Fuzzy fractional derivative model to assess the dynamics of hepatitis B infection

Abstract

Hepatitis B virus infection shall remain a public health concern in many developed and developing countries. In this paper, we formulate and analyse a simple fuzzy fractional model of HBV infection to assess the dynamics of the disease using fractional-order differential equations. To analyse the effect of the initial transmission of the disease, we computed the basic reproduction number R 0 , and used it to perform stability analysis. The results show that the disease-free and the endemic equilibrium are globally stable with respect to the value of R 0 . Numerical simulations were performed to study the variations of each sub-population with respect to time at different order (α). In general, results for the fractional model show that as the order (α) increases, the population of the susceptible and exposed individuals decreases. In contrast, the other sub-populations increase with an increase in α. Further results from the numerical analysis show that increase in α, decreases the diameter of the fuzzy triangular solutions for the susceptible and exposed individuals in the fuzzy fractional model.