Stability of a stochastic SIR system

Tornatore, Elisabetta; Buccellato, Stefania Maria; Vetro, Pasquale

doi:10.1016/j.physa.2005.02.057

Cited by 245 publications

(184 citation statements)

References 6 publications

Supporting

Mentioning

170

Contrasting

Unclassified

Order By: Relevance

“…µ is called a daily death removal rate; iii) β is the daily contact rate, i.e., the average number of contacts per infective In fact, all infectious diseases are subject to randomness in terms of the nature of transmission. Recently, Tornatore et al [16] investigate the dynamics of system (2) by perturbing the functional contact rates and modified (2) as:…”

Section: S T I T R T K + + =mentioning

confidence: 99%

“…(where σ is a positive constant), the system (3) becomes the model which has been discussed in [16]. In [16], Tornatore proved the stability of disease-free equilibrium under some restricted conditions.…”

Section: F T F T σ = =mentioning

confidence: 99%

“…In [16], Tornatore proved the stability of disease-free equilibrium under some restricted conditions. However, they didn't consider the dynamics of the endemic equilibrium.…”

Section: F T F T σ = =mentioning

confidence: 99%

“…Furthermore, we also investigate the stochastic asymptotic stability of disease free equilibria and the dynamics of endemic equilibria which has not been discussed in [16].…”

Section: F T F T σ = =mentioning

confidence: 99%

See 3 more Smart Citations

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

Xie¹,

Ma²,

Xu³

2017

View full text Add to dashboard Cite

In this paper, we propose random fluctuation on contact and recovery rates in deterministic SIR model with disease deaths in nonparametric manner and derive a new stochastic SIR model with distributed time delay and general diffusion coefficients. By analysis of the introduced model, we obtain the sufficient conditions for the regularity, existence and uniqueness of a global solution by means of Lyapunov function. Moreover, we also investigate the stochastic asymptotic stability of disease free equilibria and endemic equilibria of this model. Finally, we illustrate our general results by applications.

show abstract

Section: S T I T R T K + + =mentioning

confidence: 99%

Section: F T F T σ = =mentioning

confidence: 99%

“…In [16], Tornatore proved the stability of disease-free equilibrium under some restricted conditions. However, they didn't consider the dynamics of the endemic equilibrium.…”

Section: F T F T σ = =mentioning

confidence: 99%

“…Furthermore, we also investigate the stochastic asymptotic stability of disease free equilibria and the dynamics of endemic equilibria which has not been discussed in [16].…”

Section: F T F T σ = =mentioning

confidence: 99%

See 2 more Smart Citations

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

Xie¹,

Ma²,

Xu³

2017

View full text Add to dashboard Cite

show abstract

“…Several stochastic dynamic models describing single and multi-group disease dynamics have been investigated [20]- [29]. In [21], a stochastic multi-group SIRS epidemic dynamic models is derived and studied.…”

Section: Introductionmentioning

confidence: 99%

The Global Analysis of a Stochastic Two-Scale Network Epidemic Dynamic Model with Varying Immunity Period

Wanduku¹,

Ladde²

2017

JAMP

View full text Add to dashboard Cite

A stochastic SIR epidemic dynamic model with distributed-time-delay, for a two-scale dynamic population is derived. The distributed time delay is the varying naturally acquired immunity period of the removal class of individuals who have recovered from the infection, and have acquired natural immunity to the disease. We investigate the stochastic asymptotic stability of the disease free equilibrium of the epidemic dynamic model, and verify the impact on the eradication of the disease.

show abstract

Asymptotic dynamics of a deterministic and stochastic predator–prey model with disease in the prey species

Foryś

Qiao

Liu

2013

Math Methods in App Sciences

View full text Add to dashboard Cite

Communicated by M. A. LachowiczIn this paper, we discuss a predator-prey model with the Beddington-DeAngelis functional response of predators and a disease in the prey species. At first we study permanence and global stability of a positive equilibrium for the deterministic version of the model. Then we include a stochastic perturbation of the white noise type. We analyse the influence of this stochastic perturbation on the systems and prove that the positive equilibrium is also globally asymptotically stable in this case. The key point of our analysis is to choose appropriate Lyapunov functionals. We point out the differences between the deterministic and stochastic versions of the model.

show abstract

Stability of a stochastic SIR system

Cited by 245 publications

References 6 publications

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

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

The Global Analysis of a Stochastic Two-Scale Network Epidemic Dynamic Model with Varying Immunity Period

Asymptotic dynamics of a deterministic and stochastic predator–prey model with disease in the prey species

Contact Info

Product

Resources

About