The Impact of Vaccination on Covid-19 Disease Transmission Patterns in a Human Population: A Theoretical Analysis

Abstract

We construct a Mathematical model that describes the effect of vaccination on the dynamics of the transmission of COVID-19 disease in a human population. The model is a system of ordinary differential equations that describes the evolution of humans in a range of Covid-19 states due to emergence of an index case in a disease free region. The analysis of the model shows that effective vaccination can lead to disease eradication, where in the disease free state is locally asymptomatically stable if the basic reproductive number, and unstable when The numerical simulations suggests the use of other social measures alongside vaccination in order to avert the possibility of the disease becoming endemic.

Global Stability Analysis of a Mathematical Model on the Transmission Dynamics of Covid-19 With Vaccination

“…However, increasing the contact rates between infectious and susceptible humans will hinder the positive effect of vaccination. This agrees with the results of [9] and [10], which maintain that vaccination should be carried out in conjunction with other social measures that restrict contact rate between infectious and susceptible humans. The analysis shows that the disease free state is globally asymptotically stable in the absence of disease related death.…”

“…In this model, we describe the transmission of Covid-19 disease in an entirely susceptible human population due to the introduction of a single case and the effect of vaccination on the Disease dynamics. Using available data and with the introduction of vaccination, we obtain the Basic Reproduction Number, 𝑅 0 = 0.28 different from the results of [5], [6] and [9]. This value of 𝑅 0 suggests that the disease may likely die out due to vaccination as seen in fig.…”

“…Various methods have been used in [17][18][32][33][34][35] to show conditions of global asymptotic stability of infectious disease models. In this paper we extended an earlier work in [9] by investigating the global stability of the model exploring the technique in [17][18]. The total human population, N(t), is divided into 6 classes namely, Susceptible class, Q(t), Latent class L(t), Symptomatic class, S(t), Asymptomatic class A(t) , Recovered class R(t) and Vaccinated class V(t)).…”

“…Depending on the mode of transmission of the disease under consideration, modification can be made to the above forms to give a detail explanation of the dynamics of the disease. The concept of Symptomatic, Asymptomatic and Surface Virus as considered in [6,9], Vaccination in [9,10], Isolation and Hospitalization in [11] and convalescence in [12] are modifications of the above general infectious disease models. Nonlinear ordinary differential equations have been used to explore the complex mechanisms of the dynamics of various systems in multidisciplinary fields: for instance, they are used in economics [13], quantum physics [14], chaos [15], medicine [16] and health diseases [17].…”

“…Vaccination has the role of preventing healthy people from getting infected by a disease [21]. Various vaccination policies were studied in different mathematical models [9][10][22][23][24][25][26].…”