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A new method for constructing the multi-modal impacts on the immune systemin the chronic phase of viral infection, based on mathematical models formulated with delay-differential equations is proposed. The so called, optimal disturbances, widely used in the aerodynamic stability theory for mathematical models without delays are constructed for perturbing the steady states of the dynamical system for maximizing the perturbation-induced response. The concept of optimal disturbances is generalized on the systems with delayed argument. An algorithm for computing the optimal disturbances is developed for such systems. The elaborated computational technology is tested on a system of four nonlinear delay-differential equations which represents the model of experimental infection in mice caused by lymphocytic choriomeningitis virus. The steady-state perturbations resulting in a maximum responsewere computed with the proposed algorithm for two types of steady states characterized by a low and a high levels of viral load. The possibility of correction of the infection dynamics and the restoration of virus-specific lymphocyte functioning of the immune system by perturbing the steady states is demonstrated.

Antiangiogenic therapy is aimed at the blocking of angiogenesis, i.e., the process of new blood vessels formation, which should decrease oxygen and nutrients inflow to tumor and thus slow down its growth. This type of therapy is frequently administered together with chemotherapy, which kills rapidly proliferating tumor cells, as well as other dividing cells of the body, thus leading to significant adverse effects. However, action of bevacizumab inevitably influences the inflow of chemotherapeutic drug in tumor, therefore, optimal scheduling of drug administration is an important problem. Using a model based on consideration of the most crucial processes happening during tumor progression and therapy, we compare effectiveness of different schemes of combined chemotherapy with bevacizumab and propose new scheme of drug administration which may lead to enhanced antitumor effect compared to classical clinical scheme of simultaneous drug administration.

A generalization of the Gause competitive exclusion principle which guarantees the vanishing of at least one species in the community exceeding in number of species the number of available resources is presented. Theorems which guarantee the vanishing of a greater number of components under condition of the Malthusian vector function localizations in a set of smaller dimension are formulated. The theory developed here is applied to the case of Volterra type systems for which such vector functions are linear resource dependent and the number of resources is small.

A prototype automated system for the analysis and processing raw data of mass population screening in the Russian health centers (HCs), software program HCViewer, is developed. In it, essential elements of big data, including data filtering (i.e., detection and removal of outliers and fraud cases), statistics and spatial visualization are implemented. Testing HCViewer on the datasets of knowingly reliable, unreliable, and partially reliable bioimpedance body composition data has shown high diagnostic specificity (95.2–98.9%) and sensitivity (94.5–99.2%) of the filtering criteria. Retrospective analysis of the HCs’ bioimpedance database revealed rapid growth in the proportion of fraud cases, from 5–7% in 2009 to 43–45% in 2013–2014 (with the correction for false alarm rate), and the high level of heterogeneity in data quality, so that 80.3% of the incorrect data were generated in 20% of the HCs. This indicates inefficient management of the Russian preventive screening system and suggests incomparability and, therefore, uselessness of the related health statistics from some regions without a preliminary filtering of the underlying raw data. Our results show the potential utility of HCViewer for the dynamical quality control of the preventive screening data, as well as for the online health monitoring and modelling potential effects of various control measures aimed at the prevention of non-communicable diseases. After application of the selection criteria, a cross-sectional 2009–2015 database of bioimpedance measurements of 1.27 million individuals aged 5–96 years was formed for the assessment of population health. On the whole, fraud prevention should become the responsibility of the Russian health care system to ensure an efficiency of its function.

An axisymmetric model is suggested to simulate mechanical performance of the left ventricle of the heart. Cardiac muscle is treated as incompressible anisotropic material with active tension directed along muscle fibres. This tension depends on kinetic variables that characterize interaction of contractile proteins and regulation of muscle contraction by calcium ions. For numerical simulation of heartbeats the finite element method was implemented. The model reproduces well changes in ventricle geometry between systole and diastole, ejection fraction, pulse wave of ventricular and arterial pressure typical for normal human heart. The model also reproduces well the dependence of the stroke volume on end-diastolic and arterial pressures (the Frank–Starling law of the heart and Anrep effect). The results demonstrate that our model of cardiac muscle can be successfully applied to multiscale 3D simulation of the heart.

The paper is devoted to verification of previously proposed technique of medical ultrasound modelling [3]. A medical phantom was used as an object with well documented geometry and mechanical properties. The comparison of simulation results with raw data from ultrasound scanner is presented. A virtual B-scan is also obtained and compared with an experimental image.