We present a one-sex age-structured population dynamics deterministic model with a discrete set o... more We present a one-sex age-structured population dynamics deterministic model with a discrete set of offsprings, child care, environmenta l pressure, and spatial migration. All individuals have pre-reproductive, reproductive, and post-reproductive age intervals. Individuals of reproductive age are divided into fertile si ngle and taking child care groups. All individuals of pre-reproductive age are divided into young (under maternal care) and juvenile (offspring who can live without maternal care) classes. It is assumed that all young offsprings move together with their mother and that after the death of mother all her young offsprings are killed. The model consists of integro-partial differential equations subject to the conditions of the integral type. Number of these equations depends on a biologically possible maximal newborns number of the same generation produced by an individual. The existence and uniqueness theorem is proved, separable solutions are studied, and the long time ...
Informatica (lithuanian Academy of Sciences) - INFORMATICALT, 1999
A general model for pair formation in age, sex, and sociologically structured interact- ing human... more A general model for pair formation in age, sex, and sociologically structured interact- ing human communities is presented. More precisely, the religion factor is taken into account. The model describes dynamics of interacting religions which tolerate both uniconfessional pairs and those with different religions. Two particular models are analyzed. One of them describes the uni- confessional pairs dynamics and allows the religion change only for the sake of marriage. The other one demonstrates the evolution of communities forbidding any confession change. In the case of constant vital rates solutions of these two models are constructed and the longtime behavior of the total numbers of single adults and pairs of each community is demonstrated.
Mathematical Modelling of Population Dynamics, 2003
ABSTRACT Two asexual density-dependent population dynamic models with age-dependence and child ca... more ABSTRACT Two asexual density-dependent population dynamic models with age-dependence and child care are presented. One of them includes random diffusion while in the other the population is assumed to be non-dispersing. The population consists of the young (under maternal care), juvenile, and adult classes. Death moduli of the juvenile and adult classes in both models are decomposed into a sum of two terms. The first presents death rate by the natural causes while the other describes the environmental influence depending on the total density of the juvenile and adult individuals. An existence and uniqueness theorem is proved, a class of separable solutions is constructed, and the large time behavior of general and separable solutions is given for the non-dispersing population with stationary vital rates. Steady-state and separable solutions are constructed and the large time behavior of separable solutions is studied for the population with spatial dispersal.
A model for toxin-antibody interaction and toxin trafficking towards the endoplasmic-reticulum is... more A model for toxin-antibody interaction and toxin trafficking towards the endoplasmic-reticulum is presented. Antibody and toxin (ricin) initially are delivered outside the cell. The model involves: the pinocytotic (cellular drinking) and receptor-mediated toxin internalization modes from the extracellular into the intracellular domain, its exocytotic excretion from the cytosol back to the extracellular medium, the intact toxin retrograde transport to the endoplasmic reticulum, the anterograde toxin movement outward from the cell across the plasma membrane, the lysosomal toxin degradation, and the toxin clearance (removal from the system) flux. The model consists of a set of coupled PDEs. Using an averaging procedure, the model is reduced to a system of coupled ODEs. Both PDEs and ODEs systems are solved numerically. Numerical results are illustrated by figures and discussed.
We present results of the numerical investigation of the homogenous Dirichlet and Neumann problem... more We present results of the numerical investigation of the homogenous Dirichlet and Neumann problems to an age-sex-structured population dynamics deterministic model taking into account random mating, female's pregnancy, and spatial diffusion. We prove the existence of separable solutions to the non-dispersing population model and, by using the numerical experiment, corroborate their local stability.
The Sharpe-Lotka-McKendrick-von Foerster one-sex population model and the Fredrickson-Hoppenstead... more The Sharpe-Lotka-McKendrick-von Foerster one-sex population model and the Fredrickson-Hoppensteadt-Staroverov two-sex population one are well known in mathematical biology. But they do not describe the dynamics of populations with child care. In recent years some models were proposed to describe dynamics of wild populations with child care. Some of them are based on the notion of the density of offspring under maternal (or parental) care. However, such models do not ensure the fact that offspring under maternal (or parental) care move together with their mothers (or both parents). In recent years, to solve this problem, some models of a sex-age-structured population, based on the discrete set of newborns, were proposed and examined analytically. Numerical schemes for solving a one-sex age-structured population model with and without spatial dispersal taking into account a discrete set of offspring and child care are proposed and results are discussed in this paper. The model consist...
It was recently shown that the treatment effect of an antibody can be described by a consolidated... more It was recently shown that the treatment effect of an antibody can be described by a consolidated parameter which includes the reaction rates of the receptor-toxin-antibody kinetics and the relative concentration of reacting species. As a result, any given value of this parameter determines an associated range of antibody kinetic properties and its relative concentration in order to achieve a desirable therapeutic effect. In the current study we generalize the existing kinetic model by explicitly taking into account the diffusion fluxes of the species. A refined model of receptor-toxin-antibody (RTA) interaction is studied numerically. The protective properties of an antibody against a given toxin are evaluated for a spherical cell placed into a toxin-antibody solution. The selection of parameters for numerical simulation approximately corresponds to the practically relevant values reported in the literature with the significant ranges in variation to allow demonstration of different regimes of intracellular transport. The proposed refinement of the RTA model may become important for the consistent evaluation of protective potential of an antibody and for the estimation of the time period during which the application of this antibody becomes the most effective. It can be a useful tool for in vitro selection of potential protective antibodies for progression to in vivo evaluation.
A model for toxin inhibition of protein synthesis inside eukaryotic cells is presented. Mitigatio... more A model for toxin inhibition of protein synthesis inside eukaryotic cells is presented. Mitigation of this effect by introduction of an antibody is also studied. Antibody and toxin (ricin) initially are delivered outside the cell. The model describes toxin internalization from the extracellular into the intracellular domain, its transport to the endoplasmic reticulum (ER) and the cleavage inside the ER into the RTA and RTB chains, the release of RTA into the cytosol, inactivation (depurination) of ribosomes, and the effect on translation. The model consists of a set of ODEs which are solved numerically. Numerical results are illustrated by figures and discussed.
We present a one-sex age-structured population dynamics deterministic model with a discrete set o... more We present a one-sex age-structured population dynamics deterministic model with a discrete set of offsprings, child care, environmenta l pressure, and spatial migration. All individuals have pre-reproductive, reproductive, and post-reproductive age intervals. Individuals of reproductive age are divided into fertile si ngle and taking child care groups. All individuals of pre-reproductive age are divided into young (under maternal care) and juvenile (offspring who can live without maternal care) classes. It is assumed that all young offsprings move together with their mother and that after the death of mother all her young offsprings are killed. The model consists of integro-partial differential equations subject to the conditions of the integral type. Number of these equations depends on a biologically possible maximal newborns number of the same generation produced by an individual. The existence and uniqueness theorem is proved, separable solutions are studied, and the long time ...
Informatica (lithuanian Academy of Sciences) - INFORMATICALT, 1999
A general model for pair formation in age, sex, and sociologically structured interact- ing human... more A general model for pair formation in age, sex, and sociologically structured interact- ing human communities is presented. More precisely, the religion factor is taken into account. The model describes dynamics of interacting religions which tolerate both uniconfessional pairs and those with different religions. Two particular models are analyzed. One of them describes the uni- confessional pairs dynamics and allows the religion change only for the sake of marriage. The other one demonstrates the evolution of communities forbidding any confession change. In the case of constant vital rates solutions of these two models are constructed and the longtime behavior of the total numbers of single adults and pairs of each community is demonstrated.
Mathematical Modelling of Population Dynamics, 2003
ABSTRACT Two asexual density-dependent population dynamic models with age-dependence and child ca... more ABSTRACT Two asexual density-dependent population dynamic models with age-dependence and child care are presented. One of them includes random diffusion while in the other the population is assumed to be non-dispersing. The population consists of the young (under maternal care), juvenile, and adult classes. Death moduli of the juvenile and adult classes in both models are decomposed into a sum of two terms. The first presents death rate by the natural causes while the other describes the environmental influence depending on the total density of the juvenile and adult individuals. An existence and uniqueness theorem is proved, a class of separable solutions is constructed, and the large time behavior of general and separable solutions is given for the non-dispersing population with stationary vital rates. Steady-state and separable solutions are constructed and the large time behavior of separable solutions is studied for the population with spatial dispersal.
A model for toxin-antibody interaction and toxin trafficking towards the endoplasmic-reticulum is... more A model for toxin-antibody interaction and toxin trafficking towards the endoplasmic-reticulum is presented. Antibody and toxin (ricin) initially are delivered outside the cell. The model involves: the pinocytotic (cellular drinking) and receptor-mediated toxin internalization modes from the extracellular into the intracellular domain, its exocytotic excretion from the cytosol back to the extracellular medium, the intact toxin retrograde transport to the endoplasmic reticulum, the anterograde toxin movement outward from the cell across the plasma membrane, the lysosomal toxin degradation, and the toxin clearance (removal from the system) flux. The model consists of a set of coupled PDEs. Using an averaging procedure, the model is reduced to a system of coupled ODEs. Both PDEs and ODEs systems are solved numerically. Numerical results are illustrated by figures and discussed.
We present results of the numerical investigation of the homogenous Dirichlet and Neumann problem... more We present results of the numerical investigation of the homogenous Dirichlet and Neumann problems to an age-sex-structured population dynamics deterministic model taking into account random mating, female's pregnancy, and spatial diffusion. We prove the existence of separable solutions to the non-dispersing population model and, by using the numerical experiment, corroborate their local stability.
The Sharpe-Lotka-McKendrick-von Foerster one-sex population model and the Fredrickson-Hoppenstead... more The Sharpe-Lotka-McKendrick-von Foerster one-sex population model and the Fredrickson-Hoppensteadt-Staroverov two-sex population one are well known in mathematical biology. But they do not describe the dynamics of populations with child care. In recent years some models were proposed to describe dynamics of wild populations with child care. Some of them are based on the notion of the density of offspring under maternal (or parental) care. However, such models do not ensure the fact that offspring under maternal (or parental) care move together with their mothers (or both parents). In recent years, to solve this problem, some models of a sex-age-structured population, based on the discrete set of newborns, were proposed and examined analytically. Numerical schemes for solving a one-sex age-structured population model with and without spatial dispersal taking into account a discrete set of offspring and child care are proposed and results are discussed in this paper. The model consist...
It was recently shown that the treatment effect of an antibody can be described by a consolidated... more It was recently shown that the treatment effect of an antibody can be described by a consolidated parameter which includes the reaction rates of the receptor-toxin-antibody kinetics and the relative concentration of reacting species. As a result, any given value of this parameter determines an associated range of antibody kinetic properties and its relative concentration in order to achieve a desirable therapeutic effect. In the current study we generalize the existing kinetic model by explicitly taking into account the diffusion fluxes of the species. A refined model of receptor-toxin-antibody (RTA) interaction is studied numerically. The protective properties of an antibody against a given toxin are evaluated for a spherical cell placed into a toxin-antibody solution. The selection of parameters for numerical simulation approximately corresponds to the practically relevant values reported in the literature with the significant ranges in variation to allow demonstration of different regimes of intracellular transport. The proposed refinement of the RTA model may become important for the consistent evaluation of protective potential of an antibody and for the estimation of the time period during which the application of this antibody becomes the most effective. It can be a useful tool for in vitro selection of potential protective antibodies for progression to in vivo evaluation.
A model for toxin inhibition of protein synthesis inside eukaryotic cells is presented. Mitigatio... more A model for toxin inhibition of protein synthesis inside eukaryotic cells is presented. Mitigation of this effect by introduction of an antibody is also studied. Antibody and toxin (ricin) initially are delivered outside the cell. The model describes toxin internalization from the extracellular into the intracellular domain, its transport to the endoplasmic reticulum (ER) and the cleavage inside the ER into the RTA and RTB chains, the release of RTA into the cytosol, inactivation (depurination) of ribosomes, and the effect on translation. The model consists of a set of ODEs which are solved numerically. Numerical results are illustrated by figures and discussed.
Uploads
Papers by Vladas Skakauskas
by introduction of an antibody is also studied. Antibody and toxin (ricin) initially are delivered outside the cell.
The model describes toxin internalization from the extracellular into the intracellular domain, its transport to
the endoplasmic reticulum (ER) and the cleavage inside the ER into the RTA and RTB chains, the release of RTA
into the cytosol, inactivation (depurination) of ribosomes, and the effect on translation. The model consists of a set of ODEs which are solved numerically. Numerical results are illustrated by figures and discussed.
by introduction of an antibody is also studied. Antibody and toxin (ricin) initially are delivered outside the cell.
The model describes toxin internalization from the extracellular into the intracellular domain, its transport to
the endoplasmic reticulum (ER) and the cleavage inside the ER into the RTA and RTB chains, the release of RTA
into the cytosol, inactivation (depurination) of ribosomes, and the effect on translation. The model consists of a set of ODEs which are solved numerically. Numerical results are illustrated by figures and discussed.