In this paper we present a fractional order generalization of Perelson et al. basic hepatitis C virus (HCV) model including an immune response term. We argue that fractional order equations are more suitable than integer order ones in modeling complex systems which include biological systems. The model is presented and discussed. Also we argue that the added immune response term represents some basic properties of the immune system and that it should be included to study longer term behavior of the disease.

Zika is a fast spreading epidemic. So far it is known to have two transmission routes one via mosquito and the other is via sexual contact. It is dangerous on pregnant women otherwise it is mild

It is argued that by studying some design principles of the immune system, e.g. nonlinearity and being a complex adaptive system, one can easily find some explanations of basic properties of the system e.g. memory and tolerance.

In this paper we consider the fractional order model with two immune effectors interacting with two strain antigen. The systems may explain the recurrence of some diseases e.g. tuberculosis (TB). The stability of equilibrium points are studied. Numerical solutions of this model are given. Using integer order system the system oscillates. Using fractional order system the system converges to a stable internal equilibrium. Ulam-Hyers stability of the system has been studied.