The emergence of novel coronavirus (Covid-19) in 2019 sprung a sudden outbreak across the globe, presenting clinical and public health management challenges which led to global cancellation of conferences, travel restrictions, social distancing and closure of institutions. Thus, in considering the grave implications of the continuous spread of coronavirus disease, a SEIHRD epidemic model was formulated to gain insight into disease transmission dynamics with impacts of proposing control measures. The model captures the impact of undetected infectious individuals and detected hospitalized individuals with saturated treatment on the spread, death and recovery of Covid-19 patients in Nigeria. The model epidemic threshold and equilibria are determined, and their stabilities are analyzed. The model is validated by fitting it to data from January 28 to December 5, 2020. Results obtained suggest that decreasing the transmission rate for infective alone is not sufficient to eradicate the disease because of the presence of backward bifurcation, and we recommend that Nigerians must also adhere strictly to Covid-19 protocols in mitigating the spread and demise of coronavirus.
Cite this paper
Oke, I. I. , Oyebo, Y. T. , Fakoya, O. F. , Benson, V. S. and Tunde, Y. T. (2021). A Mathematical Model for Covid-19 Disease Transmission Dynamics with Impact of Saturated Treatment: Modeling, Analysis and Simulation. Open Access Library Journal, 8, e7332. doi: http://dx.doi.org/10.4236/oalib.1107332.
Ngonghala, C.N., Iboi, E., Eikenberry, S., Scotch, M., MacIntyre, C.R., Bonds, M.H. and Gumel, A.B. (2020) Mathematical Assessment of the Impact of Non-Pharmaceutical Interventions on Curtailing the 2019 Novel Coronavirus. Mathematical Biosciences, 325, Article ID: 108364. https://doi.org/10.1016/j.mbs.2020.108364
Center for Disease Control and Prevention (2020) Novel Coronavirus Situation Dashboard. Center for Disease Control and Prevention, Atlanta.
https://experience.arcgis.com/experirnce/685d0ace521648f8a5beeeee1b9125cd
Gumel, A.B., Iboi, E.A., Ngonghala, C.N. and Elbasha E.H. (2020) A Primer on Using Mathematics to Understand COVID-19 Dynamics: Modeling, Analysis and Simulations. Infectious Disease Modelling, 6, 148-168.
https://doi.org/10.1016/j.idm.2020.11.005
Iboi, E., Sharomi, O., Ngonghala, C. and Gumel, A.B. (2020) Mathematical Modelling and Analysis of COVID-19 Pandemic in Nigeria. Mathematical Biosciences and Engineering, 17, 7192-7220. https://doi.org/10.3934/mbe.2020369
Khan, M.A. and Atangana, A (2020) Modeling the Dynamics of Novel Coronavirus (2019-nCov) with Fractional Derivatives. Alexendria Engineering Journal, 59, 2379-2389. https://doi.org/10.1016/j.aej.2020.02.033
Lin, Q., Zhao, S., Gao, D., Lou, Y., Yang, S., Salihu, S.M., et al. (2020) A Conceptual Model for the Coronavirus Disease 2019 (COVID-19) Outbreak in Wuhan, China with Individual Reaction and Governmental Action. International Journal of Infectious Diseases, 93, 211-216. https://doi.org/10.1016/j.ijid.2020.02.058
Ivorra B. and Ferrández M. R. and Vela-Pérez M. and Ramos A. M. (2019) Mathematical Modeling of the Spread of the Coronavirus Disease (COVID-19) Taking into Account the Undetected Infections. The Case of China. Communications in Nonlinear Science and Numerical Simulation, 88, Article No. 105303.
https://doi.org/10.1016/j.cnsns.2020.105303
Zhang, J., Jia, J. and Song, X. (2014) Analysis of an SEIR Model with Saturated Incidence and Saturated Treatment Function. The Scientific World Journal, 2014, Article ID: 910421, 11 p. https://doi.org/10.1155/2014/910421
Zhang, X. and Liu, X. (2008) Backward Bifurcation of an Epidemic Model with Saturated Treatment Function. Journal of Mathematical Analysis and Application, 348, 433-443. https://doi.org/10.1016/j.jmaa.2008.07.042
Van Den Driessche, P. and Watmough, J. (2002) Reproduction Numbers and Sub-Threshold Endemic Equilibria for Compartmental Models of Disease Transmission. Mathematical Biosciences, 180, 29-48.
https://doi.org/10.1016/S0025-5564(02)00108-6
Pérez, á.G.C., Avila-Vales, E. and Emilio García-Almeida, G. (2019) Bifurcation Analysis of an SIR Model with Logistic Growth. Nonlinear Incidence and Saturated Treatment, 2019, Article ID: 9876013, 21 p. https://doi.org/10.1155/2019/9876013
Castillo-Chavez, C. and Song, B. (2004), Dynamical Models of Tuberculosis and Their Applications. Mathematical Biosciences and Engineering, 1, 361-404.
https://doi.org/10.3934/mbe.2004.1.361
Fred, B., Castillo-Chavez, C. and Song, B. (2004) Mathematical Models for Communicable Disease (CBMS-NSF Regional Conference Series in Applied Mathematics). Series No. 84, Society for Industrial and Applied Mathematics, Philadelphia, 34-37.
Nigeria Centre for Disease Control (2021) NCDC Situation Report. Nigeria Centre for Disease Control, Abuja.
https://ncdc.gov.ng/diseases/sitreps/?cat=14name=An%20update%20of%20COVID-19%20outbreak%20in%20Nigeria
Madubueze, C.E., Akabuike, N.M. and Dachollom, S. (2020) The Role of Mathematical Model in Curbing COVID-19 in Nigeria. medRxiv Preprint.
https://doi.org/10.1101/2020.07.22.20159210
Yusuf, T.T. and Idisi, O.I. (2020) Modelling the Transmission Dynamics of HIV and HBV Co-Epidemics: Analysis and Simulation. Mathematical Theory and Modeling, 10, 48-77.
