10 research outputs found
On fractional order models for Hepatitis C
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
Fractional Zaslavsky and Henon Discrete Maps
This paper is devoted to the memory of Professor George M. Zaslavsky passed
away on November 25, 2008. In the field of discrete maps, George M. Zaslavsky
introduced a dissipative standard map which is called now the Zaslavsky map. G.
Zaslavsky initialized many fundamental concepts and ideas in the fractional
dynamics and kinetics. In this paper, starting from kicked damped equations
with derivatives of non-integer orders we derive a fractional generalization of
discrete maps. These fractional maps are generalizations of the Zaslavsky map
and the Henon map. The main property of the fractional differential equations
and the correspondent fractional maps is a long-term memory and dissipation.
The memory is realized by the fact that their present state evolution depends
on all past states with special forms of weights.Comment: 26 pages, LaTe
On modeling two immune effectors two strain antigen interaction
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