Transmission dynamics of SARS-CoV-2: A modeling analysis with high-and-moderate risk populations

Salihu S Musa; Isa A Baba; Abdullahi Yusuf; Tukur A Sulaiman; Aliyu I Aliyu; Shi Zhao; Daihai He

doi:10.1016/j.rinp.2021.104290

Transmission dynamics of SARS-CoV-2: A modeling analysis with high-and-moderate risk populations

Results Phys. 2021 Jul:26:104290. doi: 10.1016/j.rinp.2021.104290. Epub 2021 May 19.

Authors

Salihu S Musa^{1

2}, Isa A Baba³, Abdullahi Yusuf^{4

5}, Tukur A Sulaiman^{4

5}, Aliyu I Aliyu⁵, Shi Zhao^{6

7}, Daihai He¹

Affiliations

¹ Department of Applied Mathematics, Hong Kong Polytechnic University, Hong Kong.
² Department of Mathematics, Kano University of Science and Technology, Wudil, Nigeria.
³ Department of Mathematics, Bayero University Kano, Nigeria.
⁴ Department of Computer Engineering, Biruni University, Istanbul, Turkey.
⁵ Department of Mathematics, Science Faculty, Federal University Dutse, Jigawa, Nigeria.
⁶ JC School of Public Health and Primary Care, Chinese University of Hong Kong, Hong Kong.
⁷ CUHK Shenzhen Research Institute, Shenzhen, China.

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 ( $R_{0}$ ) is less than 1; and unstable for $R_{0} > 1$ , and an endemic equilibrium (EE) which is globally asymptotic stability (LAS) whenever $R_{0} > 1$ . Furthermore, we find that the model undergoes a phenomenon of backward bifurcation (BB, a coexistence of stable DFE and stable EE even if the $R_{0} < 1$ ). 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; COVID-19; Pandemic; Reproduction number; Runge–Kutta.