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.

The stability of the positive solution for a fractional SIR model

2016 ◽  
Vol 10 (01) ◽  
pp. 1750014 ◽  
Author(s):  
Yingjia Guo
Keyword(s):  
Differential Equation ◽  
Positive Solution ◽  
Stability Theory ◽  
Lyapunov Stability Theory ◽  
Sir Model ◽  
Differentiable Functions ◽  
Classical Calculus ◽  
Global Positive Solution ◽  
Fractional Differential ◽  
The Stability

In order to deal with non-differentiable functions, a modification of the Riemann–Liouville definition is recently proposed which appears to provide a framework for a fractional calculus which is quite parallel with classical calculus. Based on these new results, we study on the fractional SIR model in this paper. First, we give the general solution of the fractional differential equation. And then a unique global positive solution of the SIR model is obtained. Furthermore, we get the Lyapunov stability theory. By using this stability theory, the asymptotic stability of the positive solution is analyzed.

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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