Search

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 of the stationary distribution of the system. We are relatively familiar with the understanding of the density function of random systems. This paper also gives the expression of the density function of the random system near the unique positive equilibrium. In addition, the asymptotic properties of the p-moment boundedness and solution of the stochastic population system are also studied. In particular, we use numerical simulation to verify the theoretical results in the last section. [ABSTRACT FROM AUTHOR]

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 uniqueness of the global solution, the existence of a stationary distribution, and the extinction of infected monocytes and free viruses. In particular, it is worth revealing that we get the specific form of covariance matrix in its probability density around the quasi-endemic equilibrium of the stochastic system. Finally, numerical illustrative examples are depicted to confirm our theoretical findings. [ABSTRACT FROM AUTHOR]

Gastric cancer (GC) is one of the most common and lethal cancers worldwide. In view of the prominent roles of long noncoding RNAs (lncRNAs) in cancers, we investigated the specific role and underlying mechanism of GATA binding protein 6 antisense RNA 1 (GATA6-AS1) in GC. Quantitative real-time polymerase chain reaction (qRT-PCR) detected GATA6-AS1 expression in GC cell lines. Functional assays were conducted to explore the role of GATA6-AS1 in GC. Furthermore, mechanism investigations were implemented to uncover the interaction among GATA6-AS1, microRNA-543 (miR-543), and phosphatase and tensin homolog (PTEN). In the present study, it was found that GATA6-AS1 expression is significantly downregulated in GC cell lines. Functionally, GATA6-AS1 markedly suppresses GC cell growth and migration in vitro and in vivo tumorigenesis. Besides tumor suppressor, GATA6-AS1 serves as a miR-543 sponge. Specifically speaking, GATA6-AS1 acts as a competing endogenous RNA (ceRNA) of miR-543 to upregulate the expression of PTEN, thus inactivating AKT signaling pathway to inhibit GC progression. In conclusion, this study has manifested that GATA6-AS1 inhibits GC cell proliferation and migration as a sponge of miR-543 by regulating PTEN/AKT signaling axis, offering new perspective into developing novel GC therapies. [ABSTRACT FROM AUTHOR]

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 R 0 , possible equilibria, and related asymptotic stability are first studied. Then, for the stochastic model, we obtain a critical value R 0 S , which can determine the persistence and extinction of avian influenza. It is theoretically proved that the stochastic model has a unique stationary distribution ϖ (·) if R 0 S > 1 , but the disease will go to extinction when R 0 S < 1 . Taking stochasticity into account, a quasi-endemic equilibrium T ¯ ∗ related to the endemic equilibrium of the deterministic model is defined. We develop an important lemma for solving the special Fokker–Planck equation and derive the explicit expression of the density function of the distribution ϖ (·) around the equilibrium T ¯ ∗ . Numerical simulations verify our theoretical results, and we study the impact of noise and the psychological effect on the transmission dynamics of avian influenza. [ABSTRACT FROM AUTHOR]

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 disease are obtained. Furthermore, by solving the corresponding Fokker–Planck equation, we derive that the global solution around the endemic equilibrium follows a unique probability density function. Finally, numerical simulations are employed to demonstrate the analytical results. [ABSTRACT FROM AUTHOR]

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 uniform expression of threshold value of extinction and ergodicity for this model is derived. In addition, the sufficient conditions of strong and weak persistence in the mean of phytoplankton and zooplankton are given. Our results indicate that white noise influences the dynamics of both phytoplankton and zooplankton species, which further affects the stability of phytoplankton‐zooplankton models. Some numerical examples are provided to support our theoretical results, and their explanations from the perspective of ecology are presented in this paper. [ABSTRACT FROM AUTHOR]

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. In addition, the persistence in the mean of disease is proved. Specifically, by constructing suitable stochastic Lyapunov functions, we find a domain that is positive recurrence for the solution of stochastic system. Finally, numerical simulations are employed to verify our analytical results. [ABSTRACT FROM AUTHOR]

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 positive solution. Then, conditions for extinction of the disease are established. Moreover, through constructing suitable Lyapunov functions, we derive sufficient conditions for the existence of positive recurrence of the solutions. Positive recurrence implies all the individuals can coexist and persist in the long term. Finally, numerical experiments are performed for supporting the theoretical results. [ABSTRACT FROM AUTHOR]

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 the stochastic system with any positive initial value which is fundamental in the dynamics of population modeling. Moreover, we get 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 distribution indicates that both criminal and victim will be persistent and coexistent in the long term. [ABSTRACT FROM AUTHOR]

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 eradication and wiping out of the diseases. In a biological viewpoint, the existence of a stationary distribution shows that the diseases will be prevalent and persistent in the long term. [ABSTRACT FROM AUTHOR]

Bacteria use signal transduction systems to sense and respond to their external environment. The two‐component system CpxA/CpxR senses misfolded envelope protein stress and responds by up‐regulating envelope protein factors and down‐regulating virulence factors in several animal pathogens. Dickeya dadantii is a phytopathogen equipped with a type III secretion system (T3SS) for manipulating the host immune response. We found that deletion of cpxR enhanced the expression of the T3SS marker gene hrpA in a designated T3SS‐inducing minimal medium (MM). In the ∆cpxR mutant, multiple T3SS and c‐di‐GMP regulators were also up‐regulated. Subsequent analysis revealed that deletion of the phosphodiesterase gene egcpB in ∆cpxR abolished the enhanced T3SS expression. This suggested that CpxR suppresses EGcpB levels, causing low T3SS expression in MM. Furthermore, we found that the ∆cpxR mutant displayed low c‐di‐GMP phenotypes in biofilm formation and swimming. Increased production of cellular c‐di‐GMP by in trans expression of the diguanylate cyclase gene gcpA was negated in the ∆cpxR mutant. Here, we propose that CpxA/CpxR regulates T3SS expression by manipulating the c‐di‐GMP network, in turn modifying the multiple physiological activities involved in the response to environmental stresses in D. dadantii. [ABSTRACT FROM AUTHOR]

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 distribution indicates that the diseases will be prevalent and persistent in the long term. In addition, we make up adequate conditions for complete eradication and wiping out of the diseases. Some numerical simulations are presented to illustrate our main results. [ABSTRACT FROM AUTHOR]

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 is formulated in this paper. What’s more, in both systems, we obtain sufficient conditions of extinction and ergodicity. Our results demonstrate that the weaker white noise can ensure the permanence of zooplankton and the stronger white noise can lead to the disappearance of zooplankton. Moreover, the threshold value of extinction and persistence can serve as a theoretical basis for controlling phytoplankton and zooplankton. Numerical examples are performed on the analysis results of the two cases to confirm our theoretical results. In addition, we also provide a real-life case study, the validity of the model is verified based on experimental data, and it is shown that fluctuation of external environment and the consumption of phytoplankton by zooplankton will affect the growth and number of phytoplankton. Effectively controlling the quantity of phytoplankton can delay the occurrence of water bloom or red tide. [ABSTRACT FROM AUTHOR]

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 estimation, asymptotic behavior, and global attractivity of the solutions of the stochastic system in turn. Moreover, we establish sufficient criteria for the existence and uniqueness of a stationary distribution of positive solutions of the stochastic system with the help of Lyapunov function methods. It is worth mentioning that we derive the exact expression of the local probability density for the stochastic system by solving the relevant four-dimensional Fokker–Planck equation. We find that the smaller intensity of volatility or the bigger speed of reversion is helpful for preserving the biodiversity of the species. Finally, numerical simulations are performed to support our analytical findings. [ABSTRACT FROM AUTHOR]

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 addition, sufficient conditions for the extinction of HIV infection are derived. Finally, numerical simulations are employed to confirm our theoretical results. [ABSTRACT FROM AUTHOR]

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 R0P>1. Next, by solving the corresponding Fokker‐Planck equation, the exact expression of probability density function of the stochastic model is obtained. Moreover, we establish the sufficient condition R0Q<1 for disease extinction in a long term. Finally, several empirical examples and numerical simulations are provided to verify the above theoretical results. [ABSTRACT FROM AUTHOR]

This paper is concerned with a stochastic multigroup S-DI-A model for the transmission of HIV with general incidence rate. We obtain sufficient criteria for the existence and uniqueness of an ergodic stationary distribution of the positive solutions to the model by constructing a proper stochastic Lyapunov function. The stationary distribution implies that the diseases will be persistent in the long term. Some numerical simulations are introduced to illustrate our theoretical result. [ABSTRACT FROM AUTHOR]

To capture the realistic dynamics of vegetation pattern, we study a stochastic vegetation-water model, where the vegetation consumption of general nonlinear response type is considered. This paper is the first mathematical attempt to introduce the Black–Karasinski process as the random effect in vegetation evolution. It is shown that Black–Karasinski process is a both biologically and mathematically reasonable assumption by comparison with existing stochastic modeling methods. We obtain a critical value ℛ 0 S to classify the long-term dynamical properties of the stochastic vegetation model, including the existence of stationary distribution (i.e., a reflection of vegetation persistence) and the exponential extinction of vegetation. [ABSTRACT FROM AUTHOR]

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 persistence, we find a domain which is positive recurrence for the solution of the stochastic system by constructing an appropriate Lyapunov function with regime switching. [ABSTRACT FROM AUTHOR]

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 this paper is to generalize the θ‐stochastic criterion method proposed by the recent work (Han et al. in Chaos Solit Fract 140:110238, 2020) to eliminate nonlinear telegraph perturbations. Next, via constructing several θ‐stochastic Lyapunov functions and using the generalized method, we further prove that the stochastic model have a unique ergodic stationary distribution under ℛ0C>1. Results show that the prevention and control of cholera epidemic depend on low transmission rate and small telegraph perturbations. Finally, the corresponding numerical simulations are performed to illustrate our analytical results and a practical application on the Somalia cholera outbreak is shown at the end of this paper. [ABSTRACT FROM AUTHOR]

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 positive solution, extinction, existence of positive T‐periodic solution and positive recurrence. Our results suggest that a smaller white noise is necessary to cause the existence of positive T‐periodic solution and positive recurrence of the stochastic model, while a larger white noise will accelerate the extinction of the population. In addition, numerical simulation is used to support our main results. [ABSTRACT FROM AUTHOR]

In this paper, we study the dynamical behavior of a stochastic two-compartment model of B -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 extinction of the disease are derived. Furthermore, numerical simulations are presented for supporting the theoretical results. Our results show that large noise intensity may contribute to extinction of the disease. [ABSTRACT FROM AUTHOR]

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 function. In addition, we make up adequate conditions for complete eradication and wiping out the infectious disease. In a biological interpretation, the existence of a stationary distribution implies that the disease will prevail and persist in the long term. Finally, examples and numerical simulations are introduced to validate our theoretical results. [ABSTRACT FROM AUTHOR]

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 T -periodic solution. For the model which is disturbed by both white and telegraph noises, we obtain sufficient criteria for positive recurrence of the solutions to the model by constructing a suitable stochastic Lyapunov function with regime switching. The positive recurrence implies that both prey and predator populations will be persistent in the long term. [ABSTRACT FROM AUTHOR]

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 model. By constructing proper Lyapunov functions, sufficient conditions under which the stationary distribution exists are obtained. In addition, we discuss the extinction of the disease. Furthermore, we get the accurate expression of probability density function near the endemic equilibrium of the stochastic model. Finally, several numerical simulations are carried out to verify theoretical results and examine the influence of environmental noise. [ABSTRACT FROM AUTHOR]

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. Furthermore, the extinction of microorganisms is discussed in two cases. In one case, both the prey and the predator species are extinct, and in the other case, the prey species is surviving and the predator species is extinct. Finally, numerical experiments are performed for supporting the theoretical results. [ABSTRACT FROM AUTHOR]

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 explore the new critical numbers between survival and extinction for species of the dual‐threshold chemostat model. Numerical simulations are accomplished to confirm our analytical conclusions. [ABSTRACT FROM AUTHOR]

In this paper, we consider a stochastic tuberculosis model with two kinds of treatments, that is, treatment at home and treatment in hospital. Firstly, we obtain sufficient conditions for extinction and persistence in the mean of the diseases, then in the case of persistence, we establish sufficient conditions for the existence and uniqueness of an ergodic stationary distribution of the positive solutions to the model by constructing a suitable stochastic Lyapunov function. The theoretical results show that large white noise is beneficial for eliminating TB endemic while small white noise is not. [ABSTRACT FROM AUTHOR]

• A HIV/AIDS model is established in which the model is disturbed by white noises. • The model includes the screening for virus carriers and the infected individuals seeking treatment actively. • We establish sufficient conditions for the existence of ergodic stationary distribution and disease eradication, respectively. To screen for virus carriers and for infected individuals to actively seek treatment are the key factors to curb the spread of HIV/AIDS. We propose a stochastic HIV/AIDS model to evaluate their effect. First, we theoretically prove that the solution of the stochastic model is positive and global. Second, we obtain the existence of an ergodic stationary distribution if R 0 S > 1 , and we establish sufficient conditions R 0 ′ < 1 for disease extinction. We provide examples and numerical simulations to verify our theoretical results. Finally, we analyze the impact of the above two factors on the dynamical behavior of the stochastic system, and draw conclusions regrading disease prevention and elimination. [ABSTRACT FROM AUTHOR]

In this paper, we study the dynamical behavior of a multigroup SIQS epidemic model, which is formulated as a piecewise deterministic Markov process. Sufficient conditions for extinction and persistence in the mean of the diseases are obtained. In addition, in the case of diseases persistence, we establish sufficient conditions for the existence of positive recurrence of the solutions to the model by using the stochastic Lyapunov function with regime switching. [ABSTRACT FROM AUTHOR]

In the present paper, we focus on a stochastic predator-prey model with stage structure for prey. Firstly, by using the stochastic Lyapunov function method, we obtain sufficient conditions for the existence and uniqueness of an ergodic stationary distribution of the positive solutions to the model. Then we establish sufficient conditions for extinction of the predator population in two cases. Some examples and numerical simulations are carried out to validate our analytical findings. [ABSTRACT FROM AUTHOR]

We consider a model of multi-species competition in the chemostat that includes demographic stochasticity and discrete delays. We prove that for any given initial data, there exists a unique global positive solution for the stochastic delayed system. By employing the method of stochastic Lyapunov functionals, we determine the asymptotic behaviors of the stochastic solution and show that although the sample path fluctuate, it remains positive and the expected time average of the distance between the stochastic solution and the equilibrium of the associated deterministic delayed chemostat model is eventually small, i.e. we obtain an analogue of the competition exclusion principle when the noise intensities are relatively small. Numerical simulations are carried out to illustrate our theoretical results. [ABSTRACT FROM AUTHOR]

In this article, we study two stochastic predator-prey models with distributed delay and general functional response. For the nonautonomous periodic case of the system, by utilizing Khasminskii's theory of periodic solution, we prove that the system admits a positive T-periodic solution. For the system which is perturbed by both white and colored noises, we establish sufficient conditions for the existence of positive recurrence of the solutions to the system. The existence of positive recurrence implies stochastic weak stability. [ABSTRACT FROM AUTHOR]

In this paper, we investigate a stochastic susceptible-infective-removed-infective (SIRI) epidemic model with relapse. We show that the densities of the distributions of the solutions can converge in L 1 to an invariant density or can converge weakly to a singular measure under certain condition. We also find the support of the invariant density. Moreover, we establish sharp sufficient criteria for the extinction of the disease in two cases. The results show that the smaller white noise can assure the existence of a stationary distribution which implies the persistence of the disease while the larger white noise can lead to the extinction of the disease. [ABSTRACT FROM AUTHOR]

In this paper, we propose a stochastic HIV-1 infection model with distributed delay and logistic growth. Firstly, we transfer the stochastic model with weak kernel case into an equivalent system through the linear chain technique. Then, we establish sufficient conditions for the existence of a stationary distribution of the model by constructing a suitable stochastic Lyapunov function. Moreover, we obtain sufficient criteria for extinction of the infected cells; that is, the uninfected cells are survival and the infected cells are extinct. Our results show that the smaller white noise can ensure the existence of a stationary distribution when the basic reproduction number R 0 S of the stochastic system is bigger than one, while the larger white noise can lead to the extinction of the infected cells when the basic reproduction number R 0 of the deterministic system is smaller than one. [ABSTRACT FROM AUTHOR]

In this paper, we analyse a stochastic chemostat model with distributed delay and degenerate diffusion. We transform the stochastic model with weak kernel case into an equivalent system through the linear chain technique. Since the diffusion matrix is degenerate, the uniform ellipticity condition is not satisfied. The Markov semigroup theory is used to obtain the existence and uniqueness of a stable stationary distribution. We prove the densities of the distributions of the positive solutions can converge in L 1 to an invariant density. The existence of a stable stationary distribution implies stochastic persistence of the microorganism. [ABSTRACT FROM AUTHOR]

In this paper, we consider two chemostat models with random perturbation, in which single species depends on two perfectly substitutable resources for growth. For the autonomous system, we first prove that the solution of the system is positive and global. Then we establish sufficient conditions for the existence of an ergodic stationary distribution by constructing appropriate Lyapunov functions. For the non-autonomous system, by using Has'minskii theory on periodic Markov processes, we derive it admits a nontrivial positive periodic solution. Finally, numerical simulations are carried out to illustrate our main results. [ABSTRACT FROM AUTHOR]

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 governed by Ornstein–Uhlenbeck process to simulate the random factors in the environment. Based on the existence and uniqueness of the global solution to the model and the boundedness of the p$$ p $$ order moments of the solution, several conditions are established to analyze the survival of the species. Specifically, a criteria for the existence of the stationary distribution to the stochastic system is established by constructing some suitable Lyapunov functions. And the analytical expression of the probability density function of the model around the quasi‐equilibrium is obtained. Furthermore, the extinction of species in the model is also explored. Finally, numerical simulations are carried out to illustrate the theoretical results obtained in this paper. [ABSTRACT FROM AUTHOR]