Stability analysis for HIV infection delay model with protease inhibitor

A delayed HIV infection model with apoptosis and viral loss

In this paper, a delayed human immunodeficiency virus (HIV) model with apoptosis of cells has been studied. Both immunological and intracellular delay have been incorporated to make the model more relevant. Firstly, the model has been investigated using local stability analysis. Next, the global stability analysis of steady states has been performed. The stability switch criteria taking the delay as the bifurcating parameter, leading to Hopf bifurcation has been studied. The transition of the system from order to chaos has been explored, and the analytical results have been verified by numerical simulations. The results thus can be used to describe the extensive dynamics exhibited by the model introduced in this article. The effects of apoptosis on viral load has been studied in the model numerically.

An analysis of the delay-dependent HIV-1 protease inhibitor model

In this paper, we have studied about the sensitivity analysis of the human immunodeficiency virus (HIV) protease inhibitor (PI) model and estimated the length of the delay. We have fabricated an HIV PI model accompanied with humoral immunity. Stability analysis of the constructed model about its steady states has been deliberated. We have evaluated some numerical simulations for PI model with humoral immunity by using the existing patient data.

Within-host influenza dynamics: a small-scale mathematical modeling approach

The emergence of new influenza viruses like the pandemic H1N1 influenza A virus in 2009 (A(H1N1)pdm09) with unpredictable difficulties in vaccine coverage and established antiviral treatment protocols emphasizes the need of new murine models to prove the activity of novel antiviral compounds in vivo. The aim of the present study was to develop a small-scale mathematical model based on easily attainable experimental data to explain differences in influenza kinetics induced by different virus strains in mice. To develop a three-dimensional ordinary differential equation model of influenza dynamics, the following variables were included: (i) viral pathogenicity (P), (ii) antiviral immune defense (D), and (iii) inflammation due to pro-inflammatory response (I). Influenza virus-induced symptoms (clinical score S) in mice provided the basis for calculations of P and I. Both, mono- and biphasic course of mild to severe influenza induced by three clinical A(H1N1)pdm09 strains and one European swine H1N2 virus were comparatively and quantitatively studied by fitting the mathematical model to the experimental data. The model hypothesizes reasons for mild and severe influenza with mono- as well as biphasic course of disease. According to modeling results, the second peak of the biphasic course of infection is caused by inflammation. The parameters (i) maximum primary pathogenicity, (ii) viral infection rate, and (iii) rate of activation of the immune system represent most important parameters that quantitatively characterize the different pattern of virus-specific influenza kinetics.