David A. Oluyori
Department of Mathematics, School of Physical Science, Ahmadu Bello University, Zaria, Kaduna State, Nigeria
Angel G. C. Perez
Facultad de Matematicas, Universidad Autonoma de Yucatan, Merida, Yucatan, Mexico
Victor A. Okhuese
Department of Mathematics, Nasarawa State University, Keffi, Nigeria
Department of Eastern Medicine, Government College University, Faisalabad, Pakistan
: COVID-19, epidemic model, bifurcation, saturated treatment, stability
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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