Mathematical Modelling of the Dynamics of COVID-19 Disease Transmission

Abstract

We construct a simple mathematical model that describes the dynamics of the transmission of COVID-19 disease in a human population. It accounts for the various phases of the disease and its mode of contact through infectious humans and surfaces. The contribution of asymptomatic humans in the dynamics of the disease is well represented. The model is a system of ordinary dierential equations that describes the evolution of humans in a range of COVID-19 states due to emergence of an index case. The analysis includes establishment of the basic reproduction number, R0, where, R0 < 1 signifies a disease free state that is locally asymptotically stable. A key result in this study shows some long term damped oscillatory behaviour that do not seem to end soon.

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

“…This behavior is as a result of the impact vaccination in the system. This result agrees with the recommendation that was made in [4]. However, increasing the contact rates between infectious and susceptible humans will hinder the positive effect of vaccination.…”

“…In this model, we describe the transmission of Covid-19 disease in an entirely susceptible human population due to the introduction of an index 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 = 0.3411 different from the results of [4] and [9]. This value of 𝑅 0 suggests that the disease will likely die out due to vaccination as seen in Fig.…”

“…The Coronavirus disease, known as Covid-19, is an Infectious disease caused by Severe Acute Respiratory Syndrome Coronavirus, which is a new virus of the same family as SARS-CoV2 [1], believed to have a zoonotic origin [2,3] and was identified and named by the World Health Organization (WHO) on January 10, 2020 following an ealier virus borne infection episode in Wuhan, China in December, 2019 [4]. The COVID-19 pandemic is considered as the biggest global threat worldwide because of thousands of confirmed infections, accompanied by thousands of deaths over the world [5].…”

“…In the work of [4], the authors noted that, Covid-19 pandemic ravaging the world currently, will not end soon, as the result of their work shows damping oscillations. They aver that vaccination could be a possible remedy.…”

“…Here, we include Vaccination and possible Re-infection of Recovered Covid-19 Patient alongside other features considered in [4]. We only consider human to human transmission of the disease following the introduction of an index case rather than infection from a Bat population.…”