includes disease-free equilibrium (DFE), endemic equilibrium, and the basic reproduction number. The stability analysis is performed which reveal the asymptotic stability of the DFE when the basic reproduction number R₀ < 1. The study addresses the boundedness and positivity of the solution as the time delay approaches zero. In addition, sensitivity analysis and contour plots for R₀ with different parameters offer deeper insights into the model. The impact of vaccination and vaccine inefficacy on the model dynamics is explored.