Study of HIV model via recent improved fractional differential and integral operators

A novel HIV model through fractional enlarged integral and differential operators

This article presents a novel mathematical fractional model to examine the transmission of HIV. The new HIV model is built using recently fractional enlarged differential and integral operators. The existence and uniqueness findings for the suggested fractional HIV model are investigated using Leray-Schauder nonlinear alternative (LSNA) and Banach's fixed point (BFP) theorems. Furthermore, multiple types of Ulam stability (U-S) are created for the fractional model of HIV. It is straightforward to identify that the gained findings may be decreased to many results obtained in former works of literature.

Analysis of the Fractional HIV Model under Proportional Hadamard-Caputo Operators

Modeling human immunodeficiency virus (HIV) via fractional operators has several benefits over the classical integer-order HIV model. The reason is that the fractional HIV model relies not only on the recent status but also on the former conduct of the model. Thus, we are motivated to introduce and analyze a new fractional HIV model. This article focuses on a novel fractional HIV model under the proportional Hadamard-Caputo fractional operators. The study of this model involves the existence and uniqueness (EU) of its solution and the stability examination. We employ Leray–Schauder nonlinear alternative (L-SNLA) and Banach’s fixed point theorems to analyze the EU results. In addition, for this provided model, we develop several forms of Ulam’s stability findings. As a special case of our results, we give and analyze a new fractional HIV model with Hadamard-Caputo operators. Moreover, by appropriate choice of the fractional parameters, the obtained outcomes are valid for analysis of the fractional HIV models formed by several fractional operators defined in the past literature.

Mathematical Modeling and Analysis of the Dynamics of RNA Viruses in Presence of Immunity and Treatment: A Case Study of SARS-CoV-2

The emergence of novel RNA viruses like SARS-CoV-2 poses a greater threat to human health. Thus, the main objective of this article is to develop a new mathematical model with a view to better understand the evolutionary behavior of such viruses inside the human body and to determine control strategies to deal with this type of threat. The developed model takes into account two modes of transmission and both classes of infected cells that are latently infected cells and actively infected cells that produce virus particles. The cure of infected cells in latent period as well as the lytic and non-lytic immune response are considered into the model. We first show that the developed model is well-posed from the biological point of view by proving the non-negativity and boundedness of model's solutions. Our analytical results show that the dynamical behavior of the model is fully determined by two threshold parameters one for viral infection and the other for humoral immunity. The effect of antiviral treatment is also investigated. Furthermore, numerical simulations are presented in order to illustrate our analytical results.