Periodic solution and stationary distribution of stochastic SIR epidemic models with higher order perturbation

2017 ◽  
Vol 482 ◽  
pp. 209-217 ◽  
Author(s):  
Qun Liu ◽  
Daqing Jiang ◽  
Tasawar Hayat ◽  
Bashir Ahmad
Keyword(s):  
Periodic Solution ◽  
Stationary Distribution ◽  
Higher Order ◽  
Epidemic Models ◽  
Order Perturbation ◽  
Sir Epidemic ◽  
Stochastic Sir ◽  
Sir Epidemic Models

scholarly journals A Stochastic SIR Epidemic System with a Nonlinear Relapse

2018 ◽  
Vol 2018 ◽  
pp. 1-10 ◽  
Author(s):  
Ali El Myr ◽  
Abdelaziz Assadouq ◽  
Lahcen Omari ◽  
Adel Settati ◽  
Aadil Lahrouz
Keyword(s):  
Numerical Simulations ◽  
Stationary Distribution ◽  
Stochastic Perturbations ◽  
Sir Epidemic ◽  
Spread Model ◽  
Stochastic Sir ◽  
Theoretical Results

We investigate the conditions that control the extinction and the existence of a unique stationary distribution of a nonlinear mathematical spread model with stochastic perturbations in a population of varying size with relapse. Numerical simulations are carried out to illustrate the theoretical results.

Abel-Gontcharoff pseudopolynomials and the exact final outcome of SIR epidemic models (III)

1999 ◽  
Vol 31 (2) ◽  
pp. 532-550 ◽  
Author(s):  
Claude Lefèvre ◽  
Philippe Picard
Keyword(s):  
Algebraic Structure ◽  
Preceding Paper ◽  
Epidemic Models ◽  
Unified Approach ◽  
Finite Populations ◽  
Final State ◽  
Collective Models ◽  
Markovian Models ◽  
Sir Epidemic ◽  
Sir Epidemic Models

The paper is concerned with the final state and severity of a number of SIR epidemic models in finite populations. Two different classes of models are considered, namely the classical SIR Markovian models and the collective models introduced recently by the authors. First, by applying a simple martingale argument, it is shown that in both cases, there exists a common algebraic structure underlying the exact law of the final state and severity. Then, a unified approach to these statistics is developed by exploiting the theory of Abel-Gontcharoff pseudopolynomials (presented in a preceding paper).

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