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Developing physiologically meaningful mathematical models that describe multilevel regulation in a complex network of immune processes, in particular, of the system of interferon-regulated virus production processes, is a fundamental scientific problem, within the framework of an interdisciplinary systems approach to research in immunology. Here, we have presented a detailed high-dimensional model describing HIV (human immunodeficiency virus) replication, the response of type I interferon (IFN) to the virus infection of the cell, and suppression of the action of IFN-induced proteins by HIV accessory proteins. As a result, this model includes interactions of all three processes for the first time. The mathematical model is a system of 37 nonlinear ordinary differential equations including 78 parameters. Importantly, the model describes not only the processes of the IFN response of the cell to virus infection, but also the mechanisms used by the virus to prevent effects of the IFN system.

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Subarachnoid hemorrhages due to rupture of cerebral aneurysms have a high risk of disability and mortality. Screening of the population to detect aneurysms in patients with risk factors is currently not carried out in Russia. However, the detection of clinically silent aneurysms and their subsequent prophylactic surgical treatment are justified, according to numerous studies. BACKGROUND: Demonstrate the clinical and economic feasibility of screening the population (including first-line relatives) for cerebral aneurysms using an economic and mathematical model of the RF virtual population. MATERIAL AND METHODS: Mathematical modeling was carried out using an algorithm that implements a discrete Markov chain. The virtual population consisted of 145 million people (the population of the Russian Federation). Magnetic resonance angiography 3DTOF was chosen as a screening method. Virtual patients underwent preventive surgical treatment in case of detection of aneurysm during screening. The number of aneurysms in the population, the number of aneurysmal subarachnoid hemorrhage (aSAH), the cost and outcomes of treatment, and the risk of disability were calculated. RESULTS: In the case of screening and preventive surgical treatment of aneurysms, there is a decrease in the number of aSAH by 14.3% (37.5% in first-line relatives (RPLR), which affects the reduction in mortality due to aSAH by 14.4% (24.1% in The total number of disabled people is reduced by 1.5% (5.1% for the RPHR). A shift in the structure of disability towards greater labor and social adaptation of patients was noted. An economic analysis for the entire population showed that screening saves 7.7 billion annually rubles, including in the population consisting of RPLR - 4.9 billion rubles. CONCLUSION: The created mathematical model of the virtual population demonstrated that screening and prophylactic treatment of cerebral aneurysms makes it possible to reduce the number of aSAH and associated mortality among the entire population and in the RPLR group. The number of individuals with severe disabilities is decreasing. Thus, population screening for the detection of cerebral aneurysms may be clinically effective and cost-effective in the general population, especially in RPCR.

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The infectious disease caused by human immunodeficiency virus type 1 (HIV-1) remains a serious threat to hu- man health. The current approach to HIV-1 treatment is based on the use of highly active antiretroviral therapy, which has side effects and is costly. For clinical practice, it is highly important to create functional cures that can enhance immune control of viral growth and infection of target cells with a subsequent reduction in viral load and restoration of the immune status. HIV-1 control efforts with reliance on immunotherapy remain at a conceptual stage due to the complexity of a set of processes that regulate the dynamics of infection and immune response. For this reason, it is extremely important to use methods of mathematical modeling of HIV-1 infection dynamics for theoretical analysis of possibilities of reducing the viral load by affecting the immune system without the usage of antiviral therapy. The aim of our study is to examine the existence of bi-, multistability and hysteresis properties with a meaningful mathematical model of HIV-1 infection. The model describes the most important blocks of the processes of interaction between viruses and the human body, namely, the spread of infection in productively and latently infected cells, the appearance of viral mutants and the develop- ment of the T cell immune response. Furthermore, our analysis aims to study the possibilities of transferring the clinical pattern of the disease from a more severe state to a milder one. We analyze numerically the conditions for the existence of steady states of the mathematical model of HIV-1 infection for the numerical values of model parameters correspond- ing to phenotypically different variants of the infectious disease course. To this end, original computational methods of bifurcation analysis of mathematical models formulated with systems of ordinary differential equations and delay differ- ential equations are used. The macrophage activation rate constant is considered as a bifurcation parameter. The regions in the model parameter space, in particular, for the rate of activation of innate immune cells (macrophages), in which the properties of bi-, multistability and hysteresis are expressed, have been identified, and the features characterizing transi- tion kinetics between stable equilibrium states have been explored. Overall, the results of bifurcation analysis of the HIV-1 infection model form a theoretical basis for the development of combination immune-based therapeutic approaches to HIV-1 treatment. In particular, the results of the study of the HIV-1 infection model for parameter sets corresponding to different phenotypes of disease dynamics (typical, long-term non-progressing and rapidly progressing courses) indicate that an effective functional treatment (cure) of HIV-1-infected patients requires the development of a personalized ap- proach that takes into account both the properties of the HIV-1 quasispecies population and the patient's immune status.

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The modern era of research in immunology is characterized by an unprecedented level of detail about structural characteristics of the immune system and the regulation of activities of its numerous components, which function together as a whole distributed-parameter system. Mathematical modeling provides an analytical tool to describe, analyze, and predict the dynamics of immune responses by applying a reductionist approach. In modern systems immunology and mathematical immunology as a new interdisciplinary field, a great challenge is to formulate the mathematical models of the human immune system that reflect the level achieved in understanding its structure and describe the processes that sustain its function. To this end, a systematic development of multiscale mathematical models has to be advanced. An appropriate methodology should consider (1) the intracellular processes of immune cell fate regulation, (2) the population dynamics of immune cells in various organs, and (3) systemic immunophysiological processes in the whole host organism. Main studies aimed at modeling the intracellular regulatory networks are reviewed in the context of multiscale mathematical modelling. The processes considered determine the regulation of the immune cell fate, including activation, division, differentiation, apoptosis, and migration. Because of the complexity and high dimensionality of the regulatory networks, identifying the parsimonious descriptions of signaling pathways and regulatory loops is a pressing problem of modern mathematical immunology.

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In this paper, we present a systematic approach for obtaining qualitatively and quantitatively correct mathematical models of some biological phenomena with time-lags. Features of our approach are the development of a hierarchy of related models and the estimation of parameter values, along with their non-linear biases and standard deviations, for sets of experimental data. We demonstrate our method of solving parameter estimation problems for neutral delay differential equations by analyzing some models of cell growth that incorporate a time-lag in the cell division phase. We show that these models are more consistent with certain reported data than the classic exponential growth model. Although the exponential growth model provides estimates of some of the growth characteristics, such as the population-doubling time, the time-lag growth models can additionally provide estimates of: (i) the fraction of cells that are dividing, (ii) the rate of commitment of cells to cell division, (iii) the initial distribution of cells in the cell cycle, and (iv) the degree of synchronization of cells in the (initial) cell population.

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Lymphocytic choriomeningitis virus (LCMV) infection in mice provides an example of an extraordinarily dynamic process with an extreme sensitivity of phenotype of infection to parameters of virus/host interaction. A mathematical model is developed to examine the dynamics of virus-specific cytotoxic T lymphocyte (CTL) response for LCMV infection in mice. The model, formulated by a system of nonlinear delay-differential equations, considers the interacting populations of viruses, precursor CTLs, terminally differentiated effector CTLs and total virus antigen load. Clonal elimination of virus-specific cytotoxic T cells in high-dose LCMV-Docile infection represents an example of the classical phenomenon--high zone tolerance. To describe both conventional and exhaustive CTL responses in the acute phase of LCMV-D infection two mechanisms are invoked: the high virus antigen load inhibition of T-cells proliferation via energy induction and the activation-induced cell death by apoptosis. Parameters of the model, characterizing the rates of virus and CTL production and elimination in spleen, are estimated by assimilating with the model data on the LCMV-D infection in C57BL/6 mice for low-, moderate- and high-dose infections. It is suggested that not only the clonal expansions have to be described in mathematical models as being virus regulated but also the later phases of primary immune response. Down-regulation of the primary CTL response is controlled by a network of mechanisms inducing anergy and apoptosis in activated T cells. The model is used to investigate the effect of variations in virus and CTL response parameters on LCMV infection outcome and suggest predictions for experimental studies, in particular the phenotype of LCMV-WE infection in C57BL/6 as a function of initial virus doses.

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We present an approach to studying theoretically the regularities and the kinetic characteristics of influenza A virus (IAV) infection in man. The estimates of the "numbers" (Zinkernagel et al., 1985) characterizing evolutionary established interferon and immune responses in uncomplicated IAV infection are explored by developing a multiparameter mathematical model which allows direct quantitative references to the biological reality. The system of equations of the mathematical model of antiviral immune response, applied earlier to acute hepatitis B virus infection (Marchuk et al., 1991a, b), is modified and extended to describe the joint reaction of the interferon and immune systems in IAV infection. Macrophages infiltrating the airway's epithelium are considered to be the principal source of interferon that induces antiviral resistance in lung epithelial cells. The model is formulated as a delay-differential system with about 60 parameters characterizing the rates of various processes contributing to the typical course of IAV infection. The key aspect of the adjustment between the model and various data on the immunity to influenza is the derivation of a consistent data set--the generalized picture of uncomplicated IAV infection. It serves as a consistent theoretical definition of the structure of the normal course of the infection and the antiviral immune response suitable for model fitting. The parameter estimates for the processes considered in the model are carefully discussed. The quantitative model is used to study the organization and dynamic properties of the processes contributing to IAV infection. The threshold condition for immune protection of virus-free host to infection with IAV is analyzed. The relative roles of humoral, cellular and interferon reactions for the kinetics of the uncomplicated IAV infection are studied. The contribution of parameters of virus-sensitive tissue, interferon and IAV-specific immune processes to the variations of duration and severity of the infection is quantitatively estimated by sensitivity studies. It is shown that the variations in the parameters of a virus-epithelial cell system are more influential on the severity of the infection rather than that of the antiviral immune response. The need for fine co-ordination of the kinetics of the non-specific interferon response and the adaptive antigen-specific immune reactions to provide recovery from the infection is illustrated.

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The present approach to the mathematical modelling of infectious diseases is based upon the idea that specific immune mechanisms play a leading role in development, course, and outcome of infectious disease. The model describing the reaction of the immune system to infectious agent invasion is constructed on the bases of Burnet's clonal selection theory and the co-recognition principle. The mathematical model of antiviral immune response is formulated by a system of ten non-linear delay-differential equations. The delayed argument terms in the right-hand part are used for the description of lymphocyte division, multiplication and differentiation processes into effector cells. The analysis of clinical and experimental data allows one to construct the generalized picture of the acute form of viral hepatitis B. The concept of the generalized picture includes a quantitative description of dynamics of the principal immunological, virological and clinical characteristics of the disease. Data of immunological experiments in vitro and experiments on animals are used to obtain estimates of permissible values of model parameters. This analysis forms the bases for the solution of the parameter identification problem for the mathematical model of antiviral immune response which will be the topic of the following paper (Marchuk et al., 1991, J. theor. Biol. 15).

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Considering the mathematical model of antiviral immune response, we describe a method of fitting the model to the data characterizing acute viral hepatitis B. The corresponding procedure employs an idea of sequential parameter estimation to make the problem of fitting manageable. The underlying mechanisms responsible for the quantitative manifestations of the four basic phases of acute hepatitis B are used to select the model parameters. The identified model of acute hepatitis B is then tested with regard to the following situations: the effect of HBsAg-specific antibodies on HBV challenge; the vaccination and the resistance to challenge using live hepatitis B virus; the dose of viruses--the incubation time relationships. The sensitivity of the model with respect to parameters variations is then analysed. The developed model allows us to quantitatively simulate the basic features of the antiviral immune response during acute hepatitis B and some closely related phenomena.

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