In this review paper we consider physiologically structured population models that have been widely studied and employed in the literature to model the dynamics of a wide variety of populations. However in a number of cases these have been found inadequate to describe some phenomena arising in certain real-world applications such as dispersion in the structure variables due to growth uncertainty/variability. Prompted by this, we described two recent approaches that have been investigated in the literature to describe this growth uncertainty/variability in a physiologically structured population. One involves formulating growth as a Markov diffusion process while the other entails imposing a probabilistic structure on the set of possible growth rates across the entire population. Both approaches lead to physiologically structured population models with nontrivial dispersion. Even though these two approaches are conceptually quite different, they were found in [17] to have a close relationship: in some cases with properly chosen parameters and coefficient functions, the resulting stochastic processes have the same probability density function at each time.

Flow cytometric analysis using intracellular dyes such as CFSE is a powerful experimental tool which can be used in conjunction with mathematical modeling to quantify the dynamic behavior of a population of lymphocytes. In this survey we begin by providing an overview of the mathematically relevant aspects of the data collection procedure. We then present an overview of the large body of mathematical models, along with their assumptions and uses, which have been proposed to describe the dynamics of proliferating cell populations. While much of this body of work has been aimed at modeling the generation structure (cells per generation) of the proliferating population, several recent models have considered the more fundamental task of modeling CFSE histogram data directly. Such models are analyzed and recent results are discussed. Finally, directions for future research are suggested.

The measurement of CFSE dilution by flow cytometry is a powerful experimental tool to measure lymphocyte proliferation. CFSE fluorescence precisely halves after each cell division in a highly predictable manner and is thus highly amenable to mathematical modelling. However, there are several biological and experimental conditions that can affect the quality of the proliferation data generated, which may be important to consider when modelling dye dilution data sets. Here we overview several of these variables including the type of fluorescent dye used to monitor cell division, dye labelling methodology, lymphocyte subset differences, in vitro versus in vivo experimental assays, cell autofluorescence, and dye transfer between cells.

In this paper we give a survey on modeling efforts concerning the CVRS. The material we discuss is organized in accordance with modeling goals and stresses control and transport issues. We also address basic modeling approaches and discuss some of the challenges for mathematical modeling methodologies in the context of parameter estimation and model validation.

HIV infection is multi-faceted and a multi-step process. The virus-induced pathogenic mechanisms are manifold and mediated through a range of positive and negative feedback regulations of immune and physiological processes engaged in virus-host interactions. The fundamental questions towards understanding the pathogenesis of HIV infection are now shifting to ‘dynamic’ categories: (i) why is the HIV-immune response equilibrium finally disrupted? (ii) can one modify the dynamic equilibrium for host benefit? (iii) can one predict the outcome of a system perturbation via antiviral drugs or drugs modulating the host immune response dynamics? Answering these questions requires a major interdisciplinary effort, and in particular, the development of novel mathematical approaches for a coherent quantitative description and prediction of intra-patient HIV evolution, the immunological responses to HIV infection, and the systems level homeostatic regulation of specific effector and regulatory lymphocyte populations in correlation with disease status. Here we summarized fundamental biological features of HIV infection and current mathematical modelling attempts to understand HIV pathogenesis.

RNA viruses replicate as complex and dynamic mutant distributions. They are termed viral quasispecies, in recognition of the fundamental contribution of quasispecies theory in our understanding of error-prone replicative entities. Viral quasispecies have launched a fertile field of transdiciplinary research, both experimental and theoretical. Here we review the origin and some implications of the quasispecies concept, with emphasis on internal interactions among components of the same mutant virus ensemble, a critical fact to design new antiviral strategies. We make the distinction between “intrinsic” and “extrinsic” properties of mutant distributions, and emphasize that there are several levels of complexity that can influence viral quasispecies behavior.

Viruses are obligate intracellular parasites that rely on the host cell for expansion. With the development of global analyses techniques like transcriptomics, proteomics and siRNA library screening of complete cellular gene sets, a large range of host cell factors have been discovered that either support or restrict virus growth. Here we summarize some of the recent findings and focus our discussion on the hepatitis C virus and the human immunodeficiency virus, two major pathogens that threat global health. The identification of cellular proteins affecting multiple viruses points to the existence of central regulation nodes that might be exploited for both, a quantitative description of host-virus interactions within single infected cells and the development of novel, broad-spectrum antiviral drugs.