Fractional differential equation modeling of the HBV infection with time delay and logistic proliferation

In this article, a fractional-order differential equation model of HBV infection was proposed with a Caputo derivative, delayed immune response, and logistic proliferation. Initially, infection-free and infection equilibriums and the basic reproduction number were computed. Thereafter, the stability of the two equilibriums was analyzed based on the fractional Routh–Hurwitz stability criterion, and the results indicated that the stability will change if the time delay or fractional order changes. In addition, the sensitivity of the basic reproduction number was analyzed to find out the most sensitive parameter. Lastly, the theoretical analysis was verified by numerical simulations. The results showed that the time delay of immune response and fractional order can significantly affect the dynamic behavior in the HBV infection process. Therefore, it is necessary to consider time delay and fractional order in modeling HBV infection and studying its dynamics.