Modeling and control of hepatitis B virus transmission dynamics using fractional order differential equations

Abstract

Hepatitis B virus (HBV) continues to pose a significant global health burden, necessitating the development of accurate and effective mathematical models to understand its transmission dynamics and devise optimal control strategies. In this research paper, we present a fractional order model for Hepatitis B virus transmission, incorporating the complexities of memory effects and non-local interactions in disease spread. The proposed fractional order model is formulated as a system of differential equations, with distinct compartments. We employ fractional order derivatives to capture the long-term memory and non-local interactions inherent in HBV transmission, offering a more realistic representation of the epidemic dynamics. To assess the stability and control potential of the model, we conduct rigorous mathematical analysis. The basic reproduction number is computed using the next generation matrix approach to determine the disease’s potential for spreading in the population. Critical points of the model are identified, and disease-free equilibrium points are obtained to assess their stability conditions. Furthermore, we derive endemic equilibrium points for the model, and their stability is analyzed using Jacobian transformation.To optimize control measures, sensitivity analysis of the model parameters is performed to identify influential factors affecting disease transmission. Numerical simulations of the fractional order model are implemented using the Adams-type Predictor-Corrector method, and the results demonstrate the effectiveness of the proposed control strategies in curbing the spread of HBV.