The nonlinear mixed-effects model with stochastic differential equations （SDEs） is used to model the population pharmacokinetic （PPK） data that are extended from ordinary differential equations （ODEs） by adding ...The nonlinear mixed-effects model with stochastic differential equations （SDEs） is used to model the population pharmacokinetic （PPK） data that are extended from ordinary differential equations （ODEs） by adding a stochastic term to the state equation. Compared with the ODEs, the SDEs can model correlated residuals which are ubiquitous in actual pharmacokinetic problems. The Bayesian estimation is provided for nonlinear mixed-effects models based on stochastic differential equations. Combining the Gibbs and the Metropolis-Hastings algorithms, the population and individual parameter values are given through the parameter posterior predictive distributions. The analysis and simulation results show that the performance of the Bayesian estimation for mixed-effects SDEs model and analysis of population pharmacokinetic data is reliable. The results suggest that the proposed method is feasible for population pharmacokinetic data.展开更多
Stochastic point kinetics equations(SPKEs) are a system of Ito? stochastic differential equations whose solution has been obtained by higher-order approximation.In this study, a fractional model of SPKEs has been anal...Stochastic point kinetics equations(SPKEs) are a system of Ito? stochastic differential equations whose solution has been obtained by higher-order approximation.In this study, a fractional model of SPKEs has been analyzed. The efficiency of the proposed higher-order approximation scheme has been discussed in the results section. The solutions of SPKEs in the presence of Newtonian temperature feedback have also been provided to further discuss the physical behavior of the fractional model.展开更多
This article discusses the question of how elasticity of the system is intertwined with external stochastic disturbances. The speed at which a displaced system returns to its equilibrium is a measure of density depend...This article discusses the question of how elasticity of the system is intertwined with external stochastic disturbances. The speed at which a displaced system returns to its equilibrium is a measure of density dependence in population dynamics. Population dynamics in random environments, linearized around the equilibrium point, can be represented by a Langevin equation, where populations fluctuate under locally stable (not periodic or chaotic) dynamics. I consider a Langevin model in discrete time, driven by time-correlated random forces, and examine uncertainty in locating the population equilibrium. There exists a time scale such that for times shorter than this scale the dynamics can be approximately described by a random walk;it is difficult to know whether the system is heading toward the equilibrium point. Density dependence is a concept that emerges from a proper coarse-graining procedure applied for time-series analysis of population data. The analysis is illustrated using time-series data from fisheries in the North Atlantic, where fish populations are buffeted by stochastic harvesting in a random environment.展开更多
A new approach to modeling populations incorporating stochasticity,a random environment,and individual behavior is illustrated with a specific example of two interacting populations:rabbits and grass.The derivation of...A new approach to modeling populations incorporating stochasticity,a random environment,and individual behavior is illustrated with a specific example of two interacting populations:rabbits and grass.The derivation of the system of stochastic partial differential equations(SPDEs)to show how the individual mechanisms of both populations are included.This model also has an unusual feature of a nonlocal term.The harvesting of the rabbit population is introduced as a control variable.展开更多
基金The National Natural Science Foundation of China(No.11171065,81130068)the Natural Science Foundation of Jiangsu Province(No.BK2011058)the Fundamental Research Funds for the Central Universities(No.JKPZ2013015)
文摘The nonlinear mixed-effects model with stochastic differential equations （SDEs） is used to model the population pharmacokinetic （PPK） data that are extended from ordinary differential equations （ODEs） by adding a stochastic term to the state equation. Compared with the ODEs, the SDEs can model correlated residuals which are ubiquitous in actual pharmacokinetic problems. The Bayesian estimation is provided for nonlinear mixed-effects models based on stochastic differential equations. Combining the Gibbs and the Metropolis-Hastings algorithms, the population and individual parameter values are given through the parameter posterior predictive distributions. The analysis and simulation results show that the performance of the Bayesian estimation for mixed-effects SDEs model and analysis of population pharmacokinetic data is reliable. The results suggest that the proposed method is feasible for population pharmacokinetic data.
文摘Stochastic point kinetics equations(SPKEs) are a system of Ito? stochastic differential equations whose solution has been obtained by higher-order approximation.In this study, a fractional model of SPKEs has been analyzed. The efficiency of the proposed higher-order approximation scheme has been discussed in the results section. The solutions of SPKEs in the presence of Newtonian temperature feedback have also been provided to further discuss the physical behavior of the fractional model.
文摘This article discusses the question of how elasticity of the system is intertwined with external stochastic disturbances. The speed at which a displaced system returns to its equilibrium is a measure of density dependence in population dynamics. Population dynamics in random environments, linearized around the equilibrium point, can be represented by a Langevin equation, where populations fluctuate under locally stable (not periodic or chaotic) dynamics. I consider a Langevin model in discrete time, driven by time-correlated random forces, and examine uncertainty in locating the population equilibrium. There exists a time scale such that for times shorter than this scale the dynamics can be approximately described by a random walk;it is difficult to know whether the system is heading toward the equilibrium point. Density dependence is a concept that emerges from a proper coarse-graining procedure applied for time-series analysis of population data. The analysis is illustrated using time-series data from fisheries in the North Atlantic, where fish populations are buffeted by stochastic harvesting in a random environment.
基金the input from the Optimal Control of Agent-based Model Working Group at the National Institute for Mathematical and Biological Synthesis,which is sponsored by the National Science Foundation through NSF Award DBI-1300426support from the University of Tennessee,Knoxville+3 种基金partially supported by the Department of Mathematics of the University of Tennesseepartially supported by Southern University of Science and Technology Start up fund Y01286120National Science Fundation of China grants 61873325 and 11831010partially supported by NSF under grants DMS-1007514 and DMS-1406776。
文摘A new approach to modeling populations incorporating stochasticity,a random environment,and individual behavior is illustrated with a specific example of two interacting populations:rabbits and grass.The derivation of the system of stochastic partial differential equations(SPDEs)to show how the individual mechanisms of both populations are included.This model also has an unusual feature of a nonlocal term.The harvesting of the rabbit population is introduced as a control variable.
基金supported by the National Natural Science Foundation of China(61261044,11261043,11461053)the Science and Technique Research Foundation of Ningxia Institutions of Higher Education(China)(NGY2015048)
