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Abstract: It has been known for some time that human autoimmune diseases can be triggered by viral infections. Several possible mechanisms of interactions between a virus and immune system have been analysed, with a prevailing opinion being that the onset of autoimmunity can in many cases be attributed to “molecular mimicry”, where linear peptide epitopes, processed from viral proteins, mimic normal host self-proteins, thus leading to a cross-reaction of immune response against virus with host cells. In this paper we present a mathematical model for the dynamics of an immune response to a viral infection and autoimmunity, which takes into account T cells with different activation thresholds. We show how the infection can be cleared by the immune system, as well as how it can lead to a chronic infection or recurrent infection with relapses and remissions. Numerical simulations of the model are performed to illustrate various dynamical regimes, as well as to analyse the potential impact of treatment of autoimmune disease in the chronic and recurrent states. The results provide good qualitative agreement with available data on immune responses to viral infections and progression of autoimmune diseases. [Copyright &y& Elsevier]

Fratricide between CD8+ T lymphocytes is known to occur in HTLV-I and possibly HSV-1 and HIV-1 infection. However it is not known what effect, if any, T-cell fratricide has on the course of infection. Here we present simple mathematical techniques to investigate T-cell fratricide with particular reference to HTLV-I infection. Using a general model we predict the qualitative and quantitative effect of fratricide on HTLV-I equilibrium proviral load. We also investigate the effect of fratricide on the probability of viral clearance.We show that, surprisingly, fratricide can lead either to an increase or a decrease in equilibrium proviral load. We derive the conditions necessary for fratricide to cause a decrease in load and deduce that, for the five HTLV-I-positive patients considered here, fratricide has probably caused an increase in equilibrium load. We also estimate the percentage increase in load that is attributable to fratricide and determine the parameters that should be measured in order to improve this estimate. Finally, we show that fratricide reduces the probability of viral clearance.Mathematical modelling of HTLV-I infection, as is often the case in biology, is severely hampered by a lack of experimental data. Consequently it is difficult to know what functional form a model should take. The behaviour of complex nonlinear systems is highly model-dependent. Predictions based on theoretical models are therefore sensitive to the choice of model; this is a very severe problem that undermines and limits the success of the application of mathematics to immunology. In this paper we reduce the model dependency of the results in two ways—by considering (analytically) a general model with a minimal number of assumptions and, where this is not possible, by checking (numerically) that a wide range of models yield the same results. We therefore begin to develop two practical methods for dealing with the problem of robustness in mathematical models of the immune system. [Copyright &y& Elsevier]

• The first model to include details of the geometry of the multiple sclerosis plaque. • The model explains the role of pro/anti-inflammatory cells and cytokines in the plaque. • The effects of commonly used and experimental drugs are simulated in the model. • The model should be useful as a primary outcome measure of phase II trial. Multiple sclerosis is an autoimmune disease that affects white matter in the central nervous system. It is one of the primary causes of neurological disability among young people. Its characteristic pathological lesion is called a plaque, a zone of inflammatory activity and tissue destruction that expands radially outward by destroying the myelin and oligodendrocytes of white matter. The present paper develops a mathematical model of the multiple sclerosis plaques. Although these plaques do not provide reliable information of the clinical disability in MS, they are nevertheless useful as a primary outcome measure of Phase II trials. The model consists of a system of partial differential equations in a simplified geometry of the lesion, consisting of three domains: perivascular space, demyelinated plaque, and white matter. The model describes the activity of various pro- and anti-inflammatory cells and cytokines in the plaque, and quantifies their effect on plaque growth. We show that volume growth of plaques are in qualitative agreement with reported clinical studies of several currently used drugs. We then use the model to explore treatments with combinations of such drugs, and with experimental drugs. We finally consider the benefits of early vs. delayed treatment. [ABSTRACT FROM AUTHOR]