Numerical Implementation of a Susceptible - Infected - Recovered (SIR) Mathematical Model of Covid-19 Disease in Nigeria

Abstract

In this study, we examine the dynamics of the Susceptible Infected Recovered (SIR) model in the context of the COVID-19 outbreak in Nigeria during the year 2020. The model is validated by fitting it to data on the prevalence and active cases of COVID-19, sourced from a government agency responsible for disease control. Utilizing the parameters associated with the disease prevalence, we calculate the basic reproduction number 𝑅𝑐𝑟, revealing its approximate value as 10.84. This suggests an average infection rate of around 10 human individuals, indicating the endemic nature of the disease in Nigeria. The impact of variation of recovery rate via treatment is examined, demonstrating its effectiveness in reducing disease prevalence when 𝑅𝑐𝑟 is below or above unity. To numerically implement the model, we employ the Sumudu Decomposition Method (SDM) and compare its results with the widely used Runge–Kutta fourth-order (RK4) method, implemented through the Maple software. Our findings indicate a mutual efficiency and convergence between the two methods, providing a comprehensive understanding of the COVID-19 dynamics in Nigeria.