Ergodic property, extinction and density function of a stochastic SIR epidemic model with nonlinear incidence and general stochastic perturbations

2021 ◽  
Vol 152 ◽  
pp. 111338
Author(s):  
Baoquan Zhou ◽  
Bingtao Han ◽  
Daqing Jiang
Keyword(s):  
Density Function ◽  
Epidemic Model ◽  
Ergodic Property ◽  
Sir Epidemic Model ◽  
Stochastic Perturbations ◽  
Nonlinear Incidence ◽  
Sir Epidemic ◽  
Stochastic Sir ◽  
General Stochastic

scholarly journals Stability Analysis of a Stochastic SIR Epidemic Model with Specific Nonlinear Incidence Rate

2013 ◽  
Vol 2013 ◽  
pp. 1-4 ◽  
Author(s):  
Jihad Adnani ◽  
Khalid Hattaf ◽  
Noura Yousfi
Keyword(s):  
Incidence Rate ◽  
Epidemic Model ◽  
Endemic Equilibrium ◽  
Random Perturbations ◽  
Sir Epidemic Model ◽  
Nonlinear Incidence Rate ◽  
Nonlinear Incidence ◽  
Sir Epidemic ◽  
Stochastic Sir ◽  
The Stability

We investigate a stochastic SIR epidemic model with specific nonlinear incidence rate. The stochastic model is derived from the deterministic epidemic model by introducing random perturbations around the endemic equilibrium state. The effect of random perturbations on the stability behavior of endemic equilibrium is discussed. Finally, numerical simulations are presented to illustrate our theoretical results.

scholarly journals Dynamics Analysis of a Stochastic SIR Epidemic Model

2014 ◽  
Vol 2014 ◽  
pp. 1-9 ◽  
Author(s):  
Feng Rao
Keyword(s):  
Epidemic Model ◽  
Lyapunov Functions ◽  
Dynamics Analysis ◽  
Qualitative Properties ◽  
Sir Epidemic Model ◽  
Stochastic Perturbations ◽  
Sir Epidemic ◽  
Stochastic Boundedness ◽  
Noise Type ◽  
Stochastic Sir

We investigate an SIR epidemic model with stochastic perturbations. We assume that stochastic perturbations are of a white noise type which is directly proportional to the distances of three variables from the steady-state values, respectively. By constructing suitable Lyapunov functions and applying Itô’s formula, some qualitative properties are obtained, such as the existence of global positive solutions, stochastic boundedness, and permanence. A series of numerical simulations to illustrate these mathematical findings are presented.

scholarly journals The Dynamics of a Stochastic SIR Epidemic Model with Nonlinear Incidence and Vertical Transmission

2021 ◽  
Vol 2021 ◽  
pp. 1-20
Author(s):  
Guihua Li ◽  
Yuanhang Liu
Keyword(s):  
Epidemic Model ◽  
Disease Transmission ◽  
Deterministic Model ◽  
Random Disturbance ◽  
State Variables ◽  
Sir Epidemic Model ◽  
Nonlinear Incidence ◽  
Transmission Parameters ◽  
Sir Epidemic ◽  
Stochastic Sir

In this study, we build a stochastic SIR epidemic model with vertical infection and nonlinear incidence. The influence of the fluctuation of disease transmission parameters and state variables on the dynamic behaviors of the system is the focus of our study. Through the theoretical analysis, we obtain that there exists a unique global positive solution for any positive initial value. A threshold R 0 s is given. When R 0 s < 1 , the diseases can be extincted with probability one. When R 0 s > 1 , we construct a stochastic Lyapunov function to prove that the system exists an ergodic stationary distribution, which means that the disease will persist. Then, we obtain the conditions that the solution of the stochastic model fluctuates widely near the equilibria of the corresponding deterministic model. Finally, the correctness of the results is verified by numerical simulation. It is further found that the fluctuation of disease transmission parameters and infected individuals with the environment can reduce the threshold of disease outbreak, while the fluctuation of susceptible and recovered individuals has a little effect on the dynamic behavior of the system. Therefore, we can make the disease extinct by adjusting the appropriate random disturbance.

scholarly journals Global dynamics of a novel deterministic and stochastic SIR epidemic model with vertical transmission and media coverage

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Xiaodong Wang ◽  
Chunxia Wang ◽  
Kai Wang
Keyword(s):  
Vertical Transmission ◽  
Epidemic Model ◽  
Media Coverage ◽  
Existence And Uniqueness ◽  
Deterministic Model ◽  
Reproduction Number ◽  
Global Dynamics ◽  
Sir Epidemic Model ◽  
Sir Epidemic ◽  
Stochastic Sir

AbstractIn this paper, we study a novel deterministic and stochastic SIR epidemic model with vertical transmission and media coverage. For the deterministic model, we give the basic reproduction number $R_{0}$ R 0 which determines the extinction or prevalence of the disease. In addition, for the stochastic model, we prove existence and uniqueness of the positive solution, and extinction and persistence in mean. Furthermore, we give numerical simulations to verify our results.

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