A fractional order differential equation model for Hepatitis B virus with saturated incidence

• Published in: Results in physics Vol. 24; p. 104114
• Main Authors: Simelane, S.M., Dlamini, P.G.
• Format: Journal Article
• Language: English
• Published: Elsevier B.V 01.05.2021; Elsevier
• Subjects: Adams–Bashforth-Moulton method; Caputo fractional derivative; Hepatitis B virus; Mean value theorem; Reproduction number; Routh-Hurwitz criterion; Mean value theorem; Hepatitis B virus; Routh-Hurwitz criterion; Caputo fractional derivative; Reproduction number; Adams–Bashforth-Moulton method
• ISSN: 2211-3797; 2211-3797
• DOI: 10.1016/j.rinp.2021.104114

This manuscript presents a nonlinear fractional order Hepatitis B virus (HBV) model with saturated incidence. Model governing equations are defined using Caputo fractional derivatives. We use the Adams–Bashforth-Moulton technique to compute numerical solutions of the presented epidemic model. Generally, fractional derivatives are used to model real-world phenomena that contains nonlocal effects, history and/or memory. The main objective is to develop and explore the dynamics of an HBV fractional derivative epidemic model via the Caputo definition. Firstly, we discuss the model basic properties which include positivity of solutions and the invariant regions where the solution set is bounded using the generalized fractional mean value theorem. The model dynamics are described based on the reproduction number R0. Thereafter, we use the fractional Routh-Hurwitz stability criterion as well as simple matrix algebra to determine sufficient conditions for the stability of the equilibrium points. Lastly, we present graphical representation of numerical results. The results indicate the importance of fractional order in modeling HBV transmission dynamics and ensures that by including the memory effects, the model is more appropriate and insightful for such a study.