Dynamical Analysis of the Spread of COVID-19 model and its Simulation with Vaccination and Social Distancing

Abstract

The model's creation and dynamical analysis were covered in this paper, SEIRS on the effects of vaccination and social isolation on the transmission of COVID-19. The susceptible individual subpopulation (S), the exposed individual subpopulation (E), the infected individual subpopulation (I), and the recovered individual subpopulation (R) are the four subpopulations that make up the human population in this model. This concept is founded on the notion that someone who has recovered from the illness is nonetheless vulnerable to reinfection. The carried out dynamical analysis includes the determination of the equilibrium point, the fundamental reproduction number (R_0), and evaluation of the local stability of the equilibrium point. The outcomes of the dynamical analysis show that there are two equilibrium points in the model: the endemic equilibrium point and the disease-free equilibrium point. Mathematical R_0>1 indicates the presence of an endemic equilibrium point, whereas a disease-free equilibrium point is always present. If the Routh-Hurwitz conditions are met, the endemic equilibrium point is locally asymptotically stable, but the disease-free equilibrium point is locally asymptotically stable if R_0<1. The numerical simulation results are consistent with the analyses' findings.