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Title: Transmission dynamics of SARS-CoV-2 : a modeling analysis with high-and-moderate risk populations
Authors: Musa, SS 
Baba, IA
Yusuf, A
Sulaiman, TA
Aliyu, AI
Zhao, S
He, D 
Issue Date: Jul-2021
Source: Results in physics, July 2021, v. 26, 104290
Abstract: Nigeria is second to South Africa with the highest reported cases of COVID-19 in sub-Saharan Africa. In this paper, we employ an SEIR-based compartmental model to study and analyze the transmission dynamics of SARS-CoV-2 outbreaks in Nigeria. The model incorporates different group of populations (that is, high- and- moderate risk populations) and is use to investigate the influence on each population on the overall transmission dynamics.The model, which is fitted well to the data, is qualitatively analyzed to evaluate the impacts of different schemes for controlstrategies. Mathematical analysis reveals that the model has two equilibria; i.e., disease-free equilibrium (DFE) which is local asymptotic stability (LAS) if the basic reproduction number (R0) is less than 1; and unstable for R0>1, and an endemic equilibrium (EE) which is globally asymptotic stability (LAS) whenever R0>1. Furthermore, we find that the model undergoes a phenomenon of backward bifurcation (BB, a coexistence of stable DFE and stable EE even if the R0<1). We employ Partial Rank Correlation coefficients (PRCCs) for sensitivity analyses to evaluate the model's parameters. Our results highlight that proper surveillance, especially movement of individuals from high risk to moderate risk population, testing, as well as imposition of other NPIs measures are vital strategies for mitigating the COVID-19 epidemic in Nigeria. Besides, in the absence of an exact solution for the proposed model, we solve the model with the well-known ODE45 numerical solver and the effective numerical schemes such as Euler (EM), Runge–Kutta of order 2 (RK-2), and Runge–Kutta of order 4 (RK-4) in order to establish approximate solutions and to show the physical features of the model. It has been shown that these numerical schemes are very effective and efficient to establish superb approximate solutions for differential equations.
Keywords: Bifurcation
Reproduction number
Publisher: Elsevier
Journal: Results in physics 
EISSN: 2211-3797
DOI: 10.1016/j.rinp.2021.104290
Rights: © 2021 The Author(s). Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (
The following publication Musa, S. S., Baba, I. A., Yusuf, A., Sulaiman, T. A., Aliyu, A. I., Zhao, S., & He, D. (2021). Transmission dynamics of SARS-CoV-2: A modeling analysis with high-and-moderate risk populations. Results in physics, 26, 104290 is available at
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