Transmission dynamics of symptom-dependent HIV/AIDS models

In this study, we proposed two, symptom-dependent, HIV/AIDS models to investigate the dynamical properties of HIV/AIDS in the Fujian Province. The basic reproduction number was obtained, and the local and global stabilities of the disease-free and endemic equilibrium points were verified to the deterministic HIV/AIDS model. Moreover, the indicators $ R_0^s $ and $ R_0^e $ were derived for the stochastic HIV/AIDS model, and the conditions for stationary distribution and stochastic extinction were investigated. By using the surveillance data from the Fujian Provincial Center for Disease Control and Prevention, some numerical simulations and future predictions on the scale of HIV/AIDS infections in the Fujian Province were conducted.

Stationary distribution and extinction of a stochastic HIV/AIDS model with nonlinear incidence rate

This paper studies a stochastic HIV/AIDS model with nonlinear incidence rate. In the model, the infection rate coefficient and the natural death rates are affected by white noise, and infected people are affected by an intervention strategy. We derive the conditions of extinction and permanence for the stochastic HIV/AIDS model, that is, if $ R_0^s < 1, $ HIV/AIDS will die out with probability one and the distribution of the susceptible converges weakly to a boundary distribution; if $ R_0^s > 1 $, HIV/AIDS will be persistent almost surely and there exists a unique stationary distribution. The conclusions are verified by numerical simulation.

Stationary distribution and probability density function analysis of a stochastic Microcystins degradation model with distributed delay

A stochastic Microcystins degradation model with distributed delay is studied in this paper. We first demonstrate the existence and uniqueness of a global positive solution to the stochastic system. Second, we derive a stochastic critical value $ R_0^s $ related to the basic reproduction number $ R_0 $. By constructing suitable Lyapunov function types, we obtain the existence of an ergodic stationary distribution of the stochastic system if $ R_0^s > 1. $ Next, by means of the method developed to solve the general four-dimensional Fokker-Planck equation, the exact expression of the probability density function of the stochastic model around the quasi-endemic equilibrium is derived, which is the key aim of the present paper. In the analysis of statistical significance, the explicit density function can reflect all dynamical properties of a chemostat model. To validate our theoretical conclusions, we present examples and numerical simulations.

Modeling and analysis of a stochastic giving-up-smoking model with quit smoking duration

Smoking has gradually become a very common behavior, and the related situation in different groups also presents different forms. Due to the differences of individual smoking cessation time and the interference of environmental factors in the spread of smoking behavior, we establish a stochastic giving up smoking model with quit-smoking duration. We also consider the saturated incidence rate. The total population is composed of potential smokers, smokers, quitters and removed. By using Itô's formula and constructing appropriate Lyapunov functions, we first ensure the existence of a unique global positive solution of the stochastic model. In addition, a threshold condition for extinction and permanence of smoking behavior is deduced. If the intensity of white noise is small, and $ \widetilde{\mathcal{R}}_0 < 1 $, smokers will eventually become extinct. If $ \widetilde{\mathcal{R}}_0 > 1 $, smoking will last. Then, the sufficient condition for the existence of a unique stationary distribution of the smoking phenomenon is studied as $ R_0^s > 1 $. Finally, conclusions are explained by numerical simulations.

Dynamics and optimal control of a stochastic Zika virus model with spatial diffusion

Zika is an infectious disease with multiple transmission routes, which is related to severe congenital disabilities, especially microcephaly, and has attracted worldwide concern. This paper aims to study the dynamic behavior and optimal control of the disease. First, we establish a stochastic reaction-diffusion model (SRDM) for Zika virus, including human-mosquito transmission, human-human sexual transmission, and vertical transmission of mosquitoes, and prove the existence, uniqueness, and boundedness of the global positive solution of the model. Then, we discuss the sufficient conditions for disease extinction and the existence of a stationary distribution of positive solutions. After that, three controls, i.e. personal protection, treatment of infected persons, and insecticides for spraying mosquitoes, are incorporated into the model and an optimal control problem of Zika is formulated to minimize the number of infected people, mosquitoes, and control cost. Finally, some numerical simulations are provided to explain and supplement the theoretical results obtained.

Survival analysis and probability density function of switching heroin model

We study a switching heroin epidemic model in this paper, in which the switching of supply of heroin occurs due to the flowering period and fruiting period of opium poppy plants. Precisely, we give three equations to represent the dynamics of the susceptible, the dynamics of the untreated drug addicts and the dynamics of the drug addicts under treatment, respectively, within a local population, and the coefficients of each equation are functions of Markov chains taking values in a finite state space. The first concern is to prove the existence and uniqueness of a global positive solution to the switching model. Then, the survival dynamics including the extinction and persistence of the untreated drug addicts under some moderate conditions are derived. The corresponding numerical simulations reveal that the densities of sample paths depend on regime switching, and larger intensities of the white noises yield earlier times for extinction of the untreated drug addicts. Especially, when the switching model degenerates to the constant model, we show the existence of the positive equilibrium point under moderate conditions, and we give the expression of the probability density function around the positive equilibrium point.

Dynamic modeling and analysis of Hepatitis B epidemic with general incidence

New stochastic and deterministic Hepatitis B epidemic models with general incidence are established to study the dynamics of Hepatitis B virus (HBV) epidemic transmission. Optimal control strategies are developed to control the spread of HBV in the population. In this regard, we first calculate the basic reproduction number and the equilibrium points of the deterministic Hepatitis B model. And then the local asymptotic stability at the equilibrium point is studied. Secondly, the basic reproduction number of the stochastic Hepatitis B model is calculated. Appropriate Lyapunov functions are constructed, and the unique global positive solution of the stochastic model is verified by Itô formula. By applying a series of stochastic inequalities and strong number theorems, the moment exponential stability, the extinction and persistence of HBV at the equilibrium point are obtained. Finally, using the optimal control theory, the optimal control strategy to eliminate the spread of HBV is developed. To reduce Hepatitis B infection rates and to promote vaccination rates, three control variables are used, for instance, isolation of patients, treatment of patients, and vaccine inoculation. For the purpose of verifying the rationality of our main theoretical conclusions, the Runge-Kutta method is applied to numerical simulation.

Dynamical behaviors of a Lotka-Volterra competition system with the Ornstein-Uhlenbeck process

The competitive relationship is one of the important studies in population ecology. In this paper, we investigate the dynamical behaviors of a two-species Lotka-Volterra competition system in which intrinsic rates of increase are governed by the Ornstein-Uhlenbeck process. First, we prove the existence and uniqueness of the global solution of the model. Second, the extinction of populations is discussed. Moreover, a sufficient condition for the existence of the stationary distribution in the system is obtained, and, further, the formulas for the mean and the covariance of the probability density function of the corresponding linearized system near the equilibrium point are obtained. Finally, numerical simulations are applied to verify the theoretical results.

Threshold behaviour of a stochastic SIRS Le´vy jump model with saturated incidence and vaccination

A stochastic SIRS system with $ \mathrm {L\acute{e}vy} $ process is formulated in this paper, and the model incorporates the saturated incidence and vaccination strategies. Due to the introduction of $ \mathrm {L\acute{e}vy} $ jump, the jump stochastic integral process is a discontinuous martingale. Then the Kunita's inequality is used to estimate the asymptotic pathwise of the solution for the proposed model, instead of Burkholder-Davis-Gundy inequality which is suitable for continuous martingales. The basic reproduction number $ R_{0}^{s} $ of the system is also derived, and the sufficient conditions are provided for the persistence and extinction of SIRS disease. In addition, the numerical simulations are carried out to illustrate the theoretical results. Theoretical and numerical results both show that $ \mathrm {L\acute{e}vy} $ process can suppress the outbreak of the disease.

Dynamics of a stochastic hepatitis B virus transmission model with media coverage and a case study of China

Hepatitis B virus (HBV) infection is a global public health problem and there are 257 million people living with chronic HBV infection throughout the world. In this paper, we investigate the dynamics of a stochastic HBV transmission model with media coverage and saturated incidence rate. Firstly, we prove the existence and uniqueness of positive solution for the stochastic model. Then the condition on the extinction of HBV infection is obtained, which implies that media coverage helps to control the disease spread and the noise intensities on the acute and chronic HBV infection play a key role in disease eradication. Furthermore, we verify that the system has a unique stationary distribution under certain conditions, and the disease will prevail from the biological perspective. Numerical simulations are conducted to illustrate our theoretical results intuitively. As a case study, we fit our model to the available hepatitis B data of mainland China from 2005 to 2021.

Stochastic modeling of the Monkeypox 2022 epidemic with cross-infection hypothesis in a highly disturbed environment

Monkeypox 2022, a new re-emerging disease, is caused by the Monkeypox virus. Structurally, this virus is related to the smallpox virus and infects the host in a similar way; however, the symptoms of Monkeypox are more severe. In this research work, a mathematical model for understanding the dynamics of Monkeypox 2022 is suggested that takes into account two modes of transmission: horizontal human dissemination and cross-infection between animals and humans. Due to lack of substantial knowledge about the virus diffusion and the effect of external perturbations, the model is extended to the probabilistic formulation with Lévy jumps. The proposed model is a two block compartmental system that requires the form of Itô-Lévy stochastic differential equations. Based on some assumptions and nonstandard analytical techniques, two principal asymptotic properties are proved: the eradication and continuation in the mean of Monkeypox 2022. The outcomes of the study reveals that the dynamical behavior of the proposed Monkeypox 2022 system is chiefly governed by some parameters that are precisely correlated with the noise intensities. To support the obtained theoretical finding, examples based on numerical simulations and real data are presented at the end of the study. The numerical simulations also exhibit the impact of the innovative adopted mathematical techniques on the findings of this work.

Extinction and stationary distribution of stochastic predator-prey model with group defense behavior

Considering that many prey populations in nature have group defense behavior, and the relationship between predator and prey is usually affected by environmental noise, a stochastic predator-prey model with group defense behavior is established in this paper. Some dynamical properties of the model, including the existence and uniqueness of global positive solution, sufficient conditions for extinction and unique ergodic stationary distribution, are investigated by using qualitative theory of stochastic differential equations, Lyapunov function analysis method, Itô formula, etc. Furthermore, the effects of group defense behavior and environmental noise on population stability are also discussed. Finally, numerical simulations are carried out to illustrate that the effects of environmental noise on both populations are negative, the appropriate group defense level of prey can maintain the stability of the relationship between two populations, and the survival threshold is strongly influenced by the intrinsic growth rate of prey population and the intensity of environmental noise.

Dynamics of a stochastic SIRS epidemic model with standard incidence and vaccination

A stochastic SIRS epidemic model with vaccination is discussed. A new stochastic threshold $ R_0^s $ is determined. When the noise is very low ($ R_0^s < 1 $), the disease becomes extinct, and if $ R_0^s > 1 $, the disease persists. Furthermore, we show that the solution of the stochastic model oscillates around the endemic equilibrium point and the intensity of the fluctuation is proportional to the intensity of the white noise. Computer simulations are used to support our findings.

Stationary distribution and extinction of a stochastic influenza virus model with disease resistance

Influenza is a respiratory infection caused influenza virus. To evaluate the effect of environment noise on the transmission of influenza, our study focuses on a stochastic influenza virus model with disease resistance. We first prove the existence and uniqueness of the global solution to the model. Then we obtain the existence of a stationary distribution to the positive solutions by stochastic Lyapunov function method. Moreover, certain sufficient conditions are provided for the extinction of the influenza virus flu. Finally, several numerical simulations are revealed to illustrate our theoretical results. Conclusively, according to the results of numerical models, increasing disease resistance is favorable to disease control. Furthermore, a simple example demonstrates that white noise is favorable to the disease's extinction.

Dynamics of a stochastic HBV infection model with drug therapy and immune response

Hepatitis B is a disease that damages the liver, and its control has become a public health problem that needs to be solved urgently. In this paper, we investigate analytically and numerically the dynamics of a new stochastic HBV infection model with antiviral therapies and immune response represented by CTL cells. Through using the theory of stochastic differential equations, constructing appropriate Lyapunov functions and applying Itô's formula, we prove that the disease-free equilibrium of the stochastic HBV model is stochastically asymptotically stable in the large, which reveals that the HBV infection will be eradicated with probability one. Moreover, the asymptotic behavior of globally positive solution of the stochastic model near the endemic equilibrium of the corresponding deterministic HBV model is studied. By using the Milstein's method, we provide the numerical simulations to support the analysis results, which shows that sufficiently small noise will not change the dynamic behavior, while large noise can induce the disappearance of the infection. In addition, the effect of inhibiting virus production is more significant than that of blocking new infection to some extent, and the combination of two treatment methods may be the better way to reduce HBV infection and the concentration of free virus.

Dynamics of a stochastic COVID-19 epidemic model considering asymptomatic and isolated infected individuals

Coronavirus disease (COVID-19) has a strong influence on the global public health and economics since the outbreak in 2020. In this paper, we study a stochastic high-dimensional COVID-19 epidemic model which considers asymptomatic and isolated infected individuals. Firstly we prove the existence and uniqueness for positive solution to the stochastic model. Then we obtain the conditions on the extinction of the disease as well as the existence of stationary distribution. It shows that the noise intensity conducted on the asymptomatic infections and infected with symptoms plays an important role in the disease control. Finally numerical simulation is carried out to illustrate the theoretical results, and it is compared with the real data of India.

A stochastic mussel-algae model under regime switching

We investigate a novel model of coupled stochastic differential equations modeling the interaction of mussel and algae in a random environment, in which combined effect of white noises and telegraph noises formulated under regime switching are incorporated. We derive sufficient condition of extinction for mussel species. Then with the help of stochastic Lyapunov functions, a well-grounded understanding of the existence of ergodic stationary distribution is obtained. Meticulous numerical examples are also employed to visualize our theoretical results in detail. Our analytical results indicate that dynamic behaviors of the stochastic mussel-algae model are intimately associated with two kinds of random perturbations.

Threshold dynamics of a stochastic SIHR epidemic model of COVID-19 with general population-size dependent contact rate

In this paper, we propose a stochastic SIHR epidemic model of COVID-19. A basic reproduction number $ R_{0}^{s} $ is defined to determine the extinction or persistence of the disease. If $ R_{0}^{s} < 1 $, the disease will be extinct. If $ R_{0}^{s} > 1 $, the disease will be strongly stochastically permanent. Based on realistic parameters of COVID-19, we numerically analyze the effect of key parameters such as transmission rate, confirmation rate and noise intensity on the dynamics of disease transmission and obtain sensitivity indices of some parameters on $ R_{0}^{s} $ by sensitivity analysis. It is found that: 1) The threshold level of deterministic model is overestimated in case of neglecting the effect of environmental noise; 2) The decrease of transmission rate and the increase of confirmed rate are beneficial to control the spread of COVID-19. Moreover, our sensitivity analysis indicates that the parameters $ \beta $, $ \sigma $ and $ \delta $ have significantly effects on $ R_0^s $.

Qualitative behaviour of a stochastic hepatitis C epidemic model in cellular level

In this paper, a mathematical model describing the dynamical of the spread of hepatitis C virus (HCV) at a cellular level with a stochastic noise in the transmission rate is developed from the deterministic model. The unique time-global solution for any positive initial value is served. The Ito's Formula, the suitable Lyapunov function, and other stochastic analysis techniques are used to analyze the model dynamics. The numerical simulations are carried out to describe the analytical results. These results highlight the impact of the noise intensity accelerating the extinction of the disease.

An SIS epidemic model with time delay and stochastic perturbation on heterogeneous networks

An SIS epidemic model with time delay and stochastic perturbation on scale-free networks is established in this paper. And we derive sufficient conditions guaranteeing extinction and persistence of epidemics, respectively, which are related to the basic reproduction number $ R_0 $ of the corresponding deterministic model. When $ R_0 < 1 $, almost surely exponential extinction and $ p $-th moment exponential extinction of epidemics are proved by Razumikhin-Mao Theorem. Whereas, when $ R_0 > 1 $, the system is persistent in the mean under sufficiently weak noise intensities, which indicates that the disease will prevail. Finally, the main results are demonstrated by numerical simulations.

Stability analysis and persistence of a phage therapy model

This study deals with a phage therapy model involving nonlinear interactions of the bacteria-phage-innate immune response. The main aim of this work is to analytically and numerically examine the dynamic behavior of the phage therapy model. First, we investigate the positivity and boundedness of the system. Second, we analyze the existence and local asymptotic stability of different equilibrium solutions. Third, we investigate the global stability for equilibrium without immune system and equilibrium without phages, and coexistence equilibrium by means of the Bendixson-Dulac criterion and the Lyapunov functional method, respectively. Furthermore, we discuss the persistence and nonpersistence of the system under some conditions. Finally, we perform numerical simulations to substantiate the results obtained in this research.

Persistence and extinction of a modified Leslie-Gower Holling-type Ⅱ predator-prey stochastic model in polluted environments with impulsive toxicant input

In this paper, a modified Leslie-Gower Holling-type Ⅱ two-predator one-prey stochastic model in polluted environments with impulsive toxicant input is proposed where we use an Ornstein-Uhlenbeck process to improve the stochasticity of the environment. The sharp sufficient conditions for persistence in the mean and extinction are established. The results reveal that the persistence and extinction of the species have close relationships with the toxicant and environmental stochasticity. In addition, the theoretical results are verified by numerical simulation.

Dynamics induced by environmental stochasticity in a phytoplankton-zooplankton system with toxic phytoplankton

Environmental stochasticity and toxin-producing phytoplankton (TPP) are the key factors that affect the aquatic ecosystems. To investigate the effects of environmental stochasticity and TPP on the dynamics of plankton populations, a stochastic phytoplankton-zooplankton system with two TPP is studied theoretically and numerically in this paper. Theoretically, we first prove that the system possesses a unique and global positive solution with positive initial values, and then derive some sufficient conditions guaranteeing the extinction and persistence in the mean of the system. Significantly, it is shown that the system has a stationary distribution when toxin liberation rate reaches some a critical value. Additionally, numerical analysis shows that the white noise can affect the survival of plankton populations directly. Furthermore, it has been observed that the increasing one toxin liberation rate can increase the survival chance of phytoplankton and reduce the biomass of zooplankton, but the combined effects of two liberation rates on the changes in plankton populations are stronger than that of controlling any one of the two TPP.

Initial boundary value problem for a class of p-Laplacian equations with logarithmic nonlinearity

In this paper, we discuss global existence, boundness, blow-up and extinction properties of solutions for the Dirichlet boundary value problem of the $ p $-Laplacian equations with logarithmic nonlinearity $ u_{t}-{\rm{div}}(|\nabla u|^{p-2}\nabla u)+\beta|u|^{q-2}u = \lambda |u|^{r-2}u\ln{|u|} $, where $ 1 < p < 2 $, $ 1 < q\leq2 $, $ r > 1 $, $ \beta, \lambda > 0 $. Under some appropriate conditions, we obtain the global existence of solutions by means of the Galerkin approximations, then we prove that weak solution is globally bounded and blows up at positive infinity by virtue of potential well theory and the Nehari manifold. Moreover, we obtain the decay estimate and the extinction of solutions.

Deterministic and stochastic dynamics of a modified Leslie-Gower prey-predator system with simplified Holling-type Ⅳ scheme

In this paper, a prey-predator model with modified Leslie-Gower and simplified Holling-type Ⅳ functional responses is proposed to study the dynamic behaviors. For the deterministic system, we analyze the permanence of the system and the stability of the positive equilibrium point. For the stochastic system, we not only prove the existence and uniqueness of global positive solution, but also discuss the persistence in mean and extinction of the populations. In addition, we find that stochastic system has an ergodic stationary distribution under some parameter constraints. Finally, our theoretical results are verified by numerical simulations.

Initial boundary value problem for fractional p-Laplacian Kirchhoff type equations with logarithmic nonlinearity

In this paper, we study the initial boundary value problem for a class of fractional p-Laplacian Kirchhoff type diffusion equations with logarithmic nonlinearity. Under suitable assumptions, we obtain the extinction property and accurate decay estimates of solutions by virtue of the logarithmic Sobolev inequality. Moreover, we discuss the blow-up property and global boundedness of solutions.

Modelling and analysis of a stochastic nonautonomous predator-prey model with impulsive effects and nonlinear functional response

In this paper, a new stochastic predator-prey model with impulsive perturbation and Crowley-Martin functional response is proposed. The dynamical properties of the model are systematically investigated. The existence and stochastically ultimate boundedness of a global positive solution are derived using the theory of impulsive stochastic differential equations. Some sufficient criteria are obtained to guarantee the extinction and a series of persistence in the mean of the system. Moreover, we provide conditions for the stochastic permanence and global attractivity of the model. Numerical simulations are performed to support our qualitative results.

Dynamical analysis of a stochastic SIRS epidemic model with saturating contact rate

In this paper, a stochastic SIRS epidemic model with saturating contact rate is constructed. First, for the deterministic system, the stability of the equilibria is discussed by using eigenvalue theory. Second, for the stochastic system, the threshold conditions of disease extinction and persistence are established. Our results indicate that a large environmental noise intensity can suppress the spread of disease. Conversely, if the intensity of environmental noise is small, the system has a stationary solution which indicates the disease is persistent. Eventually, we introduce some computer simulations to validate the theoretical results.

Coexistence and extinction in a data-based ratio-dependent model of an insect community

In theory, pure competition often leads to competitive exclusion of species. However, what we often see in nature is a large number of distinct predator or consumer species coexist in a community consisting a smaller number of prey or plant species. In an effort of dissecting how indirect competition and selective predation may have contributed to the coexistence of species in an insect community, according to the replicated cage experiments (two aphid species and a specialist parasitoid that attacks only one of the aphids) and proposed mathematical models, van Veen et. al. [5] conclude that the coexistence of the three species is due to a combination of density-mediated and trait-mediated indirect interactions. In this paper, we formulate an alternative model that observes the conventional law of mass conservation and provides a better fitting to their experimental data sets. Moreover, we present an initial attempt in studying the stabilities of the nonnegative steady states of this model.

Extinction and stationary distribution of a competition system with distributed delays and higher order coupled noises

A stochastic two-species competition system with saturation effect and distributed delays is formulated, in which two coupling noise sources are incorporated and every noise source has effect on two species' intrinsic growth rates in nonlinear form. By transforming the two-dimensional system with weak kernel into an equivalent four-dimensional system, sufficient conditions for extinction of two species and the existence of a stationary distribution of the positive solutions to the system are obtained. Our main results show that the two coupling noises play a significant role on the long time behavior of system.

Discrete-time population dynamics on the state space of measures

If the individual state space of a structured population is given by a metric space S, measures μ on the σ-algebra of Borel subsets T of S offer a modeling tool with a natural interpretation: μ(T) is the number of individuals with structural characteristics in the set T. A discrete-time population model is given by a population turnover map F on the cone of finite nonnegative Borel measures that maps the structural population distribution of a given year to the one of the next year. Under suitable assumptions, F has a first order approximation at the zero measure (the extinction fixed point), which is a positive linear operator on the ordered vector space of real measures and can be interpreted as a basic population turnover operator. For a semelparous population, it can be identified with the next generation operator. A spectral radius can be defined by the usual Gelfand formula.We investigate in how far it serves as a threshold parameter between population extinction and population persistence. The variation norm on the space of measures is too strong to give the basic turnover operator enough compactness that its spectral radius is an eigenvalue associated with a positive eigenmeasure. A suitable alternative is the flat norm (also known as (dual) bounded Lipschitz norm), which, as a trade-off, makes the basic turnover operator only continuous on the cone of nonnegative measures but not on the whole space of real measures.

The effects of impulsive toxicant input on a single-species population in a small polluted environment

In this paper, we study a single-species population model with pulse toxicant input in a small polluted environment. The intrinsic rate of population change is affected by the environmental toxin load and toxin in the organisms which is influenced by toxin in the environment and the food chain. A new mathematical model is established. By the Pulse Compare Theorem, we find the surviving threshold of the population and obtain the sufficient conditions of persistence and extinction of the population.

Viral dynamics of an HIV stochastic model with cell-to-cell infection, CTL immune response and distributed delays

Recent studies have demonstrated that both virus-to-cell infection and cell-to-cell transmission play an important role in the process of HIV infection. In this paper, stochastic perturbation is introduced into HIV model with virus-to-cell infection, cell-to-cell transmission, CTL immune response and three distributed delays. The stochastic integro-delay differential equations is transformed into a degenerate stochastic differential equations. Through rigorous analysis of the model, we obtain the solution is unique, positive and global. By constructing appropriate Lyapunov functions, the existence of the stationary Markov process is derived when the critical condition is bigger than one. Furthermore, the extinction of the virus for sufficiently big noise intensity is established. Numerically, we investigate that the small noise intensity of fluctuations could help to sustain the number of virions and CTL immune response within a certain range, while the big noise intensity may be beneficial to the extinction of the virus. We also examine that the influence of random fluctuations on model dynamics may be more significant than that of the delay.

Stochastic dynamics and survival analysis of a cell population model with random perturbations

We consider a model based on the logistic equation and linear kinetics to study the effect of toxicants with various initial concentrations on a cell population. To account for parameter uncertainties, in our model the coefficients of the linear and the quadratic terms of the logistic equation are affected by noise. We show that the stochastic model has a unique positive solution and we find conditions for extinction and persistence of the cell population. In case of persistence we find the stationary distribution. The analytical results are confirmed by Monte Carlo simulations.