HTLV/HIV Dual Infection: Modeling and Analysis

Transmission dynamics of a novel HIV/AIDS model through a higher-order Galerkin time discretization scheme

There are numerous contagious diseases caused by pathogenic microorganisms, including bacteria, viruses, fungi, and parasites, that have the propensity to culminate in fatal consequences. A communicable disease is an illness caused by a contagion agent or its toxins and spread directly or indirectly to a susceptible animal or human host by an infected person, animal, vector, or immaterial environment. Human immunodeficiency virus (HIV) infection, hepatitis A, B, and C, and measles are all examples of communicable diseases. Acquired immunodeficiency syndrome (AIDS) is a communicable disease caused by HIV infection that has become the most severe issue facing humanity. The research work in this paper is to numerically explore a mathematical model and demonstrate the dynamics of HIV/AIDS disease transmission using a continuous Galerkin-Petrov time discretization of a higher-order scheme, specifically the cGP(2)-scheme. Depict a graphical and tabular comparison between the outcomes of the mentioned scheme and those obtained through other classical schemes that exist in the literature. Further, a comparison is performed relative to the well-known fourth-order Ruge-Kutta (RK4) method with different step sizes. By contrast, the suggested approach provided more accurate results with a larger step size than RK4 with a smaller step size. After validation and confirmation of the suggested scheme and code, we implement the method to the extended model by introducing a treatment rate and show the impact of various non-linear source terms for the generation of new cells. We also determined the basic reproduction number and use the Routh-Hurwitz criterion to assess the stability of disease-free and unique endemic equilibrium states of the HIV model.

Analysis of an HTLV/HIV dual infection model with diffusion

In the literature, several HTLV-I and HIV single infections models with spatial dependence have been developed and analyzed. However, modeling HTLV/HIV dual infection with diffusion has not been studied. In this work we derive and investigate a PDE model that describes the dynamics of HTLV/HIV dual infection taking into account the mobility of viruses and cells. The model includes the effect of Cytotoxic T lymphocytes (CTLs) immunity. Although HTLV-I and HIV primarily target the same host, CD4⁺T cells, via infected-to-cell (ITC) contact, however the HIV can also be transmitted through free-to-cell (FTC) contact. Moreover, HTLV-I has a vertical transmission through mitosis of active HTLV-infected cells. The well-posedness of solutions, including the existence of global solutions and the boundedness, is justified. We derive eight threshold parameters which govern the existence and stability of the eight steady states of the model. We study the global stability of all steady states based on the construction of suitable Lyapunov functions and usage of Lyapunov-LaSalle asymptotic stability theorem. Lastly, numerical simulations are carried out in order to verify the validity of our theoretical results.