scholarly journals An SIS epidemic model with time delay and stochastic perturbation on heterogeneous networks

2021 ◽  
Vol 18 (5) ◽  
pp. 6790-6805
Author(s):  
Meici Sun ◽  
◽  
Qiming Liu
Keyword(s):  
Time Delay ◽  
Epidemic Model ◽  
Deterministic Model ◽  
Reproduction Number ◽  
Sufficient Conditions ◽  
Stochastic Perturbation ◽  
Scale Free ◽  
Sis Epidemic Model ◽  
The Mean ◽  
Sis Epidemic

<abstract><p>An SIS epidemic model with time delay and stochastic perturbation on scale-free networks is established in this paper. And we derive sufficient conditions guaranteeing extinction and persistence of epidemics, respectively, which are related to the basic reproduction number $ R_0 $ of the corresponding deterministic model. When $ R_0 &lt; 1 $, almost surely exponential extinction and $ p $-th moment exponential extinction of epidemics are proved by Razumikhin-Mao Theorem. Whereas, when $ R_0 &gt; 1 $, the system is persistent in the mean under sufficiently weak noise intensities, which indicates that the disease will prevail. Finally, the main results are demonstrated by numerical simulations.</p></abstract>

scholarly journals Dynamics of Stochastically Perturbed SIS Epidemic Model with Vaccination

2013 ◽  
Vol 2013 ◽  
pp. 1-12 ◽  
Author(s):  
Yanan Zhao ◽  
Daqing Jiang
Keyword(s):  
Epidemic Model ◽  
Death Rate ◽  
Deterministic Model ◽  
Reproduction Number ◽  
Dynamical Behavior ◽  
Standard Technique ◽  
Deterministic Models ◽  
Sis Epidemic Model ◽  
Disease Free ◽  
Sis Epidemic

We introduce stochasticity into an SIS epidemic model with vaccination. The stochasticity in the model is a standard technique in stochastic population modeling. In the deterministic models, the basic reproduction numberR0is a threshold which determines the persistence or extinction of the disease. When the perturbation and the disease-related death rate are small, we carry out a detailed analysis on the dynamical behavior of the stochastic model, also regarding of the value ofR0. IfR0≤1, the solution of the model is oscillating around a steady state, which is the disease-free equilibrium of the corresponding deterministic model, whereas, ifR0>1, there is a stationary distribution, which means that the disease will prevail. The results are illustrated by computer simulations.

scholarly journals The Dynamical Behaviors in a Stochastic SIS Epidemic Model with Nonlinear Incidence

2016 ◽  
Vol 2016 ◽  
pp. 1-14 ◽  
Author(s):  
Ramziya Rifhat ◽  
Qing Ge ◽  
Zhidong Teng
Keyword(s):  
Epidemic Model ◽  
Stochastic Perturbation ◽  
Threshold Value ◽  
Open Problems ◽  
Nonlinear Incidence ◽  
Sis Epidemic Model ◽  
Dynamical Behaviors ◽  
The Mean ◽  
Stochastic Sis Epidemic Model ◽  
Sis Epidemic

A stochastic SIS-type epidemic model with general nonlinear incidence and disease-induced mortality is investigated. It is proved that the dynamical behaviors of the model are determined by a certain threshold valueR~0. That is, whenR~0<1and together with an additional condition, the disease is extinct with probability one, and whenR~0>1, the disease is permanent in the mean in probability, and when there is not disease-related death, the disease oscillates stochastically about a positive number. Furthermore, whenR~0>1, the model admits positive recurrence and a unique stationary distribution. Particularly, the effects of the intensities of stochastic perturbation for the dynamical behaviors of the model are discussed in detail, and the dynamical behaviors for the stochastic SIS epidemic model with standard incidence are established. Finally, the numerical simulations are presented to illustrate the proposed open problems.

scholarly journals Analysis of a Deterministic and a Stochastic SIS Epidemic Model with Double Epidemic Hypothesis and Specific Functional Response

2020 ◽  
Vol 2020 ◽  
pp. 1-11
Author(s):  
Mouhcine Naim ◽  
Fouad Lahmidi
Keyword(s):  
Epidemic Model ◽  
Deterministic Model ◽  
Sufficient Condition ◽  
Nonlinear Incidence Rate ◽  
Local Asymptotic Stability ◽  
Sis Epidemic Model ◽  
The Stability ◽  
Stochastic Sis Epidemic Model ◽  
Disease Free ◽  
Sis Epidemic

The purpose of this paper is to investigate the stability of a deterministic and stochastic SIS epidemic model with double epidemic hypothesis and specific nonlinear incidence rate. We prove the local asymptotic stability of the equilibria of the deterministic model. Moreover, by constructing a suitable Lyapunov function, we obtain a sufficient condition for the global stability of the disease-free equilibrium. For the stochastic model, we establish global existence and positivity of the solution. Thereafter, stochastic stability of the disease-free equilibrium in almost sure exponential and pth moment exponential is investigated. Finally, numerical examples are presented.

Modelling the role of opportunistic diseases in coinfection

2018 ◽  
Vol 13 (3) ◽  
pp. 28
Author(s):  
Marcos Marvá ◽  
Rafael Bravo de la Parra ◽  
Ezio Venturino
Keyword(s):  
Epidemic Model ◽  
Recovery Rate ◽  
Reproduction Number ◽  
Backward Bifurcation ◽  
Treatment Rate ◽  
Opportunistic Disease ◽  
Sis Epidemic Model ◽  
Primary Disease ◽  
Sis Epidemic

In this paper, we formulate a model for evaluating the effects of an opportunistic disease affecting only those individuals already infected by a primary disease. The opportunistic disease act on a faster time scale and it is represented by an SIS epidemic model with frequency-dependent transmission. The primary disease is governed by an SIS epidemic model with density-dependent transmission, and we consider two different recovery cases. The first one assumes a constant recovery rate whereas the second one takes into account limited treatment resources by means of a saturating treatment rate. No demographics is included in these models.Our results indicate that misunderstanding the role of the opportunistic disease may lead to wrong estimates of the overall potential amount of infected individuals. In the case of constant recovery rate, an expression measuring this discrepancy is derived, as well as conditions on the opportunistic disease imposing a coinfection endemic state on a primary disease otherwise tending to disappear. The case of saturating treatment rate adds the phenomenon of backward bifurcation, which fosters the presence of endemic coinfection and greater levels of infected individuals. Nevertheless, there are specific situations where increasing the opportunistic disease basic reproduction number helps to eradicate both diseases.

scholarly journals A Stochastic SIS Epidemic Model with Ornstein-Uhlenbeck Process and Brown Motion

2021 ◽  
Author(s):  
Xingzhi Chen ◽  
Baodan Tian ◽  
Xin Xu ◽  
Ruoxi Yang ◽  
Shouming Zhong
Keyword(s):  
Basic Reproduction Number ◽  
Epidemic Model ◽  
Reproduction Number ◽  
Global Solutions ◽  
Uhlenbeck Process ◽  
Sis Epidemic Model ◽  
Ornstein Uhlenbeck Process ◽  
Brown Motion ◽  
Sis Epidemic ◽  
The Basic Reproduction Number

Abstract This paper studies a stochastic differential equation SIS epidemic model, disturbed randomly by the mean-reverting Ornstein-Uhlenbeck process and Brownian motion. We prove the existence and uniqueness of the positive global solutions of the model and obtain the controlling conditions for the extinction and persistence of the disease. The results show that when the basic reproduction number Rs0 < 1, the disease will extinct, on the contrary, when the basic reproduction number Rs0 > 1, the disease will persist. Furthermore, we can inhibit the outbreak of the disease by increasing the intensity of volatility or decreasing the speed of reversion ϑ, respectively. Finally, we give some numerical examples to verify these results.

scholarly journals The Behavior of an SVIR Epidemic Model with Stochastic Perturbation

2014 ◽  
Vol 2014 ◽  
pp. 1-7 ◽  
Author(s):  
Yanan Zhao ◽  
Daqing Jiang
Keyword(s):  
Epidemic Model ◽  
Lyapunov Functions ◽  
Deterministic Model ◽  
Reproduction Number ◽  
Stochastic Perturbation ◽  
Sir Epidemic Model ◽  
Sir Epidemic ◽  
Time Average ◽  
The Difference ◽  
Disease Free

We discuss a stochastic SIR epidemic model with vaccination. We investigate the asymptotic behavior according to the perturbation and the reproduction numberR0. We deduce the globally asymptotic stability of the disease-free equilibrium whenR0≤ 1and the perturbation is small, which means that the disease will die out. WhenR0>1, we derive that the disease will prevail, which is measured through the difference between the solution and the endemic equilibrium of the deterministic model in time average. The key to our analysis is choosing appropriate Lyapunov functions.

scholarly journals An SIS Epidemic Model with Infective Medium and Feedback Mechanism on Scale-Free Networks

OALib ◽  
2017 ◽  
Vol 04 (05) ◽  
pp. 1-9
Author(s):  
Xiongding Liu ◽  
Tao Li ◽  
Yuanmei Wang ◽  
Chen Wan ◽  
Jing Dong
Keyword(s):  
Epidemic Model ◽  
Feedback Mechanism ◽  
Scale Free ◽  
Sis Epidemic Model ◽  
Scale Free Networks ◽  
Sis Epidemic
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