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

Flow cytometric analysis using intracellular dyes such as CFSE is a powerful experimentaltool which can be used in conjunction with mathematical modeling to quantify the dynamicbehavior of a population of lymphocytes. In this survey we begin by providing an overviewof the mathematically relevant aspects of the data collection procedure. We then presentan overview of the large body of mathematical models, along with their assumptions anduses, 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 (cellsper generation) of the proliferating population, several recent models have considered themore fundamental task of modeling CFSE histogram data directly. Such models are analyzedand recent results are discussed. Finally, directions for future research aresuggested.

The measurement of CFSE dilution by flow cytometry is a powerful experimental tool tomeasure lymphocyte proliferation. CFSE fluorescence precisely halves after each celldivision in a highly predictable manner and is thus highly amenable to mathematicalmodelling. However, there are several biological and experimental conditions that canaffect the quality of the proliferation data generated, which may be important to considerwhen modelling dye dilution data sets. Here we overview several of these variablesincluding the type of fluorescent dye used to monitor cell division, dye labellingmethodology, 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 wediscuss is organized in accordance with modeling goals and stresses control and transportissues. We also address basic modeling approaches and discuss some of the challenges formathematical modeling methodologies in the context of parameter estimation and modelvalidation.

HIV infection is multi-faceted and a multi-step process. The virus-induced pathogenicmechanisms are manifold and mediated through a range of positive and negative feedbackregulations of immune and physiological processes engaged in virus-host interactions. Thefundamental questions towards understanding the pathogenesis of HIV infection are nowshifting to ‘dynamic’ categories: (i) why is the HIV-immune response equilibrium finallydisrupted? (ii) can one modify the dynamic equilibrium for host benefit? (iii) can onepredict the outcome of a system perturbation via antiviral drugs or drugs modulating thehost immune response dynamics? Answering these questions requires a majorinterdisciplinary effort, and in particular, the development of novel mathematicalapproaches for a coherent quantitative description and prediction of intra-patient HIVevolution, the immunological responses to HIV infection, and the systems level homeostaticregulation of specific effector and regulatory lymphocyte populations in correlation withdisease status. Here we summarized fundamental biological features of HIV infection andcurrent mathematical modelling attempts to understand HIV pathogenesis.

RNA viruses replicate as complex and dynamic mutant distributions. They are termed viralquasispecies, in recognition of the fundamental contribution of quasispecies theory in ourunderstanding of error-prone replicative entities. Viral quasispecies have launched afertile field of transdiciplinary research, both experimental and theoretical. Here wereview the origin and some implications of the quasispecies concept, with emphasis oninternal interactions among components of the same mutant virus ensemble, a critical factto design new antiviral strategies. We make the distinction between “intrinsic” and“extrinsic” properties of mutant distributions, and emphasize that there are severallevels 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 andsiRNA library screening of complete cellular gene sets, a large range of host cell factorshave been discovered that either support or restrict virus growth. Here we summarize someof the recent findings and focus our discussion on the hepatitis C virus and the humanimmunodeficiency virus, two major pathogens that threat global health. The identificationof cellular proteins affecting multiple viruses points to the existence of centralregulation nodes that might be exploited for both, a quantitative description ofhost-virus interactions within single infected cells and the development of novel,broad-spectrum antiviral drugs.