Global stability of discrete virus dynamics models with humoural immunity and latency

An ODEs multiscale model with cell proliferation for hepatitis C virus infection treated with direct acting antiviral agents

In a recent study, a mathematically identical ODE model is derived from a multiscale PDE model of hepatitis C virus infection, which helps to overcome the limitations of the PDE model in the analysis. Here, an extended proposed model is formulated for this transformed ODE model by including the hepatocyte proliferation of both uninfected and infected cells. Unlike the transformed model, the proposed model can predict the triphasic viral decline and the virus level after therapy cessation without oscillations. Numerical simulations are performed to investigate the effect of hepatocyte proliferation and therapy with direct-acting antivirals agents (DAAs). The basic reproduction number is obtained, the equilibrium points are specified, and their stability is analysed. A bifurcation analysis is performed to specify the bifurcation points and to study the effect of varying system parameters. Various viral load profiles generated by the model are confirmed to fit with reported data in the literature.

Stability of a discrete HTLV-1/SARS-CoV-2 dual infection model

Dual infection with a virus that targets the immune system, such as HTLV-1 (human T-cell lymphotropic virus class 1), combined with another virus that affects the respiratory system, such as SARS-CoV-2 (severe acute respiratory syndrome coronavirus 2), can cause serious disease and even death. Given the significance of better comprehending the dual viral infections' dynamics, researchers have been drawn to mathematical analyses of such models. This work investigates the stability of a discrete HTLV-1/SARS-CoV-2 dual infection model. Our approach involves formulating the discrete model through the discretization of the continuous-time one using NSFD (nonstandard finite difference) method. We demonstrate that the NSFD method preserves essential properties of the solutions, such as positivity and boundedness. Additionally, we determine the fixed points and establish the conditions under which they exist. Furthermore, we analyze the global stability of these fixed points utilizing the Lyapunov technique. To illustrate our analytical findings, we do numerical simulations.

A dynamically-consistent nonstandard finite difference scheme for the SICA model

In this work, we derive a nonstandard finite difference scheme for the SICA (Susceptible-Infected-Chronic-AIDS) model and analyze the dynamical properties of the discretized system. We prove that the discretized model is dynamically consistent with the continuous, maintaining the essential properties of the standard SICA model, namely, the positivity and boundedness of the solutions, equilibrium points, and their local and global stability.