本文研究了具有布朗运动的污染物对河流种群影响的时空模型的长期行为。首先在传统控制策略的基础上,创新性地引入了随机扰动,提出了一种新型的适应性控制策略,以应对环境变化带来的不确定性。证明了该模型具有全局正解和平稳分布的存...本文研究了具有布朗运动的污染物对河流种群影响的时空模型的长期行为。首先在传统控制策略的基础上,创新性地引入了随机扰动,提出了一种新型的适应性控制策略,以应对环境变化带来的不确定性。证明了该模型具有全局正解和平稳分布的存在唯一性,确保了模型的理论基础,为后续分析奠定基础。然后,考虑到污染物对河流种群的影响,将河流种群扩散模型引入控制策略,利用庞特里亚金的随机极大值原理,得到了随机河流种群扩散模型的近优性控制的充要条件。This paper studies the long-term behavior of a spatiotemporal model concerning the impact of pollutants with Brownian motion on river populations. First, based on traditional control strategies, we innovatively introduce stochastic perturbations and propose a novel adaptive control strategy to address the uncertainties brought about by environmental changes. We prove the existence and uniqueness of global positive solutions and stationary distributions for the model, ensuring its theoretical foundation and laying the groundwork for subsequent analyses. Next, considering the impact of pollutants on river populations, we incorporate the river population diffusion model into control strategies and, using Pontryagin’s stochastic maximum principle, derive the necessary and sufficient conditions for near-optimal control of the stochastic river population diffusion model.展开更多
本文建立了一类随机多种群易感者、感染者和移出者(susceptical infective and removal,SIR)传染病微分方程模型,针对模型找到与随机因素相关的阈值用于判定疾病的消亡与否.通过阈值里随机干扰的作用给出疾病防控的新方法一随机镇定.与...本文建立了一类随机多种群易感者、感染者和移出者(susceptical infective and removal,SIR)传染病微分方程模型,针对模型找到与随机因素相关的阈值用于判定疾病的消亡与否.通过阈值里随机干扰的作用给出疾病防控的新方法一随机镇定.与此同时,本文探究无病平衡点的全局稳定性并通过数据仿真实例解释上述理论结果的正确性和可行性.展开更多
The research on spatial epidemic models is a topic of considerable recent interest. In another hand, the advances in computer technology have stimulated the development of stochastic models. Metapopulation models are ...The research on spatial epidemic models is a topic of considerable recent interest. In another hand, the advances in computer technology have stimulated the development of stochastic models. Metapopulation models are spatial designs that involve movements of individuals between distinct subpopulations. The purpose of the present work has been to develop stochastic models in order to study the transmission dynamics and control of infectious diseases in metapopulations. The authors studied Susceptible-Infected-Susceptible （SIS） and Susceptible-lnfected-Recovered （SIR） epidemic schemes, using the Gillespie algorithm, Computational numerical simulations were carried in order to explore the models. The results obtained show how the dynamics of transmission and the application of control measures within each subpopulation may affect all subpopulations of the system. They also show how the distribution of control measures among subpopulations affects the efficacy of these strategies. The dynamics of the stochastic models developed in the current study follow the trends observed in the classic deterministic designs. Also, the present models exhibit fluctuating behavior. This work highlights the importance of the spatial distribution of the population in spread and control of infectious diseases. In addition, it shows how chance could play an important role in these scenarios.展开更多
This paper is concerned with a stochastic single-species system with Levy jumps in a polluted environment. Some sufficient conditions on extinction, non-persistence in the mean, weak persistence in the mean, strong pe...This paper is concerned with a stochastic single-species system with Levy jumps in a polluted environment. Some sufficient conditions on extinction, non-persistence in the mean, weak persistence in the mean, strong persistence in the mean, stability in the mean and stochastic permanence are obtained. The threshold between extinction and weak persistence in the mean is established. At the same time, under a simple condition, it is proved that this threshold also is the threshold between extinction and stability in the mean. The results reveal that L@vy jumps have significant effects to the persistence and extinction results.展开更多
Two stochastic models are derived for a susceptible-infectious-susceptible epidemic spreading through a metapopulation： a continuous time Markov chain （CTMC） model and an It6 stochastic differential equation （SDE...Two stochastic models are derived for a susceptible-infectious-susceptible epidemic spreading through a metapopulation： a continuous time Markov chain （CTMC） model and an It6 stochastic differential equation （SDE） model. The stochastic models are numerically compared. Close agreement suggests that computationally intense CTMC simulations can be approximated by simpler SDE simulations. Differential equations for the moments of the SDE probability distribution are also derived, the steady states are solved numerically using a moment closure technique, and these results are compared to simulations. The moment closure technique only coarsely approximates simulation results. The effect of model parameters on stability of the disease-free equilibrium is also numerically investigated.展开更多
In this paper, the dynamics of a stochastic model for algal bloom with nutrient recy- cling is investigated. The model incorporates a white noise term in the growth equation of algae population to describe the effects...In this paper, the dynamics of a stochastic model for algal bloom with nutrient recy- cling is investigated. The model incorporates a white noise term in the growth equation of algae population to describe the effects of random fluctuations in the environment, and a nutrient recycling term in the nutrient equation to account for the conversion of detritus into nutrient. The existence and uniqueness of the global positive solution of the model is first proved. Then we study the long-time behavior of the model. Conditions for the extinction and persistence in the mean of the algae population are established. By using the theory of integral Markov semigroups, we show that the model has an invari- ant and asymptotically stable density. Numerical simulations illustrate our theoretical results.展开更多
文摘本文研究了具有布朗运动的污染物对河流种群影响的时空模型的长期行为。首先在传统控制策略的基础上,创新性地引入了随机扰动,提出了一种新型的适应性控制策略,以应对环境变化带来的不确定性。证明了该模型具有全局正解和平稳分布的存在唯一性,确保了模型的理论基础,为后续分析奠定基础。然后,考虑到污染物对河流种群的影响,将河流种群扩散模型引入控制策略,利用庞特里亚金的随机极大值原理,得到了随机河流种群扩散模型的近优性控制的充要条件。This paper studies the long-term behavior of a spatiotemporal model concerning the impact of pollutants with Brownian motion on river populations. First, based on traditional control strategies, we innovatively introduce stochastic perturbations and propose a novel adaptive control strategy to address the uncertainties brought about by environmental changes. We prove the existence and uniqueness of global positive solutions and stationary distributions for the model, ensuring its theoretical foundation and laying the groundwork for subsequent analyses. Next, considering the impact of pollutants on river populations, we incorporate the river population diffusion model into control strategies and, using Pontryagin’s stochastic maximum principle, derive the necessary and sufficient conditions for near-optimal control of the stochastic river population diffusion model.
基金Supported by National Natural Science Foundation of China(61273126)Fundamental Research Funds for Guangzhou Universities(ZXJ3-2001)
文摘本文建立了一类随机多种群易感者、感染者和移出者(susceptical infective and removal,SIR)传染病微分方程模型,针对模型找到与随机因素相关的阈值用于判定疾病的消亡与否.通过阈值里随机干扰的作用给出疾病防控的新方法一随机镇定.与此同时,本文探究无病平衡点的全局稳定性并通过数据仿真实例解释上述理论结果的正确性和可行性.
文摘The research on spatial epidemic models is a topic of considerable recent interest. In another hand, the advances in computer technology have stimulated the development of stochastic models. Metapopulation models are spatial designs that involve movements of individuals between distinct subpopulations. The purpose of the present work has been to develop stochastic models in order to study the transmission dynamics and control of infectious diseases in metapopulations. The authors studied Susceptible-Infected-Susceptible （SIS） and Susceptible-lnfected-Recovered （SIR） epidemic schemes, using the Gillespie algorithm, Computational numerical simulations were carried in order to explore the models. The results obtained show how the dynamics of transmission and the application of control measures within each subpopulation may affect all subpopulations of the system. They also show how the distribution of control measures among subpopulations affects the efficacy of these strategies. The dynamics of the stochastic models developed in the current study follow the trends observed in the classic deterministic designs. Also, the present models exhibit fluctuating behavior. This work highlights the importance of the spatial distribution of the population in spread and control of infectious diseases. In addition, it shows how chance could play an important role in these scenarios.
文摘This paper is concerned with a stochastic single-species system with Levy jumps in a polluted environment. Some sufficient conditions on extinction, non-persistence in the mean, weak persistence in the mean, strong persistence in the mean, stability in the mean and stochastic permanence are obtained. The threshold between extinction and weak persistence in the mean is established. At the same time, under a simple condition, it is proved that this threshold also is the threshold between extinction and stability in the mean. The results reveal that L@vy jumps have significant effects to the persistence and extinction results.
文摘Two stochastic models are derived for a susceptible-infectious-susceptible epidemic spreading through a metapopulation： a continuous time Markov chain （CTMC） model and an It6 stochastic differential equation （SDE） model. The stochastic models are numerically compared. Close agreement suggests that computationally intense CTMC simulations can be approximated by simpler SDE simulations. Differential equations for the moments of the SDE probability distribution are also derived, the steady states are solved numerically using a moment closure technique, and these results are compared to simulations. The moment closure technique only coarsely approximates simulation results. The effect of model parameters on stability of the disease-free equilibrium is also numerically investigated.
基金This research is supported by the National Natural Science Foundation of China （11271260）, Innovation Program of Shanghai Municipal Education Committee （13ZZ116）, Shanghai Leading Academic Discipline Project （XTKX2012）, Hujiang Foundation of China （B14005） and China Scholarship Council.
文摘In this paper, the dynamics of a stochastic model for algal bloom with nutrient recy- cling is investigated. The model incorporates a white noise term in the growth equation of algae population to describe the effects of random fluctuations in the environment, and a nutrient recycling term in the nutrient equation to account for the conversion of detritus into nutrient. The existence and uniqueness of the global positive solution of the model is first proved. Then we study the long-time behavior of the model. Conditions for the extinction and persistence in the mean of the algae population are established. By using the theory of integral Markov semigroups, we show that the model has an invari- ant and asymptotically stable density. Numerical simulations illustrate our theoretical results.
