Daqing Jiang

• Northeast Normal University

Seasonal influenza occurs annually and is one of the most common infectious diseases in the world, posing a threat to public health security. Therefore, it is essential to study the dynamics of seasonal influenza to raise public awareness and implement scientific prevention measures. Huo et al. studied a deterministic seasonal influenza model in Ga...

With the inevitable environmental perturbations and complex population movements, the analysis of troublesome influenza is harder to proceed. Studies about the epidemic mathematical models can not only forecast the development trend of influenza, but also have a beneficial influence on the protection of health and the economy. Motivated by this, a...

To capture the underlying realistic dynamics of brucellosis infection, we propose a stochastic SEIVB-type model, where the concentration of brucella in the environment is incorporated. This paper is the first mathematical attempt to consider the Black–Karasinski process as the random effect in the modeling of epidemic transmission. It turns out tha...

A general stochastic compartment model for cholera with higher-order perturbation is proposed, which incorporates direct and indirect transmission by contaminated water. Nonlinear incidence, multiple stages of infection, multiple states of pathogen, and second-order white-noises perturbation are introduced into the model, which includes and extends...

In this study, a log-normal Ornstein–Uhlenbeck process and protection consciousness are included in a stochastic pandemic model of AIDS. For the 5-dimensional deterministic system, the local asymptotic stability of endemic equilibrium point is proved by Lyapunov function method instead of Routh–Hurwitz criterion. For stochastic system, we firstly v...

This paper is Part II of a two-part series on coexistence states study in stochastic generalized Kolmogorov systems under small diffusion. Part I provided a complete characterization for approximating invariant probability measures and density functions, while here, we focus on explicit approximations for periodic solutions in distribution. Two eas...

In this paper, we study an SICA model with a standard incidence rate, where the contact rate β\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\beta $$\end{document} is...

A stochastic influenza epidemic model where influenza virus can mutate into a mutant influenza virus is established to study the influence of environmental disturbance. And the transmission rate of the model is assumed to satisfy log-normal Ornstein–Uhlenbeck process. We verify that there exists a unique global positive solution to the stochastic m...

Controlling infectious diseases has become an increasingly complex issue, and vaccination has become a common preventive measure to reduce infection rates. It has been thought that vaccination protects the population. However, there is no fully effective vaccine. This is based on the fact that it has long been assumed that the immune system produce...

The purpose of this work is to investigate a novel stochastic SIHR epidemic model, which includes a general incidence rate and mean-reversion Ornstein–Uhlenbeck process. Firstly, the existence of global positivity of the solution is testified by Lyapunov function. Secondly, this disease will be eradicated if the reproduction number R0s<1\documentcl...

The density of a population in a natural state often fluctuates greatly, but it is not an unlimited change. Throughout the full text, we consider a stochastic predator–prey system with fear, Holling-II response function, distributed delay and mean-reverting Ornstein–Uhlenbeck process, which can better reflect the actual situation and provide theore...

Seasonal influenza occurs annually and is one of the most common infectious diseases in the world, posing a threat to public health security. Therefore, it is essential to study the dynamics of seasonal influenza to raise public awareness and implement scientific prevention measures. Huo et al. studied a deterministic seasonal influenza model in Ga...

Considering the transmission characteristics of COVID-19, we formulate a Susceptible-Exposed-Quarantine-Infected-Recovered epidemic model by five first-order differential equations to study the dynamical behaviors of diseases that have a latent period, quarantine strategy, governmental intervention and general incidence rate. After giving the basic...

Scanning the whole writing, we discuss a stochastic cooperative species system with distributed delays under the influences of Ornstein–Uhlenbeck process of mean regression. We successfully obtain the existence and uniqueness of positive solutions for stochastic system at first. Secondly, by studying the Lyapunov function, we present the existence...

In this paper, taking into account the inevitable impact of environmental perturbations on disease transmission, we primarily investigate a stochastic model for measles infection with nonlinear incidence. The transmission rate in this model follows a logarithmic normal distribution influenced by an Ornstein-Uhlenbeck (OU) process. To analyze the dy...

In this paper, assuming the certain variable satisfies the Ornstein–Uhlenbeck process, we formulate a stochastic within-host dengue model with immune response to obtain further understanding of the transmission dynamics of dengue fever. Then we analyze the dynamical properties of the stochastic system in detail, including the existence and uniquene...

In this paper, we proposed a generalized mosquito-borne epidemic model with a general nonlinear incidence rate, which was studied from both deterministic and stochastic insights. In the deterministic model, we proved that the endemic equilibrium was globally asymptotically stable when the basic reproduction number $ R_0 $ was greater than unity and...

As the evolution of species relies on not only the current state but also the past information, it is more reasonable and realistic to take delay into an ecological model. This paper deals with a stochastic predator–prey model that considers the distribution delay and assume that the intrinsic growth rate and the death rate in the model are governe...

The purpose of this work is to investigate a novel stochastic SIHR epidemic model, which includes a general incidence rate and mean-reversion Ornstein-Uhlenbeck process. Firstly, the existence of global positivity of the solution is testified by Lyapunov function. Secondly, this disease will be eradicated if R 0 s < 1 . Otherwise, if R 0 * > 1, the...

With the inevitable environmental perturbations and complex population movements, the analysis of troublesome influenza is harder to proceed. Studies about the epidemic mathematical models can not only forecast the development trend of influenza, but also have a beneficial influence on the protection of health and the economy. Motivated by this, a...

In this paper, we investigate a stochastic SIS epidemic model with logarithmic Ornstein–Uhlenbeck process and generalized nonlinear incidence. Our study focuses on the construction of stochastic Lyapunov functions to establish the threshold condition for the extinction and the existence of the stationary distribution of the stochastic system. We al...

In this paper, we construct a general four-dimensional delayed HIV infection model with virus-to-cell infection, cell-to-cell transmission, CTL immune response and parameter perturbations. By substitution, the four-dimensional delayed stochastic differential equations can be transformed into a degenerate eight-dimensional stochastic differential eq...

With the inevitable environmental perturbations and complex population movements, the analysis of troublesome influenza is harder to proceed. Studies about the epidemic mathematical models can not only forecast the development trend of influenza, but also have a beneficial influence on the protection of health and the economy. Motivated by this, a...

Two different approaches to incorporate environmental perturbations in stochastic systems are compared analytically and computationally. Then we present a stochastic model for COVID-19 that considers susceptible, exposed, infected, and recovered individuals, in which the contact rate between susceptible and infected individuals is governed by the O...

In this paper, we present a model of infection in which a virus can simultaneously infect two types of target cells. The model has a general form of infection rates in deterministic and stochastic settings, incorporating bilinear infection rates, saturated incidences and half-saturated incidences. In the deterministic case, we investigate the exist...

In this paper, considering the inevitable effects of environmental perturbations on disease transmission, we mainly study a stochastic SVEIR epidemic model in which the transmission rate satisfies the log-normal Ornstein–Uhlenbeck process and the incidence rate is general. To analyze the dynamic properties of the stochastic model, we firstly verify...

In this paper, by introducing environmental white noise and telegraph noise, we proposed a stochastic predator–prey model with the Beddington–DeAngelis type functional response and investigated its dynamical behavior. Persistence and extinction are two core contents of population model research, so we analyzed these two properties. The sufficient c...

Due to many uncertain factors, parameter values in many microorganism cultivation systems are affected to a greater or lesser extent by environmental fluctuation. In this paper, the authors develop a stochastic turbidostat model that considers white noise, formulate and analyze dynamical behavior for the stochastic model. The authors obtain the exi...

In this paper, we analyze a stochastic SIRC model with Ornstein–Uhlenbeck process. Firstly, we give the existence and uniqueness of global solution of stochastic SIRC model and prove it. In addition, the existence of ergodic stationary distributions for stochastic SIRC system is proved by constructing a suitable series of Lyapunov functions. A quas...

In this study, we develop a vector-host transmission model with general incidence rates for the dynamics ofpine wilt disease in deterministic and stochastic environments. The existence and local asymptotic stability ofequilibria are investigated in the deterministic case. We show the required conditions for the ergodic stationarydistribution and ex...

As it is widely known, the spread of infectious diseases can result in significant socioeconomic consequences and pose a threat to public health. However, biologically plausible models that incorporate stochastic interference and dual epidemic hypotheses have received limited attention. This paper aims to bridge this gap by examining a stochastic d...

In this paper, a stochastic HIV infection model with the Ornstein–Uhlenbeck process is established and studied. It is assumed that the death rate of healthy CD4+ T cells satisfies the Ornstein–Uhlenbeck process. First, we verify that the stochastic model has an unique global solution for any initial value. Then, using Markov semigroup technique, we...

In this paper, a generalized n-species Gilpin–Ayala competition system with saturation effect and nonlinear perturbations is proposed and examined. We first develop a new mathematical technique called “stochastic ϵ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \...

In this paper, we propose a stochastic SEIR-type model with asymptomatic carriers to describe the propagation mechanism of coronavirus (COVID-19) in the population. Firstly, we show that there exists a unique global positive solution of the stochastic system with any positive initial value. Then we adopt a stochastic Lyapunov function method to est...

In this paper, we examine a stochastic avian influenza model with a nonlinear incidence rate within avian populations and the psychological effect within the human population, where susceptible humans reduce their contact with infected avians as the number of infected humans increases. For the deterministic model, the basic reproduction number \(\m...

This paper considers a stochastic hybrid differential infectivity epidemic model with standard incidence perturbed by mean‐reverting Ornstein–Uhlenbeck process. Applying Lyapunov method, we first show existence and uniqueness of the global solution. Then sufficient conditions for persistence in the mean and exponential extinction of the infectious...

In this paper, we present a model of infection in which a virus can simultaneously infect two types of target cells. The model has a general form of infection rates in deterministic and stochastic settings, incorporating bilinear infection rates, saturated incidences and half-saturated incidences. In the deterministic case, we investigate the exist...

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...

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...

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...

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...

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...

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...

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...

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...

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...

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...

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...

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...

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...

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...

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...

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...

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...

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...

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...

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...

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...

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...

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...

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...

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...

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...

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...

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...

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...

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...

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...

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...

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...

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...

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...

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...

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...

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...