STABILITY AND BIFURCATION ANALYSIS OF COVID-19 MATHEMATICAL MODEL INCORPORATING CASE DETECTION
Opeyemi Odetunde1*, Mohammed Olanrewaju Ibrahim1, Olanrewaju Thomas Olotu1, Ohigweren Airenoni Uwaheren1, and Samuel Tosin Akinyemi2
1,2,3,4Department of Mathematics, University of Ilorin, P.M.B. 1515, Kwara State, Nigeria
5Global Kiddies Academy, Kaduna State, Nigeria
1*This email address is being protected from spambots. You need JavaScript enabled to view it., 2This email address is being protected from spambots. You need JavaScript enabled to view it., 3This email address is being protected from spambots. You need JavaScript enabled to view it., 4This email address is being protected from spambots. You need JavaScript enabled to view it., 5This email address is being protected from spambots. You need JavaScript enabled to view it.
ABSTRACT
COVID-19 became a household name globally in the year 2020 after it was first discovered in Wuhan, China in December 2019. It is a global pandemic that shut the economy of all nations in the larger part of year 2020 by forcing a compulsory holiday on mankind due to its threat of mass death. The menace of this pandemic was combated with the total arsenal in human capacity. One of such weapons is case detection that leads to either self-isolation or quarantine. This weapon helps to reduce the number of new cases that may arise from undetected asymptomatic/symptomatic carriers within a population. In this article, the dynamics of COVID-19 transmission were studied by developing a mathematical model incorporating case detection, the impact of sensitization, and role of early diagnosis in curbing the spread of this disease. The basic properties in terms of existence, uniqueness, and boundedness of solution for the formulated model were discussed. Also, the model was found to exhibit two equilibrium states which are categorised as the disease-free (DFE) and pandemic equilibrium states. The reproductive number for the model was computed and used to establish the stability analysis for both equilibrium states. Center manifold theory was employed to assess the bifurcation analysis of the model and the result shows that the model exhibits forward bifurcation when the reproductive number is greater than and equal to 1.
Keywords: Bifurcation, COVID-19, Case-detection, Pandemic, Reproductive Number.
Published On: 14 February 2022
