Hopf Bifurcation and Stability of Periodic Solutions for Delay Differential Model of HIV Infection of CD4 +

This paper deals with stability and Hopf bifurcation analyses of a mathematical model of HIV infection of CD4+ T-cells. The model is based on a system of delay differential equations with logistic growth term and antiretroviral treatment with a discrete time delay, which plays a main role in changing the stability of each steady state. By fixing the time delay as a bifurcation parameter, we get a limit cycle bifurcation about the infected steady state. We study the effect of the time delay on the stability of the endemically infected equilibrium. We derive explicit formulae to determine the stability and direction of the limit cycles by using center manifold theory and normal form method. Numerical simulations are presented to illustrate the results

A systems biology approach- quantification and molecular insights into influenza-A virus infection

Influenza A virus (IAV) circulating worldwide are highly contagious and can cause acute to severe respiratory disease. Annually, around 500 million individuals are infected by influenza, which causes about 500,000 deaths worldwide, including 5000-8000 deaths in Germany. In addition to,yearly epidemics, several pandemics are reported globally, recently in 2009 (influenza A/H1N1/pdm2009) which resulted in around 50 millions of deaths globally. The biological basis for the increased severity of some IAVs remains unclear. Unpredicted mutation which leads to intra-host evolution of quasi-species, and strong inflammation are important hallmarks of severe pandemic IAV infection. Understanding the differences in the pathogenicity of virus strains is an important aspect of influenza kinetic. Modeling influenza kinetics plays an integral role to understand the differences and potential mechanisms of a virulent strain compared to a less pathogenic one. Furthermore, investigating the molecular mechanisms of severe pandemic IAV (pdmIAV) is of great importance in controlling the complications and reducing the pulmonary damage. Comprehensive genome wide expression data involving both innate and adaptive immune response helps to understand molecular mechanisms of host response during severe influenza infection