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

Document Type : Research Paper

Authors

1 Department of Mathematics, Wollega University, Nekemte, Ethiopia

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

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

[1] J. Bhola, V.R. Venkateswaran and M. Koul, Corona epidemic in Indian context: predictive mathematical modelling, MedRxiv, (2020), doi: https://doi.org/10.1101/2020.04.03.20047175.
[2] C. Castillo-Chavez and B. Song, Dynamical models of tuberculosis and their applications, Math. Biosci. Eng. 1 (2004), no. 2, 361–404.
[3] E.D. Gurmu, G.B. Batu and M.S. Wameko, Mathematical model of novel COVID-19 and its transmission dynamics, Int. J. Math. Model. Comput. 10 (2020), no. 2, 141–159.
[4] E.D. Gurmu, B.K. Bole and P.R. Koya, Mathematical modelling of HIV/AIDS transmission dynamics with drug resistance compartment, Amer. J. Appl. Math. 8 (2020), no. 1, 34–45.
[5] E.D. Gurmu and P.R. Koya, Impact of chemotherapy treatment of SITR compartmentalization and modeling of human papilloma virus (HPV), IOSR J. Math. 15 (2019), no. 3, 17–29.
[6] E.D. Gurmu and P.R. Koya, Sensitivity analysis and modeling the impact of screening on the transmission dynamics of human papilloma virus (HPV), Amer. J. Appl. Math. 7 (2019), no. 3, 70–79.
[7] E. Hersh and M. Goodwin, How long is the incubation period for the Coronavirus, Healthline 13 (2020).
[8] J. Jia, J. Ding, S. Liu, G. Liao, J. LI, B. Duan, G. Wang and R. Zhang, Modeling the control of COVID-19: impact of policy interventions and meteorological factors, Electr. J. Differ. Equ. 2020 (2020), no. 23, 1–24.
[9] S. Khan, R. Siddique, M.A. Shereen, J. Liu, Q. Bai, N. Bashir and M. Xue, The emergence of a novel coronavirus (SARS-CoV-2), their biology and therapeutic options, J. Clin. Microbiol. 2020 (2020), 187–200.
[10] J.P. La Salle, The stability of dynamical systems, Soc. Industr. Appl. Math. 1976.
[11] National Health Commission of the People’s Republic of China, Diagnosis and treatment of novel coronavirus pneumonia, NHCPRC, 2020.
[12] WHO, Rational use of personal protective equipment for coronavirus disease 2019 (COVID-19), Interim. Guidance, 2020.
[13] WHO, Coronavirus disease 2019 (COVID-19) Situation Report -76, Data as reported by national authorities by 10:00 CET, 2020.
[14] C. Yang and J. Wang, A mathematical model for the novel coronavirus epidemic in Wuhan, China, MBE 17 (2020), no. 3, 2708–2724.
[15] https://www.worldometers.info/world-population/ethiopia-population/.
Volume 14, Issue 1January 2023Pages 2383-2398
• Receive Date: 13 June 2020
• Revise Date: 22 May 2022
• Accept Date: 05 July 2022