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Saul C. Mpeshe, Fuzzy fractional derivative model to assess the dynamics of hepatitis B infection, Eur. J. Math. Appl. 3 (2023), Article ID 17.

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Volume 3 (2023), Article ID 17

https://doi.org/10.28919/ejma.2023.3.17

Published: 04/09/2023

Abstract:

Hepatitis B virus infection shall remain a public health concern in many developed and developing countries. In this paper, we formulate and analyse a simple fuzzy fractional model of HBV infection to assess the dynamics of the disease using fractional-order differential equations. To analyse the effect of the initial transmission of the disease, we computed the basic reproduction number ${\mathcal R}_0$, and used it to perform stability analysis. The results show that the disease-free and the endemic equilibrium are globally stable with respect to the value of ${\mathcal R}_0$. Numerical simulations were performed to study the variations of each sub-population with respect to time at different order $(\alpha)$. In general, results for the fractional model show that as the order $(\alpha)$ increases, the population of the susceptible and exposed individuals decreases. In contrast, the other sub-populations increase with an increase in $\alpha$. Further results from the numerical analysis show that increase in $\alpha$, decreases the diameter of the fuzzy triangular solutions for the susceptible and exposed individuals in the fuzzy fractional model.

How to Cite:

Saul C. Mpeshe, Fuzzy fractional derivative model to assess the dynamics of hepatitis B infection, Eur. J. Math. Appl. 3 (2023), Article ID 17. https://doi.org/10.28919/ejma.2023.3.17