### Mathematical modeling and analysis of the transmission dynamics of novel Corona virous (Covid-19) pandemic disease

Document Type : Research Paper

Authors

1 Department of Mathematics, Arsi University, P.O.Box 193, Asella, Ethiopia

2 Department of Mathematics, Samara University, P.O.Box 132, Samara, Ethiopia

Abstract

In this paper, we have formulated a deterministic mathematical model of the novel corona virus to describe the dynamics of virus transmission in the community using a system of nonlinear ordinary differential equations. The invariant region of the solution, conditions for the positivity of the solution,  existence of equilibrium points and their stabilities analysis, sensitivity analysis and numerical simulation of the model were determined. The system of a model equation has two equilibrium points, namely the disease-free equilibrium points where the disease does not exist and the endemic equilibrium points where the disease persists.  Both local and global stability of the disease-free equilibrium and endemic equilibrium points of the model equation were established. The basic reproduction number that represents the epidemic indicator was obtained by using a next-generation matrix. The endemic states were considered to exist when the basic reproduction number was greater than one. Finally, our numerical findings were illustrated through computer simulations using MATLAB $R2015b$ with $ode45$ solver which shows the reliability of our model from the practical point of view. From our simulation results of the model, we came to realize that the number of infected people keeps decreasing if one carefully decreases the effective contact rate among protected and infectious individuals.

Keywords

[1] S. Abdulrahman, N.I. Akinwande, O.B. Awojoyogbe, and U.Y. Abubakar, Sensitivity analysis of the parameters of a mathematical model of hepatitis b virus transmission, Univer. J. Appl. Math. 1 (2013), no. 4, 230–241.
[2] M. Anderson. Mathematical biology of infectious diseases: Part 1 Nature 280 (1979), 361–367.
[3] C. Castillo-Chavez, Z. Feng, and W. Huang, On the computation of Ro and its role on global stability, Math. Approach. Emerg. Reemerg. Infec. 1 (2002), 229.
[4] T.-M. Chen, J.R., Q.-P. Wang, Z.-Y. Zhao, J.-A. Cui, and L. Yin, A mathematical model for simulating the phase-based transmissibility of a novel coronavirus, Infectious Diseases of Poverty 9 (2020), no. 1, 1–8.
[5] N. Chitnis, J.M. Hyman, and J.M. Cushing, Determining important parameters in the spread of malaria through the sensitivity analysis of a mathematical model, Bull. Math. Bio. 70 (2008), no. 5, 1272.
[6] O. Diekmann, J.A.P. Heesterbeek, and J.A. Metz, On the definition and the computation of the basic reproduction ratio R0 in models for infectious diseases in heterogeneous populations, J. Math. Bio. 28 (1990), no. 4, 365–382.
[7] S. Edward and N. Nyerere, A mathematical model for the dynamics of cholera with control measures, Appl. Comput. Math. 4 (2015), no. 2, 53–63.
[8] E.D. Gurmua, G.B. Batu, and M.S. Wameko, Mathematical model of novel covid-19 and its transmission dynamics, Int. J. Math. Modell. Comput. 10 (2020), no. 2, 141–159.
[9] J.P. La Salle, The stability of dynamical systems, Society for Industrial and Applied Mathematics, 1976.
[10] Y. Li, B. Wang, R. Peng, C. Zhou, Y. Zhan, Z. Liu, X. Jiang, and B, Zhao, Mathematical modeling and epidemic prediction of COVID-19 and its significance to epidemic prevention and control measures, Ann. Infect. Disease Epidemio. 5 (2020), no. 1, 1052.
[11] W. Ming, J.V. Huang, and C.J.P. Zhang, Breaking down of healthcare system: Mathematical modelling for controlling the novel coronavirus (2019-nCoV) outbreak in Wuhan, China, BioRxiv (2020). doi:10.1101/2020.01.27.922443
[12] Coronavirus: Common Symptoms, Preventive Measures, and How to Diagnose It; https://www.caringlyyours. com/coronavirus/, Caringly Yours. Retrieved January 28, 2020
[13] C. Wang, P.W. Horby, F.G. Hayden, and G.F. Gao, A novel coronavirus outbreak of global health concern, Lancet 395 (2020), 470–473.
[14] L. Wang, Y. Wang, Y. Chen, and Q. Qin. Unique epidemiological and clinical features of the emerging 2019 novel coronavirus pneumonia (covid-19) implicate special control measures, J. Med. Virology 92 (2020), no. 6, 568–576.
[15] World Health Organization. Naming the coronavirus disease (COVID-19) and the virus that causes it. https://www.who.int/emergencies/diseases/novel-coronavirus-2019/technical-guidance/naming-the-coronavirusdisease-(covid-2019)-and-the-virus-that-causes-it, February (2020).
[16] World Health Organization. Statement on the second meeting of the international health regulations (2005). emergency committee regarding the outbreak of novel coronavirus (2019-ncov). https://www.who.int/newsroom/detail/30-01-2020-statement-on-the-second-meeting-of-the-international-health-regulations-(2005)-emergency-committee-regarding-the-outbreak-of-novel-coronavirus-(2019-ncov), January (2020).
[17] World Health Organization. Director-general’s opening remarks at the media briefing on COVID-19 -11 March 2020. https://www.who.int/dg/speeches/detail/who-director-general-s-opening-remarks-at-the-mediabriefing-on-covid-19-11-march-2020, March 2020.
[18] C. Yang and J. Wang, A mathematical model for the novel coronavirus epidemic in Wuhan, China, MBE 17 (2020), no. 3, 2708–2724.
###### Volume 14, Issue 10October 2023Pages 327-343
• Receive Date: 24 February 2023
• Revise Date: 22 May 2023
• Accept Date: 25 May 2023