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 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.
Highlights
An immune system is body’s primary defense system that has a function to fight against microbes
Adaptive immunity consists of B lymphocytes cells (B cells) and T lymphocytes cells (T cells)
Ordinary differential equation (ODE) system that consists of first-order differential equations can be generalized to fractional differential equation (FDE) system that consists of fractional order differential equations α, with a fractional order parameter 0 < α ≤ 1 [6]
Summary
An immune system is body’s primary defense system that has a function to fight against microbes. Adaptive immunity has some capabilities such as specificity, diversity, and memory, so it can eradicate microbes effectively [1]. There are several viruses that can escape from innate immunity and infect CD4+ T cells. Based on the experiment, engineered HSCs have the ability to establish functional antivirus responses that suppressed HIV replication. It will allow suppression of infected CD4+ T cells and prevent suppression of uninfected CD4+ T cells [3]. International Journal of Mathematics and Mathematical Sciences virus-immune system interactions after a single injection of CD8+ T cells derived from HSCs. Ordinary differential equation (ODE) system that consists of first-order differential equations can be generalized to fractional differential equation (FDE) system that consists of fractional order differential equations α, with a fractional order parameter 0 < α ≤ 1 [6]. We perform numerical simulation to support the mathematical model interpretation
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