Dynamics of a Nonautonomous Stochastic SIS Epidemic Model with Double Epidemic Hypothesis

Qi, Haokun; Liu, Lidan; Meng, Xinzhu

doi:10.1155/2017/4861391

Cited by 61 publications

(31 citation statements)

References 44 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…May [12] has pointed out that because of the continuous interference of the environment, the biological parameters in the ecosystem such as birth rates, intraspecific competition coefficients, death rates and other parameters may have some degree of random fluctuation. Parameter perturbation induced by white noise is an important and common form to describe the effect of stochasticity [13][14][15][16][17]. In recent years, many famous susceptible-infected-recovered-susceptible stochastic models have been formulated (see e.g.…”

Section: Introductionmentioning

confidence: 99%

Dynamics analysis of stochastic epidemic models with standard incidence

et al. 2019

View full text Add to dashboard Cite

In this paper, two stochastic SIRS epidemic models with standard incidence were proposed and investigated. For the non-autonomous periodic model, the sufficient criteria for extinction of the disease are obtained firstly. Then we show that the stochastic system has at least one nontrivial positive T-periodic solution under some conditions. For the model that are both disturbed by the white noise and telephone noise, we construct a suitable Lyapunov functions to verify the existence of a unique ergodic stationary distribution. Meanwhile, the sufficient condition for the extinction of the disease is also established. Finally, examples are introduced to illustrate the theoretical analysis. MSC: 60H10; 65C30; 91B70

show abstract

Section: Introductionmentioning

confidence: 99%

Dynamics analysis of stochastic epidemic models with standard incidence

et al. 2019

View full text Add to dashboard Cite

show abstract

“…Meng Zhang et al considered the preventive control of computer worm's transmission through Internet [12]. Recently discussions regarding impulsive disturbance based on state feedback have dominated the research in field of control theory and optimization [13][14][15][16][17][18]. Enlightened by those research about impulsive model, we construct a state feedback impulsive SIS model to analyze the therapy control of animal infectious diseases.…”

Section: Introductionmentioning

confidence: 99%

State feedback impulsive therapy to SIS model of animal infectious diseases

Liu

Zhang

Chen

2019

Physica A: Statistical Mechanics and its Applications

View full text Add to dashboard Cite

h i g h l i g h t s• A state feedback impulsive model is constructed to analyze the treatment of animal epidemics.• The existence of order-1 periodic solution to an impulsive system is proved.• The stability of the order-1 periodic solution is proved with a novel method. a b s t r a c tControlling animal infectious diseases and its related infra microbes is of great significance to public health, since a lot of infectious diseases originate from animal epidemics and they often threaten human health. A state feedback impulsive model is constructed to depict the transmission and treatment of animal epidemics. Basing on the impulsive model, the existence of order-1 periodic solution and its stability are proved with a novel method. The theoretical results indicate that the impulsive treatment triggered by the number of infectious is an efficient approach to control animal infectious disease from breakout. Numerical simulation is presented to support the theoretical conclusion in the end.

show abstract

“…There is no denying that this phenomenon is ubiquitous in the ecosystem. Therefore numerous scholars have introduced the effect of stochastic perturbation on diseases [41][42][43][44][45][46][47][48][49][50]. To the best of our knowledge, the research on global dynamics of the stochastic SEIQR epidemic model with imperfect vaccination is not too much yet.…”

Section: Introductionmentioning

confidence: 99%

Analysis and Numerical Simulations of a Stochastic SEIQR Epidemic System with Quarantine-Adjusted Incidence and Imperfect Vaccination

Meng

Wang

2018

Computational and Mathematical Methods in Medicine

Self Cite

View full text Add to dashboard Cite

This paper considers a high-dimensional stochastic SEIQR (susceptible-exposed-infected-quarantined-recovered) epidemic model with quarantine-adjusted incidence and the imperfect vaccination. The main aim of this study is to investigate stochastic effects on the SEIQR epidemic model and obtain its thresholds. We first obtain the sufficient condition for extinction of the disease of the stochastic system. Then, by using the theory of Hasminskii and the Lyapunov analysis methods, we show there is a unique stationary distribution of the stochastic system and it has an ergodic property, which means the infectious disease is prevalent. This implies that the stochastic disturbance is conducive to epidemic diseases control. At last, computer numerical simulations are carried out to illustrate our theoretical results.

show abstract

Dynamics of a Nonautonomous Stochastic SIS Epidemic Model with Double Epidemic Hypothesis

Cited by 61 publications

References 44 publications

Dynamics analysis of stochastic epidemic models with standard incidence

Dynamics analysis of stochastic epidemic models with standard incidence

State feedback impulsive therapy to SIS model of animal infectious diseases

Analysis and Numerical Simulations of a Stochastic SEIQR Epidemic System with Quarantine-Adjusted Incidence and Imperfect Vaccination

Contact Info

Product

Resources

About