Delayed Dynamics Of Seair Model For Covid-19 With Vaccination

Abstract

COVID-19 is an infectious disease caused by SARS-CoV-2, a virus that belongs to the coro navirus subfamily, a collection of connected RNA viruses. It has affected many countries globally, including Ethiopia. This study aims to develop and analyze a mathematical model of COVID-19 transmission dynamics and apply it as a case study in Ethiopia. For this , a system of non-linear ordinary differential equations has been used to formulate a deterministic mathematical model with six compartments to describe the dynamics of the COVID-19 infec tion. We investigated the model’s dynamical behavior and carried out a qualitative analysis. The system has two equilibrium points, the endemic equilibrium point and the disease free equilibrium point. Utilizing the next-generation matrix, the fundamental reproduction number R0 was calculated, and the stability of the equilibrium points was examined. According to the qualitative analysis, the disease-free equilibrium point is stable both locally and globally if R0 < 1, and the endemic equilibrium point is similarly stable both locally and globally if R0 > 1 in certain circumstances. Additionally, bifurcation analyses have been carried out to reveal the dynamics of coronavirus disease transmission. The COVID-19 prediction is more accurate when the time delay period is included in the model. A logical and more accurate representation of the SVEAIR model was created by adding a delay period for incubation. The dynamical behavior of the model will not match the current situation without the delay period. A stability loss of the endemic equilibrium point at R0 > 1 and approaches to the disease free equilibrium point resulted from the effect of incubation time. The Hopf bifurcation phenomenon can alter the system’s behavior and cause periodic oscillations. The qualitative analysis of the newly developed SVEAIR model is proven by comparing its predictions with the data collected from the Ethiopian Minister of Health. Finally, numerical simulation is presented using Mathlab2017b software to check the validity of the analytical results presented in the two models.