Analysis of Fractional Order Mathematical Model of Hematopoietic Stem Cell Gene-Based Therapy

• Main Authors: Mohammad Imam Utoyo, Windarto, Aminatus Sa’adah
• Format: Article
• Language: English
• Published: Hindawi Limited 2018-01-01
• Series: International Journal of Mathematics and Mathematical Sciences
• Online Access: http://dx.doi.org/10.1155/2018/6180892
• ISSN: 0161-1712; 1687-0425

Hematopoietic stem cell (HSC) has been discussed as a basis for gene-based therapy aiming to cure immune system infections, such as HIV. This therapy protects target cells from infections or specifying technic and immune responses to face virus by using genetically modified HSCs. A mathematical model approach could be used to predict the dynamics of HSC gene-based therapy of viral infections. In this paper, we present a fractional mathematical model of HSC gene-based therapy with the fractional order derivative α∈0,1. We determine the stability of fractional model equilibriums. Based on the model analysis, we obtained three equilibriums, namely, free virus equilibrium (FVE) E0, CTL-Exhaustion Equilibrium (CEE) E1, and control immune equilibrium (CIE) E2. Besides, we obtained Basic Reproduction Number R0 that determines the existence and stability of the equilibriums. These three equilibriums will be conditionally locally asymptotically stable. We also analyze the sensitivity of parameters to determine the most influence parameter to the spread of therapy. Furthermore, we perform numerical simulations with variations of α to illustrate the dynamical HSC gene-based therapy to virus-system immune interactions. Based on the numerical simulations, we obtained that HSC gene-based therapy can decrease the concentration of infected cells and increase the concentration of the immune cells.