Vitalii Volodymyrovich Akimenko

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• PhD
• Professor (Full) at University of Manitoba

The implicit impact of vaccination on susceptible cells (epithelial layer) is studied on the basis of stability analysis of age-structured epidemic model of susceptible cells, infected cells and cells of lesion tissue (dysplasia and cancer), human papillomavirus (HPV). The efficacy of the vaccine indirectly influences the coefficients of the system...

Stability analysis of nonlinear age-of-infection and -immunity structured SVLIAR-type model of susceptible, vaccinated, latent, COVID-19 infected, asymptomatic and recovered sub-classes of population dynamics is carried out in this paper. The SVLIAR model uses five age variables - age of vaccine immunity of vaccinated individuals, age of virus infe...

The numerical method for simulation of age-structured SIPCV epidemic model with age-structured sub-classes of susceptible, infectious, precancerous and cancer cells and unstructured population of human papilloma virus (HPV) dynamics with incubation period is developed. Convergence of the numerical approximations is studied both theoretically and nu...

The numerical method for simulation dynamics of nonlinear epidemic model of age-structured sub-populations of susceptible, infectious, precancerous and cancer cells and unstructured population of human papilloma virus (HPV) is developed (SIPCV model). Cell population dynamics is described by the initial-boundary value problem for the delayed semi-l...

Stability analysis of an autonomous epidemic model of an age-structured sub-populations of susceptible, infected, precancerous and cancer cells and unstructured sub-population of human pap-illoma virus (HPV) (SIPCV epidemic model) aims to gain an insight into the features of cervical cancer disease. The model considers the immune functional respons...

This article studies nonlinear n-resource-consumer autonomous system with age-structured consumer population. The model of consumer population dynamics is described by a delayed transport equation, and the dynamics of resource patches are described by ODE with saturated intake rate. The delay models the digestion period of generalist consumer and i...

In this paper we study a nonlinear resource-consumer model with age-structured consumer population feeding in n resource patches. While the consumer population dynamics are described by a semi-linear transport equation with delay, resource dynamics are described by ordinary differential equations. The delay models the lagged effect of food intake o...

This paper focuses on the study of continuous age-structured models, or more general, physiologically structured models, which used for detailed and accurate study of population dynamics in many ecological, biological applications and medicine. In contrast to simpler unstructured models, these models allow us to relate the individual life-histories...

We study a nonlinear age‐structured model of locust population dynamics with variable time of egg incubation that describes the phase shifting and behavior of desert locust, Schistocerca gregaria. The model is based on the 2‐compartment system of transport equations with nonlinear density‐dependent fertility rates with time delay in boundary condit...

In this article we study a nonlinear age-structured consumer population model with density-dependent death and fertility rates, and time delays that model incubation/gestation period. Density dependence we consider combines both positive effects at low population numbers (i.e., the Allee effect) and negative effects at high population numbers due t...

Stability analysis of nonlinear age-structured model of population dynamics with finite age reproductive window and density-dependent death rate and femail mating function.

The models and methods of data analysis in applied scientific studies (in Ukrainian).

This paper is devoted to the study of an age-structured SIR epidemic system on the basis of the model of polycyclic population dynamics of susceptible, infected and recovered individuals. This model was con- sidered as a nonlinear competitive system of three initial-boundary value problems for the nonlinear transport equations with non-local inte...

This paper is devoted to the study of evolutionary dynamics of monocyclic age-structured population including effect of nonlinear mortality (population growth feedback) and proliferation. The total population is considered as partitioned by fixing age into two subpopulations. Individuals of first population are born, mature, die and can at the fina...

This paper is devoted to the study of evolutionary dynamics of monocyclic age-structured population including the effect of non-linear mortality (population growth feedback) and proliferation. For this purpose we developed the explicit conservative two layer difference schemes for the initial-boundary value problems for the semi-linear transport eq...

This paper is devoted to the development of explicit recurrent algorithm and numerical study of properties of travelling wave solutions of two age-structured population dynamics models with nonlinear death rates and polycyclic reproduction condition. Death rate of first model is a power function with arbitrary exponent of total number of individual...

In this paper we study the nonlinear age-structured model of a polycyclic two-phase population dynamics including delayed effect of population density growth on the mortality. Both phases are modelled as a system of initial boundary values problem for semi-linear transport equation with delay and initial problem for nonlinear delay ODE. The obtaine...

We develop a numerical method and study the equilibria and dynamical regimes of age-structured predator-prey model of di-trophic food web modules.

We study the indicators and conditions of equilibria and outbreaks in desert locust population dynamics.

In this work the explicit recurrent algorithms are developed for solving two different age-structured nonlinear models of polycyclic population dynamics with density-dependent death rates. This work continues the study in paper [1] for polycyclic population including the effect of nonlinear mortality (population growth feedback) and proliferation....

We study the dynamical regimes of quiescent and proliferating cells population dynamics.

One was considered non-linear age-structured model of population dynamics based on the initial-boundary value problem for the non-linear hyperbolic equation with integral boundary condition. This model describes the evolutionary dynamics of polycyclic population with non-linear species death rate. Latest controls the feedback influence of populatio...

This work is devoted to the study of evolutionary dynamics of poly-cyclic age-structured one-sex population. It extends the work in [1], [2] for polycyclic population including the effect of nonlinear mortality (popula-tion growth feedback) and proliferation. Further, the population is assumed to have two types of individuals, proliferating and qui...

We study the nonlinear evolutionary dynamics of the monocyclic cell population including the effect of proliferation and nonlinear effect of mortality on the population growth. The total population is considered as partitioned by fixing age into two subpopulations. First of them consists of species which birth, age, can die in some age and divide w...

We use the analytical approach and numerical modeling to analyze the dynamics of the population of biological cells based on the polycyclic age-structured model. We reduce the initial–boundary-value problem for transport equation to the Volterra integral equation of the second kind and solve it by infinite convergent series. For the initial–boundar...

The analysis of existence of equilibria and oscillating dynamical regimes of age-structured model with dencity-dependent death rate.

We develop the numerical method and perform numerical experiments for the initial-boundary value problem for the system of semi-linear transport equations which describes the evolutionary dynamics of age-structured monocyclic cell population. We have considered the academical test on the parameterized set of algebraic function for incoming in model...

In this paper, we analyze the temporal evolution of the monocyclic age-structured cells aggregation using the exact analytical solution of the system of temporal-age initial-boundary problems for the transport equations. We consider the set of income equation coefficients as a set of parametrical algebraic functions with compact sets of parameter d...

We consider an age-structured model of biological cell aggregation evolution on the basis of initial-boundary problem for the linear partial differential equations of hyperbolic type – transport equations with special non-local boundary conditions which describes the cell population dynamics. We have analyzed the evolution of the cells aggregation...

We have analyzed the evolution of the cells aggregation in the frame of polycyclic age-structured model using both the analytical technique and numerical simulation approaches. In the first case we have reduced the temporal-age initial boundary problem for the transport equation to the Volterra integral equation and have resolved it used infinite c...

Procedure of spliting of logistic equation of population dynamics allowed to get the hierarchical N 2 Lotka -Volterra system for competitive objects and reduce of this system to the aggregate of independent equations of Bernoulli. This approach allows obtain the analytical solution of Lotka-Volterra system and got asymptotic of solution at t→∞ the...

A two-level hierarchical organization system is used to consider a model for the optimal control of funds and competitive ability of an information–communication company. The model is based on a control problem for ordinary differential equations (that characterize the dynamics of funds) and on an initial–boundary-value problem for multidimensional...

We consider the system of quasilinear parabolic equations of the Lotke−Volterra (diffusive model) with discontinuous coefficients for the problem of companies competition. Explicit three-layered difference schemes, which correspond to the maximum principle, were constructed with usage of the integral interpolation method. On testing examples for gr...

The paper considers a dynamic model of monocyclic cell aggregation based on an initial–boundary-value problem for hyperbolic transport equations. An analytic solution to the problem and conditions of its continuous differentiability are found. Numerical calculations for classes that differ in the smoothness of input model parameters are carried out...

The model of optimum control of monocyclic cell aggregation in the set of piece-wise constant control functions is considered. The explicit analytic form of solution of the optimum control problem for criteria when cells density attains the required level is found. The numerical computation of dynamics of monocycle cells aggregation for control fun...

A model of optimal control of underflooding of restricted areas by groundwater on the basis of the initial boundary value problem for a parabolic type quasilinear equation is considered. For the initial boundary value problem the maximum principle is proved, sufficient conditions of the existence and uniqueness of a generalized solution, sufficient...

The conceptual model of Decision Making Support System (DMSS) of optimum control of flooding of territories is created. The basic algorithm of information objects which ensure functioning of system is developed..

An initial–boundary-value problem for a multidimensional integro-differential equation with degenerate parabolicity is considered. Based on the maximum-principle theorem and splitting method, a nonlinear monotonic high-order (higher than the first) numerical scheme is constructed for an implicit two-layer scheme. For the error of a numerical soluti...

The complex formalized model of decision support for the optimal control by the life cycle of innovative enterprise products is built in the article. The system analyze methods is using for models designed.

A model of competitive innovation diffusion is considered. The model is based on the Lotka-Volterra system and an initial-boundary problem for a system of quasilinear parabolic equations. The maximum principle is proved for the problem of diffusion of two competitive innovations, and sufficient conditions of existence of optimum control are obtaine...

An initial-boundary-value problem for a system of degenerate parabolic integro-differential equations is considered. The sufficient conditions for the existence and uniqueness of its generalized solution and for the existence of at least one optimal control for a given performance functional are obtained. A stable numerical solution to the initial-...

For the problem of optimal allocation of resource in two-level hierarchical control system of a group of enterprises we consider two techniques for elimination of uncertainty for setting parameters of enterprises, i.e., the method of integral convolution and the guaranteed method (maximization method). We obtained analytical solutions for controlli...

Scenarios of migration are considered as applied to the problem of optimal control of transregional migration with zero risk of overpopulation or insufficient population and migration with obtaining the minimum of the objective functional and minimizing risk. Numerical algorithms for the scenarios considered are developed. The algorithms are implem...

For the system of 1-dimentional integro–differential parabolic equations with degeneration the stable numerical algorithm of optimum control is built on the class of piecewise-smooth functions.

An organizational two-level hierarchic system is used to examine control models for interregional migration under conditions of social risks. The Cauchy problem is used to solve the multidimensional transport equation (Problem A1) and a system of ordinary linear differential equations (Problem A2). For the models proposed, sufficient conditions for...

A problem of convective heat and mass transfer for a two-dimensional cylindrical domain (φ is a symmetrical model of the Bridgeman ampoule) is considered on the basis of system of nonstationary Navier-Stokes equations. A numerical algorithm is developed and computations of the Grasgof number G R = 5 × 105 for a short and a long cylinders were done....

The Cauchy problem for a two-dimensional transport equation is considered. Two-layer certainly monotonous explicit second-order scheme, steady at large values of the difference Courant number, and an implicit two-layered certainly monotonous second-order scheme are developed based on the maximum principle for multilayered nonlinear difference schem...

Paper is devoted to the development of generalized model of administrative management and decision making for the system of flooding monitoring in big cities. The mathematical model of the computer system of estimation, forecasting and decision making for a flooding monitoring is developed on the basis of general model of ecological monitoring syst...

The bimodal hierarchical system for control of atmospheric air pollution by industrial enterprises is developed by the system analysis tools for regional centers for ecological monitoring. The solution of the optimal control problem is obtained on the set of piecewise constant functions.

A mathematical model and a block diagram of a system for making administrative decisions in distributed monitoring systems under the conditions of mixed information are developed by methods of systems analysis. The structure of applied decision-making systems for supporting information systems of analysis and prediction of atmospheric air pollution...

The structure scheme of developed information system (IS) of analysis and forecasting of an industrial cities atmosphere boundary layer pollution by stationary sources is considered in the article. IS allows to carry out the complex analysis of pollution of air at a new qualitative and quantitative level, using specified mathematical models and met...

For the two-dimensional parabolic equation (turbulent diffusion equation) by means of the method of nonlinear monotone smoothing using the decomposition scheme, we construct the two-layer implicit monotone scheme of the second order. We prove stability of the developed schemes, obtain majorizing estimations for nonlinear difference operators and es...

The decision support system of ecological monitoring of atmosphere under the conditions of fuzzy information is considered. The general mathematical algorithm of decision making developed in this work includes the methods of constructing a set of acceptable alternatives, forming the criterion for a choice of optimal decision for an air pollution mo...

The nonlinear monotone high order schemes are considered for the atmosphere pollution modeling problem in the three-dimensional domain from the local source described by the parabolic equation of the common type and the nonlinear turbulence system b − ε. The investigation of the numerical solution errors for linear and nonlinear, monotone and non m...

Two-layer and three-layer monotone stable difference schemes of the second and higher orders of accuracy are constructed for one-dimensional and multidimensional transport equations by the method of nonlinear regularization. For the multidimensional equation, an efficient explicit three-layer monotone stable scheme having such an accuracy is constr...

On the basis of methods of nonlinear monotonisation the second order implicit two-layer scheme for the transport equation is developed. The estimations for nonlinear numerical operators are obtained and the convergence of solution of nonlinear numerical scheme is proved.

A maximum principle is established for a family of multilayer nonlinear difference schemes. Monotone stable difference schemes are obtained for parabolic equations on the sets of two- and three-layer second-order difference schemes using nonlinear difference operators.

Monotone difference schemes were created, for elliptic and parabolic equations by using the special linear difference operators on the set of second order approximation difference schemes. Using the method of numerical experiments for differ Reynolds numbers, it was carried out comparativ estimations of numerical errors for different monotone schem...

We consider the problem of conditions for the existence of multiple singular integrals of a certain class at inner and boundary points of a domain. We obtain the quadrature and cubature formulas for calculating multiple singular integrals and present the corresponding estimates for the formulas.

The method of inverse problems permits determination of unknown parameters of a mathematical model of a technological object by using the information about some physical fields. If stable algorithms are developed, then the error of determination of the parameters versus the measurement error of fields may be determined with the help of a computer....

A correct mathematical formulation is proposed for the problem of controlling cooling during hardening of elastoplastic samples. The optimal controls for surface and through hardening were found from a numerical experiment.

A mathematical model of high-temperature induction heating of a two-layer bimetallic cylindrical specimen with an allowance for the effect of thermoelastoplastic loading has been developed on the basis of the inverse problem method. The results of a mathematical experiment on determining the optimum heating conditions connected with abrupt changes...

A hindering factor in devising a technology of treating bimetallic materials is the lack of realistic possibilities of estimating the contact stresses and temperature fields on the interfaces of actual objects, and consequently the enforced transition to lengthy slow heating in special protective atmospheres (e.g., against oxidation), which makes p...