Stability Analysis and Optimal Control of a Hepatitis B Virus Transmission Model  in the Presence of Vaccination and Treatment Strategy

Pensiri Yosyingyong; Ratchada Viriyapong

doi:10.14456/nujst.2022.17

Authors

Pensiri Yosyingyong Department of Mathematics, Faculty of Science, Naresuan University, Phitsanulok, 65000 Thailand
Ratchada Viriyapong Department of Mathematics, Faculty of Science, Naresuan University, Phitsanulok, 65000 Thailand

DOI:

https://doi.org/10.14456/nujst.2022.17

Keywords:

hepatitis B virus, HBV chronic carrier, vaccination, vertical transmission, optimal control

Abstract

In this paper, the dynamics of hepatitis B virus (HBV) infection is studied through a mathematical model. The model includes vaccination class of population, vertical transmission of newborns and treatment of both acute HBV infected individuals and chronic HBV carriers. The stability of equilibria both locally and globally is analyzed. The result shows that the basic reproduction number becomes threshold value i.e. the disease-free equilibrium is globally stable when it is less than unity, and the infection is uniformly persistent and the endemic equilibrium is globally stable when it is greater than one. Further, an optimal control model is developed to seek the strategy to minimize the transmission of HBV. There are three control variables within the model which are prevention by vaccination, treatment of acute infected and treatment of chronic HBV carriers. Our numerical results show that among three controls, treatment of acute infected individuals gives the best impact in reducing the HBV infection. However, with three controls together, they give the best strategy in reducing overall HBV infection.

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