Daqing Jiang

Daqing Jiang
Northeast Normal University · School of Mathematics and Statistics

About

422
Publications
44,511
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8,724
Citations
Citations since 2016
219 Research Items
5517 Citations
201620172018201920202021202202004006008001,000
201620172018201920202021202202004006008001,000
201620172018201920202021202202004006008001,000
201620172018201920202021202202004006008001,000

Publications

Publications (422)
Article
Full-text available
This paper is concerned with the stochastic dynamics of a multi-group stochastic SEIRI epidemic model with logistic population growth, standard incidence rate, and Markovian switching. For this purpose, we first show that the solution of the stochastic system is positive and global. Then we obtain sufficient conditions for the extinction of disease...
Article
Full-text available
Although the long‐term dynamics of the prey‐predator model has analyzed in the passing decades, the threshold of extinction and persistence has not been well unified, especially the higher order perturbation affects the phytoplankton‐zooplankton dynamics. Here, we formulate a stochastic phytoplankton‐zooplankton model with nonlinear perturbation. A...
Article
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In this study, considering the Ornstein–Uhlenbeck process to perturb the infection rate, we develop a HTLV-I infection model with general infection form. By constructing several suitable Lyapunov functions and a compact set, and then using the strong law of numbers and Fatou’s lemma, we obtain sufficient conditions for the existence and uniqueness...
Article
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In this paper, we examine a stochastic prey-predator system with fear effect and general anti-predator behavior. To tackle the impact of stochastic perturbations, we first propose a p-stochastic threshold method to construct several necessary p-Lyapunov functions. Then by defining a quasi-carrying capacity x∗, sufficient conditions are established...
Article
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Due to the continuous interference of environmental white noise, the dynamical behaviors of a stochastic SIQR epidemic model with mean-reverting Ornstein–Uhlenbeck process and standard incidence are considered. Several conclusions can be verified after dimensionality reduction. We study the existence and uniqueness of positive solution by construct...
Article
Full-text available
In this paper, we propose a stochastic SEIRS rabies epidemic models with two patches to investigate the spatial spread of rabies under the influence of environmental noise. Adopting a new technique to construct the stochastic Lyapunov functions, we obtain the sufficient conditions for the existence of an ergodic stationary distribution. In addition...
Article
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In this paper, we consider a high-dimensional stochastic HIV/AIDS model that incorporates both multiple stages treatment and higher order perturbation. Firstly, we establish sufficient criteria for the existence of a unique ergodic stationary distribution by making use of stochastic Lyapunov analysis method. Stationary distribution shows that the d...
Article
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In this paper, we investigate the dynamics of a high‐dimensional human immunodeficiency virus (HIV)/acquired immunodeficiency syndrome (AIDS) model with treatment and standard incidence, which is perturbed by telegraph noise. The switching is formulated by a continuous time Markov chain. Firstly, we show the existence and uniqueness of the global p...
Article
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Due to many uncertain factors, the microorganism flocculation models could be affected by environmental noise. The paper aims to discuss the dynamical behavior of a stochastic microorganism flocculation model, including the extinction and the persistence. Moreover, the expression of density function near the positive equilibrium point is explicitly...
Article
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This paper develops the spread dynamics of a 11-dimensional stochastic multi-host zoonotic model for the dog-CFB-human transmission of rabies, which is formulated as a piecewise deterministic Markov process. We firstly prove the existence of the global unique positive solution. Then we obtain sufficient conditions for the extinction and persistence...
Article
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In this paper, we study a three-dimensional stochastic vegetation–water model in arid ecosystems, where the soil water and the surface water are considered. First, for the deterministic model, the possible equilibria and the related local asymptotic stability are studied. Then, for the stochastic model, by constructing some suitable stochastic Lyap...
Article
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Considering the important role that food chains play in ecosystems, in this paper, we study a three-species stochastic food chain model in which the growth rates and death rates are governed by Ornstein–Uhlenbeck process. The main purpose of this paper is to study the dynamic properties of the model. We first prove the existence and uniqueness of t...
Article
Full-text available
Phytoplankton is an important indicator organism to evaluate the quality of water environment, which may reflect the nutritional level of the sea area. Conversely, environmental conditions can directly affect the community structure of phytoplankton. A stochastic phytoplankton–zooplankton model considering non-degenerate and degenerate diffusions i...
Article
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In this paper, we develop and study a stochastic logistic model by incorporating diffusion and two Ornstein–Uhlenbeck processes, which is a stochastic non-autonomous system. We first show the existence and uniqueness of the global solution of the system with any initial value. After that, we study the pth moment boundedness, asymptotic pathwise est...
Article
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Since November 2019, each country in the world has been affected by COVID-19, which has claimed more than four million lives. As an infectious disease, COVID-19 has a stronger transmission power and faster propagation speed. In fact, environmental noise is an inevitable important factor in the real world. This paper mainly gives a new random infect...
Article
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Considering the cannibalism behavior of many groups of animals in nature, a two-stage model of social insects with egg cannibalism and nonlinear perturbations is constructed and investigated in this paper. First, we establish sufficient conditions for the existence and uniqueness of an ergodic stationary distribution ψ(⋅) of the stochastic model. I...
Article
A stochastic chemostat model in random environments that is driven by Brownian motions and subjected to Markov regime switching is considered. The new break-even concentration, i.e., critical value between persistence in mean and extinction is explored for the microorganism species. Moreover, sufficient conditions for ergodicity and positive recurr...
Article
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In this paper, we developed and studied a stochastic HIV model with nonlinear perturbation. Through a rigorous analysis, we firstly showed that the solution of the stochastic model is positive and global. Then, by employing suitable stochastic Lyapunov functions, we prove that the stochastic model admit a unique ergodic stationary distribution. In...
Article
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In order to study the effect of nonlinear perturbation on virus infection of target cells, in this paper, we propose a stochastic virus infection model with multitarget cells and exposed state. Firstly, by constructing novel stochastic Lyapunov functions, we theoretically prove that the solution of the stochastic model is positive and global. Secon...
Article
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Recently, the stochastic θ-threshold method has been proposed to analyze the impact of second-order perturbations on disease persistence. In this paper, considering the complexity of the environmental variations in the actual situation, we construct and study a stochastic staged progression HIV/AIDS infection model with third-order perturbations. F...
Article
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Considering the survival regulation mechanisms of many groups of animals and the complexity of random variations in ecosystem, in this paper, we mainly formulate and study a stochastic non-autonomous population model with Allee effects and two mean-reverting Ornstein–Uhlenbeck processes. First, the biological implication of introducing the Ornstein...
Article
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Considering the profound ecological implication of Allee effect, and the effects after incorporating it into models of population dynamics, a stochastic predator–prey model with Holling-(n+1) functional response and weak Allee effect is mainly investigated in this paper. Firstly, we verify the existence of unique global positive solution to the mod...
Article
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In this paper, we investigate an SIRI epidemic model with nonlinear incidence rate and high‐order stochastic perturbation. First, we obtain a stochastic threshold R0P related to the basic reproduction number R0. A key contribution of our paper is to derive the existence and uniqueness of an ergodic stationary distribution of the stochastic model if...
Article
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In this paper, we consider a stochastic SIR epidemic model with general disease incidence rate and perturbation caused by nonlinear white noise and Le´\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidema...
Article
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Many turbidostat models are affected by environmental noise due to various complicated and uncertain factors, and Ornstein-Uhlenbeck process is a more effective and precise way. We formulate a stochastic turbidostat system incorporating Ornstein-Uhlenbeck process in this paper and develop dynamical behavior for the stochastic model, which includes...
Article
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Infectious disease transmission, mainly affected by media coverage and stochastic perturbations, has imposed great social financial burden on the community in the past few decades and even threatened public health. However, there are few studies devoted to the theoretical dynamics of epidemic models with media coverage and biologically reasonable s...
Article
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Considering the effect of stochasticity including white noise and colored noise, this paper aims to study a hybrid stochastic cholera epidemic model with waning vaccine‐induced immunity and nonlinear telegraph perturbations. First, we derive a critical value ℛ0C related to the basic reproduction number ℛ0 of the deterministic model. The key aim of...
Article
This paper focuses on the spread dynamics of an HIV/AIDS model with multiple stages of infection and treatment, which is disturbed by both white noise and telegraph noise. Switching between different environmental states is governed by Markov chain. Firstly, we prove the existence and uniqueness of the global positive solution. Then we investigate...
Article
Echinococcosis, one of the most serious zoonotic diseases, has a severe impact on the human health and economic development. This paper mainly focuses on the effect of stochastic variability on transmission dynamics of echinococcosis. A stochastic model describing the transmission of echinococcus granulosus in dog-livestock-human is proposed. By us...
Article
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Birth vaccinations are becoming more common in society. In this paper, we describe the developed stochastic susceptible-vaccinated-infected-recovered (SVIR) epidemic model with vaccination of newborns that enable us to concern the stationary distribution and further density function. By constructing a series suitable Lyapunov function, we derive th...
Article
In this paper, a stochastic HIV model with CD4+ T-cell proliferation, cell-free infection and cell-to-cell transmission is proposed. By constructing suitable Lyapunov function, we establish the existence of unique and ergodic stationary distribution of the model. Moreover, by using asymptotic analysis and employing the Fokker-Planck equation, we de...
Article
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Due to the complex set of abiotic and biotic interaction variables in the ecosystems, the dynamics of animal populations are generally considered to be driven in astate‐dependent manner. This paper presents an analysis of a stochastic Nicholson's blowflies model with distributed delay, which consists of the existence and uniqueness of globally posi...
Article
Focusing on the unpredictability of person-to-person contacts and the complexity of random variations in nature, this paper will formulate a stochastic SIR epidemic model with nonlinear incidence rate and general stochastic noises. First, we derive a stochastic critical value R0S related to the basic reproduction number R0. Via our new method in co...
Article
The present paper deals with the problem of a stochastic predator-prey model with continuous time delay. In the case that the integral kernel is the function ae−at, the persistence in the mean and extinction of this solution are derived by making use of Lyapunov analysis methods. Numerical simulations for a hypothetical set of parameter values are...
Article
Time delay, where it depends on the current state and on the past situation, is often occurred in biological activities, for example, the process by which microorganism consume nutrients into their available biomass is not instantaneous. This investigation inspects the dynamic behavior of stochastic turbidostat model coupled with distributed delay...
Article
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This paper pays main attention to the dynamics behaviors of a stochastic echinococcosis infection model with environmental noise. The existence and uniqueness of the stochastic model is showed in this paper. We obtain the sufficient condition of the ergodic stationary distribution. What is more, the condition of extinction of the stochastic model i...
Conference Paper
In this paper, a nonautonomous delay differential equation of microorganism flocculation is established by considering the influence of external conditions such as seasonal alternation and ocean current movement on the ecological function of microorganism population. At the same time, the dynamic change characteristics of microorganism population i...
Article
In this article, a stochastic differential equation model is proposed to investigate how the environmental noise affects the transmission dynamics of the interaction between crime, criminality and victimization with the influence of case reporting through the short message service (SMS). We prove that there is a unique global positive solution of t...
Article
During the HIV infection process in vitro cell cultures, recent experimental and mathematical investigations have revealed that there are two fundamentally distinct viral transmission modes: cell-free infection and cell-to-cell transmission. A stochastic HIV model with latent infection, cell-free infection and cell-to-cell transmission is formulate...
Article
A stochastic SEI (Susceptible-Exposed-Infected) epidemic model with general distributed delay is studied in this paper. First, we prove the existence and uniqueness of a global positive solution to the stochastic system. By means of the Lyapunov method, we verify the existence of a stationary distribution of the positive solution under a stochastic...
Article
In this paper, we analyze a stochastic multigroup DS-DI-A model for the transmission of HIV. We establish sufficient conditions for the existence and uniqueness of an ergodic stationary distribution of positive solutions to the system by constructing a series of suitable Lyapunov functions. Moreover, we make up adequate conditions for complete erad...
Article
This paper considers a stochastic chemostat model with degenerate diffusion. Firstly, the Markov semigroup theory is used to establish sufficient criteria for the existence of a unique stable stationary distribution. The authors show that the densities of the distributions of the solutions can converge in L1 to an invariant density. Then, condition...
Article
In this paper, we present a stochastic hepatitis B virus (HBV) infection model and the dynamic behaviors of the model are investigated. When the fraction of vertical transmission μωνC is not considered to be new infections, the existence and ergodicity of the stationary distribution of the model are obtained by constructing a suitable Lyapunov func...
Article
In this paper, we consider a Lotka–Volterra food chain chemostat model that incorporates both distributed delay and stochastic perturbations. We obtain sufficient conditions for the existence of stationary distribution by constructing suitable Lyapunov functions. Stationary distribution indicates the two species in the chemostat can coexist in the...
Article
Full-text available
This article focuses on a stochastic viral model with distributed delay and CTL responsiveness. It is shown that the viral disease will be extinct if the stochastic reproductive ratio is less than one. However, when the stochastic reproductive ratio is more than one, the viral infection system consists of an ergodic stationary distribution. Further...
Article
A stochastic waterborne disease model is analyzed to reveal the effects of the white noise and telegraph noise. For this stochastic model, a critical quantity \(R_0^s\) is derived, which depends on not only model parameters but also environmental noises. If \(R_0^s>1\), then this model admits an ergodic stationary distribution. One of the most impo...
Article
In this paper, we analyze the salient features of a stochastic multigroup SEI epidemic model. We obtain sufficient criteria for the existence and uniqueness of an ergodic stationary distribution of positive solutions to the system by establishing a series of suitable Lyapunov functions. In a biological viewpoint, the existence of a stationary distr...
Preprint
Many turbidostat models are affected by environmental noise due to various complicated and uncertain factors, and Ornstein-Uhlenbeck process is a more effective and precise way. We formulate a stochastic turbidostat system incorporating Ornstein-Uhlenbeck process in this paper, develop dynamical behavior for the stochastic model, which include the...
Article
In this paper, we are concerned with the global dynamical behavior of a multigroup SVIR epidemic model, which is formulated as a piecewise-deterministic Markov process. We first obtain sufficient criteria for extinction of the diseases. Then we establish sufficient criteria for persistence in the mean of the diseases. Moreover, in the case of persi...
Article
In this paper, we study the dynamical behavior of a stochastic two-compartment model of [Formula: see text]-cell chronic lymphocytic leukemia, which is perturbed by white noise. Firstly, by constructing suitable Lyapunov functions, we establish sufficient conditions for the existence of a unique ergodic stationary distribution. Then, conditions for...
Article
Full-text available
Recently, considering the temporary immunity of individuals who have recovered from certain infectious diseases, Liu et al. (Phys A Stat Mech Appl 551:124152, 2020) proposed and studied a stochastic susceptible-infected-recovered-susceptible model with logistic growth. For a more realistic situation, the effects of quarantine strategies and stochas...
Article
This paper considers a stochastic aquatic toxin-mediated predator-prey model. Our main aim is to investigate the effects of environmental toxins and white noise on the population dynamics of this model. First, we prove that there is a global positive solution for any given initial value. Then we show the existence of a unique stationary distributio...
Article
Combining a deterministic SEQIHRS model proposed by Sahu et al. (2015) and the present mathematical modelling of media coverage effect (2020), a hybrid stochastic SEQIHR model, perturbed by both nonlinear white noise and colored noise, is formulated and studied for the transmission dynamics of an infectious disease with media coverage, quarantine s...
Article
This study investigated the impact of white noise on the HIV/AIDS model with a cytotoxic T lymphocyte (CTL) immune response. The model introduced the interactions between the virus and two kinds of target cells, CD4+ T cells and macrophages. It was theoretically proved that the solution of the stochastic model is positive and global, as well as the...
Article
In this paper, we analyze a higher-order stochastically perturbed multigroup staged-progression model for the transmission of HIV with saturated incidence rate. We obtain sufficient conditions for the existence and uniqueness of an ergodic stationary distribution of positive solutions to the system by establishing a suitable stochastic Lyapunov fun...
Article
Full-text available
In this paper, an HIV infection model with latent infection, Beddington-DeAngelis infection function, B-cell immune response and four time delays is formulated. The well-posedness of the model solution is rigorously derived, and the basic reproduction number $\mathcal{R}_0$ and the B-cell immune response reproduction number $\mathcal{R}_1$ are also...
Article
Considering the complexity of random variations in ecosystem, a n-species Gilpin-Ayala competition system with nonlinear noises is studied in this paper. Using our developed ϵ-stochastic criterion method in eliminating nonlinear perturbations, we construct several suitable Lyapunov functions to obtain the threshold for the existence and uniqueness...
Article
In this paper, we investigate an SIR epidemic model with varying population sizes and regime switching in a two patch setting. Sufficient conditions for extinction and persistence in the mean of the diseases are obtained. In addition, we establish sufficient conditions for the existence of positive recurrence of the solutions to the model in the ca...
Article
This paper discusses the dynamics of a Gilpin–Ayala competition model of two interacting species perturbed by white noise. We obtain the existence of a unique global positive solution of the system and the solution is bounded in [Formula: see text]th moment. Then, we establish sufficient and necessary conditions for persistence and the existence of...
Article
In this paper, we analyze a stochastic rabies epidemic model which is perturbed by both white noise and telegraph noise. First, we prove the existence of the unique global positive solution. Second, by constructing an appropriate Lyapunov function, we establish a sufficient condition for the existence of a unique ergodic stationary distribution of...
Article
In this paper, we construct and analyze a stochastic predator–prey system where apart from direct predation the prey population is affected by the fear induced from predators. We obtain sufficient criteria for the existence and uniqueness of an ergodic stationary distribution of positive solutions to the system by establishing a series of suitable...
Article
Considering the great effect of vaccination and the unpredictability of environmental variations in nature, a stochastic Susceptible-Vaccinated-Infected-Susceptible (SVIS) epidemic model with standard incidence and vaccination strategies is the focus of the present study. By constructing a series of appropriate Lyapunov functions, the sufficient cr...
Article
Full-text available
This paper deals with a stochastic predator‐prey model in chemostat which is driven by Markov regime switching. For the asymptotic behaviors of this stochastic system, we establish the sufficient conditions for the existence of the stationary distribution. Then, we investigate, respectively, the extinction of the prey and predator populations. We e...
Article
Full-text available
In this paper, we study the dynamical behavior of a stochastic food chain chemostat model, in which the white noise is proportional to the variables. Firstly, we prove the existence and uniqueness of the global positive solution. Then by constructing suitable Lyapunov functions, we show the system has a unique ergodic stationary distribution. Furth...
Article
Full-text available
The mathematical model with time delay is often more practical because it is subject to current and past state. What remains unclear are the details, such as how time delay and sudden environmental changes influence the dynamic behavior of systems. The purpose of this paper is to analyze the long-time behavior of a stochastic Nicholson’s blowflies...
Article
In this paper, we study the dynamical behavior of a higher order stochastically perturbed HIV/AIDS model with differential infectivity and amelioration. We derive sufficient criteria for the existence and uniqueness of an ergodic stationary distribution of positive solutions to the system by establishing a series of suitable Lyapunov functions. In...
Article
Focusing on the results of Rajasekar (2020) and the continuous dynamics of stochastic differential equation (SDE) developed by Mao (1997), a stochastic SIRSI epidemic model with saturation incidence rate and logistic growth is investigated in this paper. First, we propose and prove that the unique solution of stochastic model is globally positive....
Article
In this paper, we analyze two stochastic predator–prey models with distributed delay and stage structure for prey. For the nonautonomous periodic case of the model, by using Khasminskii’s theory of periodic solution, we show that the system has at least one positive [Formula: see text]-periodic solution. For the model which is disturbed by both whi...