Dynamics of an SEIRS COVID-19 Epidemic Model with Saturated Incidence and Saturated Treatment Response: Bifurcation Analysis and Simulations

  1. Department of Mathematics, School of Physical Science, Ahmadu Bello University, Zaria, Kaduna State, Nigeria
  2. David A. Oluyori
  3. Angel G. C. Perez
  4. Facultad de Matematicas, Universidad Autonoma de Yucatan, Merida, Yucatan, Mexico
  5. Victor A. Okhuese
  6. Department of Mathematics, Nasarawa State University, Keffi, Nigeria
  7. Muhammad Akram
  8. Department of Eastern Medicine, Government College University, Faisalabad, Pakistan

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Abstract

In this work, we study the dynamics of the Coronavirus Disease 2019 pandemic using an SEIRS model with saturated incidence and treatment rates. We derive the basic reproduction number R_0 and study the local stability of the disease-free and endemic states. Since the condition R_0<1 for our model does not determine if the disease will die out, we study the backward bifurcation and Hopf bifurcation to understand the dynamics of the disease at the occurrence of a second wave and the kind of treatment measures needed to curtail it. We present some numerical simulations considering the symptomatic and asymptomatic infections and make a comparison with the reported COVID-19 data for Nigeria. Our results show that the limited availability of medical resources favours the emergence of complex dynamics that complicates the control of the outbreak

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  1. Version published to 10.52542/tjdu.1.1.39-56
  2. Version published to 10.1101/2020.08.28.20183723v2 on medRxiv
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    Table 1: Rigor

    Institutional Review Board Statementnot detected.
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    Blindingnot detected.
    Power Analysisnot detected.
    Sex as a biological variablenot detected.

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    Due to the limitations in the number of hospital beds and intensive care units that exist in every country, we believe that this model is more realistic than those with a linear treatment response, which grows at the same rate irrespectively of the number of infected people at a given time. We have extended the results published in [2], where a similar model was studied for a general disease, but the authors there did not delve into the study of bifurcation dynamics. In the present paper, we discussed the backward and Hopf bifurcation of model (1) to help government and policy makers decide an efficient response plan to combat a second wave of the COVID-19 pandemic, which has been widely reported in places like Asia and Europe. Epidemiologically, we understand the role of reproduction number in controlling disease, but there are times that R0 < 1 does not represent the eradication of the disease and at that critical phase a reemergence can occur which may be more endemic than the first. Our analysis showed that model (1) presents the phenomenon of backward bifurcation for certain values of the parameters. When this type of bifurcation occurs, the eradication of the epidemic may not be guaranteed by simply reducing the basic reproduction number R0 below unity; instead, R0 should be further reduced to a critical value Rc < 1. We performed some numerical simulations for model (1) using a set of parameter values fitted to the reported data of the COVID-19 pandemic in Nigeria coll...

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  4. Version published to 10.1101/2020.08.28.20183723v1 on medRxiv