We present a Caputo fractional order mathematical model that describes the cellular infection of the Hepatitis B virus and the immune response of the body with Holling type II functional response. We study the existence of unique positive solutions and the local and global stability of virus-free and endemic equilibria. Finally, we present numerical results using the Adam-type predictor–corrector iterative scheme.

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The techniques and methods that help to obtain necessary and sufficient conditions to determine the local stability of linearized systems are paramount. In this paper, a corollary of the Gershgorin’s circle theorem was used to establish the local stability of different epidemic models with three or more states including, a Tuberculosis model, an SEIRS model, vector-host model and a-Staged HIV/AIDS Model. It was observed that no matter the state or the dimension of the system or matrix, this corollary can be used to analyse the local stability for both disease-free and endemic equilibria, by establishing that when R0 < 1, the Jacobian matrix evaluated at the disease free equilibrium will have negative eigenvalues or negative real part eigenvalues. Thus, the disease-free equilibrium is stable but when R0 > 1, the Jacobian matrix evaluated at the endemic equilibrium will have negative eigenvalues or negative real part eigenvalues making the endemic equilibrium is stable.

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We present a Caputo fractional order mathematical model that describes the cellular infection of Hepatitis B virus and the immune response of the body. We study the existence of unique positive solutions, and the local and global stability of the virus free and endemic equilibria. Finally, we present numerical results using the Adam-type predictor-corrector iterative scheme.