Hepatitis-B disease modelling of fractional order and parameter calibration using real data from the USA

Abstract

<p>In this paper, a new mathematical model of Hepatitis B is studied to investigate the transmission dynamics of the Hepatitis B virus (HBV). Many diseases can start from the womb and find us humans throughout our lives. These diseases are specific abnormal conditions that negatively affect the structure or function of all or part of an organism and do not suddenly occur in any region due to external injury. In this study, we focus on HBV, and we state the graphics, interpretations, and detailed information about the disease and the newly established mathematical model of the disease. A fractional order differential equation system with a memory effect is used to model anomalous processes and to understand the effect of past infection events on the future spread dynamics of the system. In the model, susceptible, latent, acute, carrier, and recovered populations are taken into account by considering vertical transmission, which provides information about the inter-generational course of the disease. However, the migration effect is also used in the model due to the risk of disease transmission and increased migration in recent years. The course of the disease is examined using real data from the USA. Moreover, the model's positivity and boundedness are studied, and the equilibrium points are calculated. Additionally, the stability conditions for the disease-free equilibrium (DFE) are stated. A parameter calibration technique is used to determine the most accurate parameter values in the model. Finally, we provide numerical results and their biological interpretations to estimate the future course of the disease. The paper addresses the current migration problem with the migration parameter in the model. These differences from the literature can be regarded as important novelties of the paper.</p>