A fractional-order HBV infection model with constant vaccination strategy

Abstract

Fractional calculus represents a generalization of the ordinary differentiation and integration to non-integer and complex order. Motivated by this situation, the idea of modeling HBV infection involving constant vaccination by fractional order differential equations (FODE) arises. We developed a fractional SIRC model, in which they presented a detailed analysis for the asymptotic stability of disease-free and positive fixed point. First we show the positive solution of the HBV model in fractional order. However, analytical and closed solutions of these types of fractional equations cannot generally be obtained. As a consequence, approximate and numerical techniques are explored. We use the multi-step generalized differential transform method to approximate the numerical solution. Finally we compare our numerical results with nonstandard numerical method and forth order Runge-Kutta method.