STABILITY AND BIFURCATION ANALYSIS OF A FRACTIONAL-ORDER DELAY DIFFERENTIAL MODEL FOR HEPATITIS B EPIDEMICS

Hepatitis B virus (HBV) infection is contagious and can cause chronic liver disease, and there is often a delay between the time of infection and the onset of symptoms. To represent the dynamics of HBV transmission accurately, a fractional-order delay epidemiological model is presented in this study. Incubation time for hepatitis B is usually about 90–180 days but can vary according to an individuals health. Assuming the incubation period of HBV transmission is a time delay, we develop a fractional-order delay epidemiological model to improve the prediction accuracy of the model. To demonstrate that the model is well-posed and biologically feasible, we discuss the existence analysis, positivity, and boundedness of the solution. Furthermore, we assess the sensitivity of the proposed model to reproductive numbers and investigate sufficient conditions for local dynamics. A bifurcation analysis of the model is also discussed in detail and it is shown that the model exhibits backward bifurcation without delay but undergoes Hopf bifurcation when there is delay. The effect of delay and fractional order on hepatitis B transmission dynamics is also discussed. Lastly, we provided a detailed numerical analysis of the model using the Adams-Bashforth numerical procedure to validate the theoretical results.