Modified Model and Stability Analysis of the Spread of Hepatitis B Virus Disease
American Journal of Applied Mathematics
Volume 7, Issue 1, February 2019, Pages: 13-20
Received: Jun. 18, 2018; Accepted: Apr. 28, 2019; Published: May 29, 2019
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Birke Seyoum Desta, Department of Mathematics, Hawassa University, Hawassa, Ethiopia
Purnachandra Rao Koya, Department of Mathematics, Hawassa University, Hawassa, Ethiopia
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In this study the infected population is classified into two categories viz., chronic and acute and thus developed a five compartmental SEICIAR model. Also, both vaccination and treatments are included and studied their impact on the spread of hepatitis B virus. The present model is biologically meaningful and mathematically well posed since the solutions are proved to be positive as well as bounded. The basic reproduction number RO of the model is derived using the next generation matrix method. Further, the equilibrium points of the model are identified and mathematical analysis pertaining to their stability is conducted using Routh – Hurtiz criteria. It is shown that the disease free equilibrium point is locally and globally stable If RO<1. On the other hand, the endemic equilibrium point is proved to be stable if RO>1. Also, the numerical simulation study of the model is carried out using ode45 of MATLAB: Rung – Kutta order four. It is observed that, if the vaccination and treatment rates are increased then the infective population size decreases and evenfall to zero over time. Hence, it is concluded that the use of vaccination and treatment at the highest possible rates is essential so as to control the spread hepatitis B virus.
Hepatitis B Virus, Vaccination, Treatment, Mathematical Model, Basic Reproduction Number, Stability Analysis, Numerical Simulation
To cite this article
Birke Seyoum Desta, Purnachandra Rao Koya, Modified Model and Stability Analysis of the Spread of Hepatitis B Virus Disease, American Journal of Applied Mathematics. Vol. 7, No. 1, 2019, pp. 13-20. doi: 10.11648/j.ajam.20190701.13
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This article is an open access article distributed under the Creative Commons Attribution License ( which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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