We examine a nonlinear dynamical model that depicts the interaction between cancerous cells and an oncolytic virus. For best modelling the disease, we use the Caputo fractional derivative in piecewise approaches. By employing piecemeal techniques, we treat a compartment in the body that contains infectious and non-infectious cells. More precisely, the solvability and Ulam-Hyers (U-H) stability results are considered using standard concepts. Further, to support our investigation with numerical results, we apply the Euler method to develop an approximation solution. It connected with numerous graphical representations of the system using various arbitrary ordering and varying values of the isolation parameters. Here we remark that the multi-step behavior that certain problems exhibit, is one of important issues naturally. This paper introduces the idea of piecewise derivative with the goal of modeling real-world issues that follow multiples processes. With the help of the used approach, we investigate the cancer disease model and its transmission dynamical behavior with crossover effect.

Humans have been affected by various epidemic diseases, mostly are airborne and exhibit high transmission rates. Given these nature properties, quarantine measures are essential to control the spread of the diseases effectively. Motivated by this fact, and due to the successful use of mathematical modeling, we investigate a SIR model with quarantine and vaccination compartments. This model uses a system of fractional differential equations (SIQVR-based) with specific parameters to track the dynamics of model variables. We examine the well-posedness and boundedness results via standard tools. An effective threshold parameter ℛ_0 is determined using a generation matrix and equilibrium points of the model are obtained. To effectively manage the transmission of infection within the outlined model, we employ the strategy of optimal control. This approach involves implementing control measures and interventions guided by mathematical optimization techniques to minimize the spread of disease. These control strategies may encompass vaccination campaigns, quarantine protocols, social distancing measures and other preventive actions. Further, to evaluate the effectiveness of proposed model and the applied optimal control strategy, we conduct a series of numerical simulations. Computational results involve running the model under different scenarios, considering a range of parameters and meticulously analyzing the resulting outcomes.

This article examines the possibilities of adapting approximate solutions of boundary value problems for differential equations using physics-informed neural networks (PINNs) to changes in data about the physical entity being modelled. Two types of models are considered: PINN and parametric PINN (PPINN). The former is constructed for a fixed parameter of the problem, while the latter includes the parameter for the number of input variables. The models are tested on three problems. The first problem involves modelling the bending of a cantilever rod under varying loads. The second task is a non-stationary problem of a thermal explosion in the plane-parallel case. The initial model is constructed based on an ordinary differential equation, while the modelling object satisfies a partial differential equation. The third task is to solve a partial differential equation of mixed type depending on time. In all cases, the initial models are adapted to the corresponding pseudo-measurements generated based on changing equations. A series of experiments are carried out for each problem with different functions of a parameter that reflects the character of changes in the object. A comparative analysis of the quality of the PINN and PPINN models and their resistance to data changes has been conducted for the first time in this study.

We introduce an epidemic disease reaction–diffusion model to study the transmission of the varicella-zoster virus in both space and time. More precisely, we present a system of partial differential equations with the Neumann boundary conditions (NBC) concerned to model the evolution of the virus. Firstly, the wellposedness results of the model are studied using the semigroup theory. Then, the boundedness of the solutions is also derived. Further, the basic reproduction number (BRN) for the proposed model is determined using the eigenvalue problem. Moreover, asymptotic profiles of the equilibrium points of the susceptible and infected compartments of the model are investigated. Finally, the advantage of the spatiotemporal model and the above theoretical results are validated with numerical experiments.

We establish a class of nonlinear fractional differential systems with distributed time delays in the controls and impulse effects. We discuss the controllability criteria for both linear and nonlinear systems. The main results required a suitable Gramian matrix defined by the Mittag–Leffler function, using the standard Laplace transform and Schauder fixed-point techniques. Further, we provide an illustrative example supported by graphical representations to show the validity of the obtained abstract results.

We study the well-posedness for solutions of an initial-value boundary problem on a two-dimensional space with source functions associated to nonlinear fractional diffusion equations with the Riemann-Liouville derivative and nonlinearities with memory on a two-dimensional domain. In order to derive the existence and uniqueness for solutions, we mainly proceed on reasonable choices of Hilbert spaces and the Banach fixed point principle. Main results related to the Mittag-Leffler functions such as its usual lower or upper bound and the relationship with the Mainardi function are also applied. In addition, to set up the global-in-time results, $ L^p-L^q $ estimates and the smallness assumption on the initial data function are also necessary to be applied in this research. Finally, the work also considers numerical examples to illustrate the graphs of analytic solutions.

Development of personalized medicine is determined by the synergy of scientists from several fields of medicine, mathematics, computer science and instrumentation.Approaches based on modern methods of measuring, signal processing and machine learning complement the main methods for studying biological processes, make it possible to identify the mechanisms of the disease and personalize the treatment strategy.The article is devoted to the study of models and methods that characterize the processes of cerebral blood flow autoregulation for methodological support of measuring systems in the field of digital personalized medicine.Analysis of systemic arterial pressure and blood flow velocity in the arteries of the base of the brain signals, which characterize the cerebral blood flow autoregulation, makes it possible to determine the nature of the violation of cerebral autoregulation processes in patients.The article proposes to use fractal methods for signal analysis based on the calculation of the Hölder multifractal spectrum and the correlation dimension of signals.The advantage of fractal methods is that they can be applied to signals without a characteristic scale that are scale invariant.

A mathematical model of autoregulation of cerebral circulation in the human body for obtaining additional information to make decisions about choosing a treatment plan has been presented in the paper. The fractal analysis methods based on wavelet leaders, which made it possible to expand the traditional approach to assessing the interaction between systemic arterial pressure and linear blood flow velocity formed the basis of the developed nonlinear model of autoregulation. The application of the developed methods to assessing the state of the autoregulation system in a healthy volunteer and a patient with cerebral pathology was exemplified

This study analyzes the conditions for creating the energy density necessary to obtain supercritical fluids of substances with parameters (temperature T > 1 eV, density N > 1022 cm−3, specific energy density ε > 100 kJ/g). The calculations are carried out on the basis of the one-dimensional (1D) two-temperature (2T) magneto hydrodynamic radiation model, which takes into account the physical processes occurring in the energy storage, switching system and the pulsed plasma load-a cylindrical compressible conductive shell. Developing a mathematical model, we assumed that physical processes were self-consistent. The simulation results were presented as time dependences of the main process parameters. Calculations showed that it becomes possible to sharpen the radiation pulse and pressure in the shock wave. As a result, we formulated the requirements for a laboratory energy source to establish the characteristics of a current pulse flowing through a conductive cylindrical shell and its dimensions (radius and thickness) necessary to achieve the goal.

The authors carried out the study of the state of systemic and cerebral hemodynamics in normal conditions and in various neurosurgical pathologies using modern signal processing methods. The results characterize the condition for the mechanisms of cerebral circulation Institute of Computer Science and Control, Higher School of Cyber-Physical Systems and Control regulation, which allows for finding a solution to fundamental and specific clinical problems for the effective treatment of patients with various pathologies. The proposed method is based on the continuous wavelet transform of systemic arterial pressure and blood flow velocity signals in the middle cerebral artery recorded by non-invasive methods of photoplethysmography and transcranial doppler ultrasonography. The study of these signals in real-time in the frequency range of Mayer waves makes it possible to determine the cerebral autoregulation state in certain diseases before and after surgical interventions. The proposed method uses a cross-wavelet spectrum, which helps obtain wavelet coherence and a phase shift between the wavelet coefficients of systemic arterial pressure signals and blood flow velocity in the Mayer wave range. The obtained results enable comparing the proposed method with that based on the short-time Fourier transform. The comparison showed that the proposed method has higher sensitivity to changes in cerebral autoregulation and better localization of changes in time and frequency.

In the article, the possibility of processing voting results in the case of a team of experts with different efficiency in assessing the situation has been considered. The experts were expected to decide whether or not a patient was suffering from a specific disease. The most intelligent combination of the individual expert's votes into a collective council's decision was required. Our algorithm was based on the Neumann - Pearson principle of minimizing the type 2 error probability at a fixed type 1 error probability. The team of experts with different qualifications was shown to be able to draw a correct conclusion with a high probability.

The article discusses a problem of naturally fractured reservoir modeling because some reservoirs exhibit the flow processes characterized by anomalous kinetics that do not obey Gaussian statistics. For this reason, the classical approach to the well test interpretation, its generalizations, and their transformation to a more complex model taking into account the fractal structure of fracture networks have been considered. The obtained results indicated the validity of the application of the fractal model to the interpretation of the well-test data where a power-law time dependence of the producing bottom-hole pressure was observed. Moreover, some symptoms were formulated whereby someone could identify the fractal well-stream behavior using the well-test data. Finally, the main issues for further studies the authors refer to the determination of the fractal parameters and the fractal model validation in laboratory experiments.

A method of protecting territories in a river basin during flash floods by creating a multi-stage system of intercepting flood control systems with temporarily filled reservoirs, with a phased construction of waterworks on side tributaries, including secondary ones. Using the computer programs developed by the authors, the operating modes of the hydroelectric system were simulated for a possible variant of placing their sections on the lateral tributary of the river: in the lower reaches- a traditional hydro system with an earth dam and a concrete spillway, including bottom holes and a surface spillway; upstream- an additional hydro system with a filtering dam made of gabion masonry, into which the missing accumulating volume is redistributed. The calculation of the social effect resulting from the considered method of protection by assessing the reduction of economic damage for settlements located in the downstream of the main flood control hydroelectric complex with participation in the cutoff of the flood peak of an additional temporarily filled reservoir located upstream of the river is performed.

The promotion of cotton in regions with long daylight hours is a priority for genetics. The creation of a new breeding material for a crop with a short growing season of 95-110 days makes it possible to organize the production of this fiber in the south of Russia. The studies were carried out in 2014-2020 at the experimental sites of the Volgograd State Agrarian University. Growth, development, ecological and biological characteristics were studied on new cotton varieties PGSSH 1 and PGSSH 7 in conditions of light chestnut soils. Field experiments were carried out according to generally accepted methods. As a result, it was found that the growing season of new varieties of cotton corresponds to the conditions of the season in the Volgograd region. Boll opening is celebrated from 25 August to 20 September. Bushes form 4 to 18 fruits, 58% are located in the middle tier. The limiting growth and development factors include sharp drops in daytime and nighttime temperatures in spring (up to 150C). In some years, cold and rainy weather in July leads to the development of diseases on plants. However, new varieties of cotton have time to mature and form high quality fiber. Hot, dry weather does not adversely affect plant growth and development. The potential yield of these varieties reaches 3.3-3.5 t / ha. These varieties have good prospects for implementation. The development of varietal agricultural technology will ensure the organization of cotton production in areas with long daylight hours.

In the paper, the authors present a method for determining the distribution class to which a selected random vector with medical parameters as components belongs. The method is based on the statistical significance test. The optimal selection problem for the significance level where the probability of the vector identification error is minimal has been solved. In order to tackle the problem, the authors used the prior information on belonging the vector components to the definite distribution class in which the statistical relationship between the medical parameters was taken into account. The developed mathematical model of patient condition should serve as support of decision-making on further treatment tactics.

Due to the increase in the number of floods, the urgent task is to reduce the risk of flooding the important areas. The existing hydraulic structures for flood accumulation may no longer be enough; therefore, it is necessary to place new objects in the river basin. The paper proposes an improved previous mathematical model for the analysis and selection of the location and basic parameters of self-regulating hydroelectric systems in a river basin using computer modelling with the possibility of parallel computations. It is possible to quickly evaluate the results of adding new structures and their contribution to reducing the risk of floods.

Mathematical models are described in which the circulatory system of an organism is considered as a multifractal object. The solution to two problems is given. The first one is associated with the normal state of the body’s life support system, namely, to heat transfer in human skin. The equations of hydrodynamics and heat transfer are the basis of the model. Quantitative results of calculating heat fluxes in three layers of the dermis are presented. The second problem is a violation of fractality due to the presence of arteriovenous malformation in the vascular system of the brain. Blood flow modeling in the presence of malformation was performed using the SolidWorks 2017 Flow Simulation software product. Data on blood velocity and blood flow in vessels for various cases of malformation are presented.

The paper presents the numerical simulation results of the energy characteristics of a laser based on no equilibrium plasma of multiply charged ions. Plasma is created in a small inductive extended Z-discharge with a power system on heterogeneous forming lines. The requirements for the distribution of the lines parameters providing the creation of the energy density and power density necessary for the generation of radiation in the “water window” region have been established.

This paper deals with cervical cancer which is the second most common cancer in females and a major cause of death in the world now a days. Detection of symptoms of cervical cancer basically focused at an advance stage. But it is possible to detect cancer at an early stage through diagnosis and screening. The detection through diagnosis at early stages provides the incentive for the primary prevention and helps to slow down the rapid progression of cervical cancer. Considering diagnosis system a time-dependent variable, here we formulate a new mathematical model on cervical cancer considering susceptible human population, cancer patients and diagnosis. This model gives a framework for understanding how early diagnosis increases the chances for cancer patients to be cancer free by providing proper treatment. To explore the in-depth study of the system, we find the basic reproduction number R_0 . We analyze and compare the local stability of the equilibrium points of both the systems in the presence and absence of diagnosis. We investigate analytically as well as numerically the causal effect of diagnosis for reducing the cancer patient at an early stage. Furthermore, we enhance the role of diagnosis by using optimal control strategies to prevent the cervical cancer.

In this article a new mathematical model for a laser metal ablation by ultra-short duration laser pulses is proposed. The computational process is based on a two-temperature hydrodynamic model for electrons and ions. Some improvements are made and wide-range equation of state for metals is included in model. The results of the computer simulation of ablation depth for aluminum and copper are compared with experimental data at a different laser fluency values. We obtained a good agreement between the experimental and calculated data on the ablation depth.