Mathematical Model for Transmission Dynamics of Novel COVID-19 with Sensitivity Analysis

Gurmu, Eshetu Dadi; Motuma, Solomon Tolcha; Wedajo, Alemu Geleta

doi:10.22075/ijnaa.2022.20615.2179

Mathematical Model for Transmission Dynamics of Novel COVID-19 with Sensitivity Analysis

Document Type : Research Paper

Authors

Eshetu Dadi Gurmu ¹

Solomon Tolcha Motuma ²

Alemu Geleta Wedajo ¹

¹ Department of Mathematics, Wollega University, Nekemte, Ethiopia

² Department of Mathematics, Addis Ababa Science and Technology University, Addis Ababa, Ethiopia

10.22075/ijnaa.2022.20615.2179

Abstract

In this paper, a deterministic compartmental model of COVID-19 was formulated to describe the transmission dynamics of the disease. The theory of the stability of differential equations is used to study the qualitative behavior of the system. The basic reproduction number representing the epidemic indicator is obtained using the next generation matrix. The local and global stability of the disease-free equilibrium and the endemic equilibrium point of the model equation was established. The results show that if the basic reproduction number is less than one, then the solution converges to a disease-free equilibrium state and the disease-free equilibrium is asymptotically stable. The endemic states are considered to exist when the basic reproduction number for each disease is greater than one. Numerical simulation carried out on the model revealed that an increase in level of transmission levels in individuals has an effect on reducing the prevalence of COVID19 and COVID19 disease. In addition, a sensitivity analysis of the model equation was performed on the key parameters to find out their relative significance and potential impact on the transmission dynamics of COVID-19.

Keywords

Model

Global Stability

Sensitivity

Reproduction Number

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