Mathematical Analysis of the Effectiveness of Screening for Intracranial Aneurysms in First-Degree Relatives of Persons with Subarachnoid Hemorrhage.

OBJECTIVE: Population screening for aneurysms in patients with risk factors and preventive surgical treatment are beneficial according to numerous studies. One of the most significant risk factors is heredity, namely, the presence of first-degree relatives (FDR) with aneurysmal subarachnoid hemorrhage (aSAH). Nevertheless, there are still no generally accepted approaches or evidence bases regarding the benefits of the aneurysm screening strategy. METHODS: Mathematical modeling of the dynamics of aneurysm development in the population was carried out using an algorithm implementing a discrete Markov's chain. To implement the model, all probabilities of events and distributions are taken from available literature sources. Three-dimensional time of flight noncontrast magnetic resonance angiography was chosen as a screening method. Patients underwent preventive surgical treatment if an aneurysm was detected. RESULTS: Screening and preventive treatment in the general population reduces the prevalence of aneurysms by 1.74% (3.44% in the FDR group) and the prevalence of aSAH by 14.36% (37.48% in the FDR group). Mortality due to aSAH was reduced by 14.44%. The number of disabilities also decreases. The occurrence of deep disability was reduced by 20.2% in the FDR group. Economic analysis of the part of the population consisting of FDRs showed annual savings of ies also decr CONCLUSIONS: The mathematical model demonstrated that screening and preventive treatment of cerebral aneurysms can reduce aSAH-associated morbidity and mortality. In the FDR group, there was decrease in the prevalence of aSAH and decrease in associated mortality. Screening for cerebral aneurysms is cost-effective.

Numerical study of chronic hepatitis B infection using Marchuk-Petrov model.

In this work, we briefly describe our technology developed for computing periodic solutions of time-delay systems and discuss the results of computing periodic solutions for the Marchuk-Petrov model with parameter values, corresponding to hepatitis B infection. We identified the regions in the model parameter space in which an oscillatory dynamics in the form of periodic solutions exists. The respective solutions can be interpreted as active forms of chronic hepatitis B. The period and amplitude of oscillatory solutions were traced along the parameter determining the efficacy of antigen presentation by macrophages for T- and B-lymphocytes in the model.. The oscillatory regimes are characterized by enhanced destruction of hepatocytes as a consequence of immunopathology and temporal reduction of viral load to values which can be a prerequisite of spontaneous recovery observed in chronic HBV infection. Our study presents a first step in a systematic analysis of the chronic HBV infection using Marchuk-Petrov model of antiviral immune response.

Stochastic Modelling of HIV-1 Replication in a CD4 T Cell with an IFN Response.

A mathematical model of the human immunodeficiency virus Type 1 (HIV-1) life cycle in CD4 T cells was constructed and calibrated. It describes the activation of the intracellular Type I interferon (IFN-I) response and the IFN-induced suppression of viral replication. The model includes viral replication inhibition by interferon-induced antiviral factors and their inactivation by the viral proteins Vpu and Vif. Both deterministic and stochastic model formulations are presented. The stochastic model was used to predict efficiency of IFN-I-induced suppression of viral replication in different initial conditions for autocrine and paracrine effects. The probability of virion excretion for various MOIs and various amounts of IFN-I was evaluated and the statistical properties of the heterogeneity of HIV-1 and IFN-I production characterised.

Prediction of Specific Antibody- and Cell-Mediated Responses Using Baseline Immune Status Parameters of Individuals Received Measles-Mumps-Rubella Vaccine.

A successful vaccination implies the induction of effective specific immune responses. We intend to find biomarkers among various immune cell subpopulations, cytokines and antibodies that could be used to predict the levels of specific antibody- and cell-mediated responses after measles-mumps-rubella vaccination. We measured 59 baseline immune status parameters (frequencies of 42 immune cell subsets, levels of 13 cytokines, immunoglobulins) before vaccination and 13 response variables (specific IgA and IgG, antigen-induced IFN-γ production, CD107a expression on CD8+ T lymphocytes, and cellular proliferation levels by CFSE dilution) 6 weeks after vaccination for 19 individuals. Statistically significant Spearman correlations between some baseline parameters and response variables were found for each response variable (p < 0.05). Because of the low number of observations relative to the number of baseline parameters and missing data for some observations, we used three feature selection strategies to select potential predictors of the post-vaccination responses among baseline variables: (a) screening of the variables based on correlation analysis; (b) supervised screening based on the information of changes of baseline variables at day 7; and (c) implicit feature selection using regularization-based sparse regression. We identified optimal multivariate linear regression models for predicting the effectiveness of vaccination against measles-mumps-rubella using the baseline immune status parameters. It turned out that the sufficient number of predictor variables ranges from one to five, depending on the response variable of interest.

Functional cure of a chronic virus infection by shifting the virus - host equilibrium state.

The clinical handling of chronic virus infections remains a challenge. Here we describe recent progress in the understanding of virus - host interaction dynamics. Based on the systems biology concept of multi-stability and the prediction of multiplicative cooperativity between virus-specific cytotoxic T cells and neutralising antibodies, we argue for the requirements to engage multiple immune system components for functional cure strategies. Our arguments are derived from LCMV model system studies and are translated to HIV-1 infection.

Sensitivity of SARS-CoV-2 Life Cycle to IFN Effects and ACE2 Binding Unveiled with a Stochastic Model.

Mathematical modelling of infection processes in cells is of fundamental interest. It helps to understand the SARS-CoV-2 dynamics in detail and can be useful to define the vulnerability steps targeted by antiviral treatments. We previously developed a deterministic mathematical model of the SARS-CoV-2 life cycle in a single cell. Despite answering many questions, it certainly cannot accurately account for the stochastic nature of an infection process caused by natural fluctuation in reaction kinetics and the small abundance of participating components in a single cell. In the present work, this deterministic model is transformed into a stochastic one based on a Markov Chain Monte Carlo (MCMC) method. This model is employed to compute statistical characteristics of the SARS-CoV-2 life cycle including the probability for a non-degenerate infection process. Varying parameters of the model enables us to unveil the inhibitory effects of IFN and the effects of the ACE2 binding affinity. The simulation results show that the type I IFN response has a very strong effect on inhibition of the total viral progeny whereas the effect of a 10-fold variation of the binding rate to ACE2 turns out to be negligible for the probability of infection and viral production.

Examining the cooperativity mode of antibody and CD8+ T cell immune responses for vaccinology.

A fundamental unsolved issue in vaccine design is how neutralizing antibodies and cytotoxic CD8+ T cells cooperate numerically in controlling virus infections. We hypothesize on a viewpoint for the multiplicative cooperativity between neutralizing antibodies and CD8+ T cells and propose how this might be exploited for improving vaccine-induced protective immunity.

Intracellular Life Cycle Kinetics of SARS-CoV-2 Predicted Using Mathematical Modelling.

SARS-CoV-2 infection represents a global threat to human health. Various approaches were employed to reveal the pathogenetic mechanisms of COVID-19. Mathematical and computational modelling is a powerful tool to describe and analyze the infection dynamics in relation to a plethora of processes contributing to the observed disease phenotypes. In our study here, we formulate and calibrate a deterministic model of the SARS-CoV-2 life cycle. It provides a kinetic description of the major replication stages of SARS-CoV-2. Sensitivity analysis of the net viral progeny with respect to model parameters enables the identification of the life cycle stages that have the strongest impact on viral replication. These three most influential parameters are (i) degradation rate of positive sense vRNAs in cytoplasm (negative effect), (ii) threshold number of non-structural proteins enhancing vRNA transcription (negative effect), and (iii) translation rate of non-structural proteins (positive effect). The results of our analysis could be used for guiding the search for antiviral drug targets to combat SARS-CoV-2 infection.

Modeling of the HIV-1 Life Cycle in Productively Infected Cells to Predict Novel Therapeutic Targets.

There are many studies that model the within-host population dynamics of Human Immunodeficiency Virus Type 1 (HIV-1) infection. However, the within-infected-cell replication of HIV-1 remains to be not comprehensively addressed. There exist rather few quantitative models describing the regulation of the HIV-1 life cycle at the intracellular level. In treatment of HIV-1 infection, there remain issues related to side-effects and drug-resistance that require further search "...for new and better drugs, ideally targeting multiple independent steps in the HIV-1 replication cycle" (as highlighted recently by Teldury et al., The Future of HIV-1 Therapeutics, 2015). High-resolution mathematical models of HIV-1 growth in infected cells provide an additional analytical tool in identifying novel drug targets. We formulate a high-dimensional model describing the biochemical reactions underlying the replication of HIV-1 in target cells. The model considers a nonlinear regulation of the transcription of HIV-1 mediated by Tat and the Rev-dependent transport of fully spliced and singly spliced transcripts from the nucleus to the cytoplasm. The model is calibrated using available information on the kinetics of various stages of HIV-1 replication. The sensitivity analysis of the model is performed to rank the biochemical processes of HIV-1 replication with respect to their impact on the net production of virions by one actively infected cell. The ranking of the sensitivity factors provides a quantitative basis for identifying novel targets for antiviral therapy. Our analysis suggests that HIV-1 assembly depending on Gag and Tat-Rev regulation of transcription and mRNA distribution present two most critical stages in HIV-1 replication that can be targeted to effectively control virus production. These processes are not covered by current antiretroviral treatments.

Corrigendum: Spatial Lymphocyte Dynamics in Lymph Nodes Predicts the Cytotoxic T Cell Frequency Needed for HIV Infection Control.

[This corrects the article DOI: 10.3389/fimmu.2019.01213.].

Spatial Lymphocyte Dynamics in Lymph Nodes Predicts the Cytotoxic T Cell Frequency Needed for HIV Infection Control.

The surveillance of host body tissues by immune cells is central for mediating their defense function. In vivo imaging technologies have been used to quantitatively characterize target cell scanning and migration of lymphocytes within lymph nodes (LNs). The translation of these quantitative insights into a predictive understanding of immune system functioning in response to various perturbations critically depends on computational tools linking the individual immune cell properties with the emergent behavior of the immune system. By choosing the Newtonian second law for the governing equations, we developed a broadly applicable mathematical model linking individual and coordinated T-cell behaviors. The spatial cell dynamics is described by a superposition of autonomous locomotion, intercellular interaction, and viscous damping processes. The model is calibrated using in vivo data on T-cell motility metrics in LNs such as the translational speeds, turning angle speeds, and meandering indices. The model is applied to predict the impact of T-cell motility on protection against HIV infection, i.e., to estimate the threshold frequency of HIV-specific cytotoxic T cells (CTLs) that is required to detect productively infected cells before the release of viral particles starts. With this, it provides guidance for HIV vaccine studies allowing for the migration of cells in fibrotic LNs.