A fractional order model for the transmission dynamics of hepatitis B virus with two-age structure in the presence of vaccination
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Date
Authors
Tilahun, Getachew Teshome
Woldegerima, Woldegebriel Assefa
Mohammed, Nesredin
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Publisher
Taylor and Francis Open
Abstract
In this study, we proposed a fractional order model of hepatitis B virus transmission dynamics with two-age structure under vaccination. A qualitative analysis of the model is performed. Basic reproduction number of the model is determined. Local stability conditions of disease-free equilibrium point are proven by using fractional Ruth-Hurwitz conditions. Global stability conditions of both disease-free and endemic equilibrium points are shown by constructing appropriate Lyapunov functions. Sensitivity analysis was done by using normalized forward sensitivity index approach. Numerical simulation is performed to investigate the effect of memory on hepatitis B disease dynamics by varying order of derivatives and to simulate the effects of vaccinating newborns immediately after birth, vaccinating children and adult vaccination. Then, we compared their effects on hepatitis B disease dynamics in the sense of control and elimination. It is observed that the number of infective individuals decreases faster and even falls to zero over a long run for the model with memory than memory-less model. Comparing results between vaccination of different ages show that increasing newborn vaccination immediately after birth has the highest effect on hepatitis B disease control.
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Keywords
Hepatitis B virus (HBV), Memory, Fractional order, Age structure, Mathematical model, Vaccination, Basic reproduction number
Sustainable Development Goals
Citation
Getachew Teshome Tilahun, Woldegebriel Assefa Woldegerima & Nesredin Mohammed (2021) A fractional order model for the transmission dynamics of hepatitis B virus with two-age structure in the presence of vaccination, Arab Journal of Basic and Applied Sciences, 28:1,87-106, DOI: 10.1080/25765299.2021.1896423.