Stochastic dynamics of the transmission of Dengue fever virus between mosquitoes and humans

2021 ◽  
pp. 2150062
Author(s):  
Manjing Guo ◽  
Lin Hu ◽  
Lin-Fei Nie
Keyword(s):  
Dengue Fever ◽  
Stochastic Dynamics ◽  
Sufficient Conditions ◽  
Lyapunov Methods ◽  
Differential Model ◽  
Persistence In The Mean ◽  
Global Positive Solution ◽  
The Mean ◽  
And Behavior ◽  
The Impact

Considering the impact of environmental white noise on the quantity and behavior of vector of disease, a stochastic differential model describing the transmission of Dengue fever between mosquitoes and humans, in this paper, is proposed. By using Lyapunov methods and Itô’s formula, we first prove the existence and uniqueness of a global positive solution for this model. Further, some sufficient conditions for the extinction and persistence in the mean of this stochastic model are obtained by using the techniques of a series of stochastic inequalities. In addition, we also discuss the existence of a unique stationary distribution which leads to the stochastic persistence of this disease. Finally, several numerical simulations are carried to illustrate the main results of this contribution.

Study on a susceptible–infected–vaccinated model with delay and proportional vaccination

2018 ◽  
Vol 11 (08) ◽  
pp. 1850102 ◽  
Author(s):  
Shuqi Gan ◽  
Fengying Wei
Keyword(s):  
Positive Solution ◽  
Epidemic Model ◽  
Sufficient Conditions ◽  
Sufficient Condition ◽  
Stochastic Epidemic ◽  
Persistence In The Mean ◽  
Global Positive Solution ◽  
The Mean ◽  
Stochastic Epidemic Model

A susceptible–infected–vaccinated epidemic model with proportional vaccination and generalized nonlinear rate is formulated and investigated in the paper. We show that the stochastic epidemic model admits a unique and global positive solution with probability one when constructing a proper [Formula: see text]-function therewith. Then a sufficient condition that guarantees the disappearances of diseases is derived when the indicator [Formula: see text]. Further, if [Formula: see text], then we obtain that the solution is weakly permanent with probability one. We also derived the sufficient conditions of the persistence in the mean for the susceptible and infected when another indicator [Formula: see text].

scholarly journals Dynamics of a single predator multiple prey model with stochastic perturbation and seasonal variation

Filomat ◽  
2021 ◽  
Vol 35 (2) ◽  
pp. 535-549
Author(s):  
Hong-Wen Hui ◽  
Lin-Fei Nie
Keyword(s):  
Seasonal Variation ◽  
Sufficient Conditions ◽  
Stochastic Perturbation ◽  
Analysis Method ◽  
Ultimate Boundedness ◽  
Persistence In The Mean ◽  
Global Positive Solution ◽  
The Mean ◽  
Stochastically Ultimate Boundedness ◽  
Theoretical Results

Considering various factors are stochastic rather than deterministic in the evolution of populations growth, in this paper, we propose a single predator multiple prey stochastic model with seasonal variation. By using the method of solving an explicit solution, the existence of global positive solution of this model are obtained. The method is more convenient than Lyapunov analysis method for some population models. Moreover, the stochastically ultimate boundedness are considered by using the comparison theorem of stochastic differential equation. Further, some sufficient conditions for the extinction and strong persistence in the mean of populations are discussed, respectively. In addition, by constructing some suitable Lyapunov functions, we show that this model admits at least one periodic solution. Finally, numerical simulations clearly illustrate the main theoretical results and the effects of white noise and seasonal variation for the persistence and extinction of populations.

A generalized stochastic competitive system with Ornstein–Uhlenbeck process

2020 ◽  
pp. 2150001
Author(s):  
Baodan Tian ◽  
Liu Yang ◽  
Xingzhi Chen ◽  
Yong Zhang
Keyword(s):  
Dynamical Behavior ◽  
Sufficient Conditions ◽  
Competitive System ◽  
Uhlenbeck Process ◽  
Stochastic Perturbations ◽  
Stochastic Permanence ◽  
Persistence In The Mean ◽  
Ornstein Uhlenbeck Process ◽  
Global Positive Solution ◽  
The Mean

A generalized competitive system with stochastic perturbations is proposed in this paper, in which the stochastic disturbances are described by the famous Ornstein–Uhlenbeck process. By theories of stochastic differential equations, such as comparison theorem, Itô’s integration formula, Chebyshev’s inequality, martingale’s properties, etc., the existence and the uniqueness of global positive solution of the system are obtained. Then sufficient conditions for the extinction of the species almost surely, persistence in the mean and the stochastic permanence for the system are derived, respectively. Finally, by a series of numerical examples, the feasibility and correctness of the theoretical analysis results are verified intuitively. Moreover, the effects of the intensity of the stochastic perturbations and the speed of the reverse in the Ornstein–Uhlenbeck process to the dynamical behavior of the system are also discussed.

Dynamics of a stochastic delayed avian influenza model with mutation and temporary immunity

2021 ◽  
pp. 2150029
Author(s):  
Ting Kang ◽  
Qimin Zhang
Keyword(s):  
Avian Influenza ◽  
Deterministic Model ◽  
Sufficient Conditions ◽  
Human Populations ◽  
Deterministic System ◽  
Persistence In The Mean ◽  
Global Positive Solution ◽  
The Mean ◽  
White Noises ◽  
Temporary Immunity

In this paper, the dynamic behaviors are studied for a stochastic delayed avian influenza model with mutation and temporary immunity. First, we prove the existence and uniqueness of the global positive solution for the stochastic model. Second, we give two different thresholds [Formula: see text] and [Formula: see text], and further establish the sufficient conditions of extinction and persistence in the mean for the avian-only subsystem and avian-human system, respectively. Compared with the corresponding deterministic model, the thresholds affected by the white noises are smaller than the ones of the deterministic system. Finally, numerical simulations are carried out to support our theoretical results. It is concluded that the vaccination immunity period can suppress the spread of avian influenza during poultry and human populations, while prompt the spread of mutant avian influenza in human population.

scholarly journals Dynamics of a stochastic phytoplankton-toxic phytoplankton-zooplankton system under regime switching

2021 ◽  
Author(s):  
He Liu ◽  
Chuanjun Dai ◽  
Hengguo Yu ◽  
Qing Guo ◽  
Jianbing Li ◽  
...  
Keyword(s):  
White Noise ◽  
Regime Switching ◽  
Existence And Uniqueness ◽  
Sufficient Conditions ◽  
Aquatic Environments ◽  
Combined Effects ◽  
Toxic Phytoplankton ◽  
Persistence In The Mean ◽  
Global Positive Solution ◽  
The Mean

In this paper, a stochastic phytoplankton-toxic phytoplankton-zooplankton system with Beddington-DeAngelis functional response, where both the white noise and regime switching are taken into account, is studied analytically and numerically. The aim of this research is to study the combined effects of the white noise, regime switching and toxin-producing phytoplankton (TPP) on the dynamics of the system. Firstly, the existence and uniqueness of global positive solution of the system is investigated. Then some sufficient conditions for the extinction, persistence in the mean and the existence of a unique ergidoc stationary distribution of the system are derived. Significantly, some numerical simulations are carried to verify our analytical results, and show that high intensity of white noise is harmful to the survival of plankton populations, but regime switching can balance the different survival states of plankton populations and decrease the risk of extinction. Additionally, it is found that an increase in the toxin liberation rate produced by TPP will increase the survival change of phytoplankton, while it will reduce the biomass of zooplankton. All these results may provide some insightful understanding on the dynamics of phytoplankton-zooplankton system in randomly disturbed aquatic environments.

The global dynamics of stochastic Holling type II predator-prey models with non constant mortality rate

Filomat ◽  
2017 ◽  
Vol 31 (18) ◽  
pp. 5811-5825
Author(s):  
Xinhong Zhang
Keyword(s):  
Mortality Rate ◽  
Stochastic Model ◽  
Sufficient Conditions ◽  
Positive Periodic Solution ◽  
Global Dynamics ◽  
Type Ii ◽  
Predator Prey ◽  
Persistence In The Mean ◽  
The Mean ◽  
Predator Prey Models

In this paper we study the global dynamics of stochastic predator-prey models with non constant mortality rate and Holling type II response. Concretely, we establish sufficient conditions for the extinction and persistence in the mean of autonomous stochastic model and obtain a critical value between them. Then by constructing appropriate Lyapunov functions, we prove that there is a nontrivial positive periodic solution to the non-autonomous stochastic model. Finally, numerical examples are introduced to illustrate the results developed.

ASYMPTOTIC BEHAVIOR OF A STOCHASTIC DELAYED CHEMOSTAT MODEL WITH NUTRIENT STORAGE

2018 ◽  
Vol 26 (02) ◽  
pp. 225-246 ◽  
Author(s):  
SHULIN SUN ◽  
XIAOFENG ZHANG
Keyword(s):  
Asymptotic Behavior ◽  
Time Delay ◽  
Function Analysis ◽  
Sufficient Conditions ◽  
Classical Approach ◽  
Nutrient Storage ◽  
Chemostat Model ◽  
Global Positive Solution ◽  
The Mean ◽  
Simulation Results

In this paper, a stochastic delayed chemostat model with nutrient storage is proposed and investigated. First, we state that there is a unique global positive solution for this stochastic system. Second, using the classical approach of Lyapunov function analysis, this stochastic delayed chemostat model is discussed in detail. We establish some sufficient conditions for the extinction of the microorganism, furthermore, we prove that the microorganism will become persistent in the mean in the chemostat under some conditions. Finally, the obtained results are illustrated by computer simulations, and simulation results reveal the effects of time delay on the persistence and extinction of the microorganism.

Dynamics of a stochastic predator–prey model with mutual interference

2014 ◽  
Vol 07 (03) ◽  
pp. 1450026 ◽  
Author(s):  
Kai Wang ◽  
Yanling Zhu
Keyword(s):  
Numerical Simulation ◽  
Positive Solution ◽  
Sufficient Conditions ◽  
Stochastic Perturbation ◽  
Mutual Interference ◽  
Predator Prey ◽  
Predator Prey Model ◽  
Persistence In The Mean ◽  
The Mean ◽  
Globally Positive Solution

In this paper, a stochastic predator–prey (PP) model with mutual interference is considered. Some sufficient conditions for the existence of globally positive solution, non-persistence in the mean, weak persistence in the mean, strong persistence in the mean and almost surely extinction of the the model are established. Moreover, the threshold between weak persistence in the mean and almost surely extinction of the prey is obtained. Some examples are given to show the feasibility of the results by numerical simulation. It is significant that such a model is firstly proposed with stochastic perturbation.

Dynamics of a stochastic SIRS epidemic model with standard incidence under regime switching

2021 ◽  
pp. 2150074
Author(s):  
Jiang Xu ◽  
Yinong Wang ◽  
Zhongwei Cao
Keyword(s):  
Lyapunov Function ◽  
Stochastic System ◽  
Epidemic Model ◽  
Regime Switching ◽  
Sufficient Conditions ◽  
Sirs Epidemic Model ◽  
Persistence In The Mean ◽  
The Mean ◽  
Stochastic Sirs Epidemic Model ◽  
Stochastic Lyapunov Function

The goal of this paper is to introduce and initiate a study of a stochastic SIRS epidemic model with standard incidence which is perturbed by both white and telegraph noises. We first show persistence in the mean and then establish the sufficient conditions for extinction of the disease. Moreover, in the case of persistence, we obtain sufficient conditions for the existence of positive recurrence of the solutions by means of structuring suitable stochastic Lyapunov function with regime switching. Meanwhile, the threshold between persistence in the mean and extinction of the stochastic system is also obtained. Finally, we test our theory conclusion by simulations.

Dynamical behaviors of a prey-predator model with foraging arena scheme in polluted environments

2021 ◽  
Vol 71 (1) ◽  
pp. 235-250
Author(s):  
Xin He ◽  
Xin Zhao ◽  
Tao Feng ◽  
Zhipeng Qiu
Keyword(s):  
Periodic Solution ◽  
Stochastic System ◽  
Sufficient Conditions ◽  
Numerical Examples ◽  
Dynamical Behaviors ◽  
Analytical Results ◽  
Persistence In The Mean ◽  
The Mean ◽  
Predator Model

Abstract In this paper, a stochastic prey-predator model is investigated and analyzed, which possesses foraging arena scheme in polluted environments. Sufficient conditions are established for the extinction and persistence in the mean. These conditions provide a threshold that determines the persistence in the mean and extinction of species. Furthermore, it is also shown that the stochastic system has a periodic solution under appropriate conditions. Finally, several numerical examples are carried on to demonstrate the analytical results.

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