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

Abstract

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 ∈ (0, 1]. We determine the stability of fractional model equilibriums. Based on the model analysis, we obtained three equilibriums, namely, free virus equilibrium (FVE) 0 , CTL-Exhaustion Equilibrium (CEE) 1 , and control immune equilibrium (CIE) 2 . Besides, we obtained Basic Reproduction Number 0 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 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.

A fractional order model for the transmission dynamics of hepatitis B virus with two-age structure in the presence of vaccination

“…Sensitivity index allows to measure the relative change in basic reproduction number when parameter value changes. For this, we use normalized forward sensitivity index of basic reproduction number with respect to a given parameter using similar approach used (Tilahun, Makinde, & Malonza, 2017;Utoyo & Sa'adah, 2018). Definition 4.1.…”

“…Definition 4.1. (Utoyo & Sa'adah, 2018) Normalized forward sensitivity index of basic reproduction number (R 0 ) with respect to the given parameter k is defined as Y R 0 k ¼ @R o @k k R 0 : Using the above formula, we obtained the sign of the sensitivity index for each parameter in basic reproduction number, as summarized in Table 2.…”

Fractional soliton dynamics of electrical microtubule transmission line model with local M-derivative

“…The reason behind that FD activates the description of the memory and hereditary attributes inherent in numerous materials and mechanisms. So, there is an exponential need to study and use the differential of fractional-order as proposed by Rihan and Utoyo [39,40]. Some of the current examinations in biological science proposed that MT dynamics in the adult brain function is the crucial process of learning and memory and it may be agreed in degenerative maladies, such as Alzheimerʼs disease.…”

“…Some of the current examinations in biological science proposed that MT dynamics in the adult brain function is the crucial process of learning and memory and it may be agreed in degenerative maladies, such as Alzheimerʼs disease. This enhances the likelihood of targeting MT dynamics in the making of current therapeutic agents as can be noticed in [40,41]. FC is also appropriate for designing the electrical attributes of biological models.…”