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.

Dynamics of SARS-CoV-2 infection model with two modes of transmission and immune response.

In this paper, we propose a new within-host model which describes the interactions between SARS-CoV-2, host pulmonary epithelial cells and cytotoxic T lymphocyte (CTL) cells. Furthermore, the proposed model takes into account the lytic and nonlytic immune responses and also incorporates both modes of transmission that are the virus-to-cell infection through extracellular environment and the cell-to-cell transmission via virological synapses. The well-posedness of the model as well as the existence of equilibria are established rigorously. Moreover, the dynamical behaviour of the model is further examined by two threshold parameters, and the biological aspects of the analytical results are further presented.

Dynamics of a Class of HIV Infection Models with Cure of Infected Cells in Eclipse Stage.

In this paper, we propose two HIV infection models with specific nonlinear incidence rate by including a class of infected cells in the eclipse phase. The first model is described by ordinary differential equations (ODEs) and generalizes a set of previously existing models and their results. The second model extends our ODE model by taking into account the diffusion of virus. Furthermore, the global stability of both models is investigated by constructing suitable Lyapunov functionals. Finally, we check our theoretical results with numerical simulations.

Stability Analysis of an Improved HBV Model with CTL Immune Response.

To better understand the dynamics of the hepatitis B virus (HBV) infection, we introduce an improved HBV model with standard incidence function, cytotoxic T lymphocytes (CTL) immune response, and take into account the effect of the export of precursor CTL cells from the thymus and the role of cytolytic and noncytolytic mechanisms. The local stability of the disease-free equilibrium and the chronic infection equilibrium is obtained via characteristic equations. Furthermore, the global stability of both equilibria is established by using two techniques, the direct Lyapunov method for the disease-free equilibrium and the geometrical approach for the chronic infection equilibrium.

Modeling the adaptive immune response in HBV infection.

The aim of this work is to investigate a new mathematical model that describes the interactions between Hepatitis B virus (HBV), liver cells (hepatocytes), and the adaptive immune response. The qualitative analysis of this as cytotoxic T lymphocytes (CTL) cells and the antibodies. These outcomes are (1) a disease free steady state, which its local stability is characterized as usual by R (0) < 1, (2) and the existence of four endemic steady states when R (0) > 1. The local stability of these steady states depends on functions of R (0). Our study shows that although we give conditions of stability of these steady states, not all conditions are feasible. This rules out the local stability of two steady states. The conditions of stability of the two other steady states (which represent the complete failure of the adaptive immunity and the persistence of the disease) are formulated based on the domination of CTL cells response or the antibody response.