International Journal of Mathematical Sciences and Computing(IJMSC)

ISSN: 2310-9025 (Print), ISSN: 2310-9033 (Online)

Published By: MECS Press

IJMSC Vol.7, No.4, Dec. 2021

Mathematical Modeling for COVID-19 Transmission Dynamics and the Impact of Prevention Strategies: A Case of Ethiopia

Full Text (PDF, 1179KB), PP.43-59

Views:1   Downloads:0


Akalu Abriham, Demsis Dejene, Tadele Abera, Abayneh Elias

Index Terms

COVID-19 Disease, Mathematical Model, prevention and control, Impact, Ethiopia.


At the end of 2019 the novel coronavirus disease (COVID-19) was declared as a major health hazard by the world health organization (WHO) and the only available way of stopping this threat was via non-pharmaceutical approach. Most authors have studied COVID-19 transmission dynamics using mathematical modeling by involving the basic (major) compartments. In this study we have formulated a mathematical model for the transmission dynamics of COVID-19 which incorporates almost all possible scenarios at present. We have also analyzed the impact of prevention and control strategies. The model has satisfied all the basic properties that infectious disease model should fulfill; Boundedness, positivity of its solutions, stability analysis, epidemic equilibrium point, basic reproduction number and local stability of the disease free equilibrium. We introduced a self-protection parameter, m to analyze the impact of physical distancing, staying at home, using masks, washing hands and so on. The impact of isolation and quarantine has been analyzed and their effects on the number of Exposed, infected and dead people were clearly discussed. In addition to these, the effects of symptomatic and asymptomatic individuals on the value of basic reproduction number have been examined. The numerical simulations of this study indicate that the government should increase isolation, quarantine and self-protection rates. Additionally to minimize the contact rate between susceptible and asymptotic individuals, self-protection at all cost and everywhere has to be done, so that both symptomatic and importantly asymptomatic individuals stop transmitting the virus.

Cite This Paper

Akalu Abriham, Demsis Dejene, Tadele Abera, Abayneh Elias," Mathematical Modeling for COVID-19 Transmission Dynamics and the Impact of Prevention Strategies: A Case of Ethiopia ", International Journal of Mathematical Sciences and Computing(IJMSC), Vol.7, No.4, pp. 43-59, 2021. DOI: 10.5815/ijmsc.2021.04.05


[1]Chan JF, Yuan S, Kok KH, et al. (2020). A familial cluster of pneumonia associated with the 2019 novel coronavirus indicating person-to-person transmission: a study of a family cluster. Lancet 2020; 395:514.

[2]WHO Emergency Committee. Statement on the second meeting of the International Health Regulations (2005) Emergency Committee regarding the outbreak of novel coronavirus (COVID-19). Geneva: WHO, 2020.

[3]Chayu Yang and Jin Wang. A mathematical model for the novel coronavirus epidemic in Wuhan, China, Mathematical Biosciences and Engineering. (2020) MBE, 17(3): 2708–2724

[4]National Health Commission of the People’s Republic of China. 2020.

[5]WHO novel coronavirus (2019-nCoV) situation reports. Available from:

[6]World Health Organization. Coronavirus disease 2019 (COVID-19): situation report, 82. 2020. Available from:

[7] Guarner J. Three Emerging Coronaviruses in Two Decades: The Story of SARS, MERS, and Now COVID-19. American Journal of Clinical Pathology. 2020; 153(4): 420-421. ajcp/aqaa029 10. 

[8]Mahase E. Coronavirus covid-19 has killed more people than SARS and MERS combined, despite lower case fatality rate. BMJ (Clinical Research Ed.). 2020 Feb; 368:m641.

[9]Chatterjee K, Chatterjee K, Kumar A, Shankar S. Healthcare impact of COVID-19 epidemic in India: A stochastic mathematical model. Medical Journal Armed Forces India. 2020. Available from: https://doi. org/10.1016/j.mjafi.2020.03.022. 12. 

[10]Khan T, Ullah Z, Ali N, Zaman G. Modeling and control of the hepatitis B virus spreading using an epidemic model. Chaos, Solitons and Fractals. 2019; 124: 1–9. 033

[11]Herbert W. Hethcote (2000), “The Mathematics of Infectious Diseases”, Society for Industrial and Applied Mathematics, Vol. 42, No. 4, pp. 599–653.

[12]Michael Hohle, Erik Jorgensen, Philip D. O’Neill (2005), “Inference in disease transmission experiments by using stochastic epidemic models”, Appl. Statist. 54, Part 2, pp. 349–366.

[13]Paiva HM, Afonso RJM, de Oliveira IL, Garcia GF (2020) A data-driven model to describe and forecast the dynamics of COVID-19 transmission. PLoS ONE 15(7): e0236386. https://

[14]Kayla Henneman, Dan Van Peursem, Victor C. Huber (2013), “Mathematical modeling of influenza and a secondary bacterial infection”, Wseas Transactions on Biology and Biomedicine, Issue 1, Volume 10.

[15]Frank Ball (1990), “Poission Approximation for Some Epidemic Models”, J. Applied Probabilty, 27, 479-490.

[16]Michael Y. Li. An Introduction to Mathematical Modeling of Infectious Diseases, University of Alberta Edmonton, AB Canada. Springer International Publishing AG 2018.

[17]M. Choisy, J.-F. Guégan, and P.  Rohani. Encyclopedia of Infectious Diseases:Modern Methodologies, Copyright © 2007 John Wiley & Sons,Inc. page 379-404

[18]Liliana Perez, suzana Dragicevic. An agent-based approach for modeling dynamics of contagious disease spread. International Journal of Health Geographics. (2009, 8:50 doc.10.1186/1476-072X-8-50

[19]C. Rothe, M. Schunk, P. Sothmann, G. Bretzel, G. Froeschl, C. Wallrauch, et al., Transmission of 2019-nCoV Infection from an asymptomatic contact in Germany, N. Engl. J. Med., 2020.

[20]Sheng Bin, Gengxin Sun and Chih-Cheng Chen. Spread of Infectious Disease Modeling and Analysis of Different Factors on Spread of Infectious Disease Based on Cellular Automata. International journal of environmental research and public health. (2019)

[21]Chen et al. A mathematical model for simulating the phase-based transmissibility of a novel coronavirus. (2020)

[22]Juan Zhang. Modeling the Transmission of Middle East Respirator Syndrome Corona Virus in the Republic of Korea (2015) Article in PLoS ONE DOI: 10.1371/journal.pone. 0144778

[23]Yichi Li, Bowen Wang. Mathematical Modeling and Epidemic Prediction of COVID-19 and Its Significance to Epidemic Prevention and Control Measures. (2020) Annals of Infectious Disease and Epidemiology. Volume 5 | Issue 1 | Article 1052

[24]Frank G. Ball (1991), “Dynamic Population Epidemic Model”, Mathematical Biosciences 107:299-324.

[25]Estimated effectiveness of symptom and risk screening to prevent the spread of COVID-19. Katelyn Gostic, Ana CR Gomez, Riley O Mummah, Adam J Kucharski, James O Lloyd-Smith. Epidemology and global health.

[26]B. Ivorraa, M.R. Ferrándezb, M. Vela-Pérezc, A.M. Ramosd . Mathematical modeling of the spread of the coronavirus disease 2019 (COVID-19) considering its particular characteristics. The case of China. Institute de mathematical interdisciplinary.

[27]Z. Liu , P. Magal  , O. Seydi  , G. Webb.  A COVID-19 epidemic model with latency period, Infectious Disease Modelling 5 (2020) 323-337.

[28]A. Anirudh, Mathematical modeling and the transmission dynamics in predicting the Covid-19 - What next in combating the pandemic. Infectious Disease Modeling 5 (2020). 366-374.

[29]S. M.MANOU-ABI, J. BALICCHI. Analysis of the covid-19 epidemic in French overseas department Mayotte based on a modified deterministic and stochastic SEIR model. doi:

[30]Z. Abbasi, I. Zamani and A.H.A. Mehra et al. Optimal Control Design of Impulsive SQEIAR Epidemic Models with Application to COVID-19. Chaos, Solitons and Fractals 139 (2020) 110054.

[31]S. Annas, Muh. Isbar Pratama and Muh. Rifandi et al. Stability analysis and numerical simulation of SEIR model for pandemic COVID-19 spread in Indonesia. Chaos, Solitons and Fractals 139 (2020) 110072.

[32]S. Contreras, H.A. Villavicencio and D. Medina-Ortiz et al. A multi-group SEIRA model for the spread of COVID-19 among heterogeneous populations. Chaos, Solitons and Fractals 136 (2020) 109925.

[33]S.M. Kassa, J.B.H. Njagarah and Y.A. Terefe . Analysis of the mitigation strategies for COVID-19: From mathematical modelling perspective. Chaos, Solitons and Fractals 138 (2020) 109968.

[34]Isabel al. COVID-19 in East Africa: National Projections of Total and Severe Infections under Different Lockdown Scenarios. Center for Disease Dynamics, Economics & Policy. 2020.

[35]Abul Mukid Md. Mukaddes and Mridul Sannyal. Transmission Dynamics of COVID-19 in Bangladesh- A Compartmental Modeling Approach. Shahjalal University of Science and Technology, Bangladesh.

[36]Edwiga Kishinda Renald, Katharina Kreppel, Dmitry Kuznetsov, " Desirable DogRabies Control Methods in an Urban setting in Africa - a Mathematical Model ", International Journal of Mathematical Sciences and Computing(IJMSC), Vol.6, No.1, pp.49-67, 2020. DOI: 10.5815/ijmsc.2020.01.05

[37]Shaobo He, Yuexi Peng and Kehui Sun. SEIR Modeling of the COVID-19 and its Dynamics. Nonlinear Dyn, Springer Nature B.V. 2020.

[38]Alberto Godio , Francesca Pace and Andrea Vergnano. SEIR Modeling of the Italian Epidemic of SARS-CoV-2 Using Computational Swarm Intelligence. International journal of environmental research and public health. 2020, 17, 3535; https://doi:10.3390/ijerph17103535

[39]Haileyesus Tessema Alemneh and Getachew Teshome Tilahun. Mathematical Modeling and Optimal Control Analysis of COVID-19 in Ethiopia.

[40]G. Birkhoff, G.C Rota, Ordinary Differential Equations. Boston: Ginn; 1982.

[41]Ega, T. T., Luboobi, L. S., and Kuznetsov, D. (2015). Modeling the dynamics of rabies transmission with vaccination and stability analysis. Applied and Computational Mathematics, 4(6):409–419.

[42]B.Tang et al. An updated estimation of the risk of transmission of the novel coronavirus (2019-nCov). Infectious Disease Modeling. 5(2020) p248-255.