Modeling the dynamical behavior of the interaction of T-cells and human immunodeficiency virus with saturated incidence

Abstract

In the last forty years, the rise of HIV has undoubtedly become a major concern in the field of public health, imposing significant economic burdens on affected regions. Consequently, it becomes imperative to undertake comprehensive investigations into the
mechanisms governing the dissemination of HIV within the human body. In this work, we devise a mathematical model that elucidates the intricate interplay between CD4+ Tcells and viruses of HIV, employing the principles of fractional calculus. The production
rate of CD4+ T-cells, like other immune cells depends on factors like age, health status, and the presence of infections or diseases. Therefore, we incorporate a variable source term in the dynamics of HIV infection with saturated incidence rate to enhance the precision of our findings. We introduce the fundamental concepts of fractional operators as a means of scrutinizing the proposed HIV model. To facilitate a deeper understanding of our system, we represent an iterative scheme that elucidates the trajectories of solution pathways of the system. We present the time series analysis of our model through numerical findings to conceptualize and understand the key factors of the system. In addition to this, we present the phase portrait and the oscillatory behavior of the system
with the variation of different input parameters. These information can be utilized to predict the long-term behavior of the system, including whether it will converge to a steady state or exhibit periodic or chaotic oscillations.

Generalization of Bernoulli polynomials to find optimal solution of fractional hematopoietic stem cells model

“…The modeling of complex biological and medical phenomena using fractional calculus approaches has gained significant attention in recent years. Several studies have demonstrated the effectiveness of these techniques in capturing the inherent memory effects and non-local properties of various systems [20][21][22]. Kanth and Devi [23] conducted numerical simulations based on the Adams-Bashforth approach for a fractal-fractional order autoimmune disease framework, aiming to investigate the role of viruses in autoimmune disease progression.…”