scholarly journals Asymptotic Behavior and Stability of Stochastic SIR Model with Variable Diffusion Rates

2017 ◽  
Vol 08 (08) ◽  
pp. 1031-1044 ◽  
Author(s):  
Xianhua Xie ◽  
Li Ma ◽  
Jingfei Xu
Keyword(s):  
Asymptotic Behavior ◽  
Sir Model ◽  
Variable Diffusion ◽  
Diffusion Rates ◽  
Stochastic Sir ◽  
Stochastic Sir Model

scholarly journals Asymptotic behavior of global positive solution to a stochastic SIR model

2011 ◽  
Vol 54 (1-2) ◽  
pp. 221-232 ◽  
Author(s):  
Daqing Jiang ◽  
Jiajia Yu ◽  
Chunyan Ji ◽  
Ningzhong Shi
Keyword(s):  
Asymptotic Behavior ◽  
Positive Solution ◽  
Sir Model ◽  
Global Positive Solution ◽  
Stochastic Sir ◽  
Stochastic Sir Model

scholarly journals Classification of Asymptotic Behavior in a Stochastic SIR Model

2016 ◽  
Vol 15 (2) ◽  
pp. 1062-1084 ◽  
Author(s):  
N. T. Dieu ◽  
D. H. Nguyen ◽  
N. H. Du ◽  
G. Yin
Keyword(s):  
Asymptotic Behavior ◽  
Sir Model ◽  
Stochastic Sir ◽  
Stochastic Sir Model

scholarly journals Modelling the spread of American foulbrood in honeybees

2013 ◽  
Vol 10 (88) ◽  
pp. 20130650 ◽  
Author(s):  
Samik Datta ◽  
James C. Bull ◽  
Giles E. Budge ◽  
Matt J. Keeling
Keyword(s):  
Monte Carlo ◽  
Markov Chain ◽  
Control Strategies ◽  
Sir Model ◽  
Model Parameters ◽  
American Foulbrood ◽  
Inspection Period ◽  
Stochastic Sir ◽  
Stochastic Sir Model ◽  
The Impact

We investigate the spread of American foulbrood (AFB), a disease caused by the bacterium Paenibacillus larvae , that affects bees and can be extremely damaging to beehives. Our dataset comes from an inspection period carried out during an AFB epidemic of honeybee colonies on the island of Jersey during the summer of 2010. The data include the number of hives of honeybees, location and owner of honeybee apiaries across the island. We use a spatial SIR model with an underlying owner network to simulate the epidemic and characterize the epidemic using a Markov chain Monte Carlo (MCMC) scheme to determine model parameters and infection times (including undetected ‘occult’ infections). Likely methods of infection spread can be inferred from the analysis, with both distance- and owner-based transmissions being found to contribute to the spread of AFB. The results of the MCMC are corroborated by simulating the epidemic using a stochastic SIR model, resulting in aggregate levels of infection that are comparable to the data. We use this stochastic SIR model to simulate the impact of different control strategies on controlling the epidemic. It is found that earlier inspections result in smaller epidemics and a higher likelihood of AFB extinction.

scholarly journals Global analysis of stochastic SIR model with variable diffusion rates

2018 ◽  
Vol 49 (2) ◽  
pp. 155-182 ◽  
Author(s):  
Pitchaimani M. ◽  
Rajasekar S.P.
Keyword(s):  
Equilibrium Solution ◽  
Deterministic Model ◽  
Global Analysis ◽  
Sir Epidemic Model ◽  
Treatment Rate ◽  
Stochastic Version ◽  
Sir Epidemic ◽  
Variable Diffusion ◽  
Stochastic Sir ◽  
Stochastic Sir Model

In this article, a stochastic SIR epidemic model with treatment rate in a population of varying size is proposed and investigated. For the stochastic version, we briefly discuss the existence of global unique solutions and using the Lyapunov function, the disease free equilibrium solution is globally asymptotic stabe if $\mathcal{R}_0\leq1$ and the endemic equilibrium solution is obtained when $\mathcal{R}_0>1$. The main attention is paid to the $p$th-moment exponentially stable on the system, proved under suitable assumptions on the white noise perturbations and the optimal control for the deterministic model. Finally numerical simulations are done to show our theoretical results and to demonstrate the complicated dynamics of the model.

scholarly journals Stochastic SIR model with jumps

2013 ◽  
Vol 26 (8) ◽  
pp. 867-874 ◽  
Author(s):  
Xianghua Zhang ◽  
Ke Wang
Keyword(s):  
Sir Model ◽  
Stochastic Sir ◽  
Stochastic Sir Model
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