scholarly journals Stationary Distribution and Dynamic Behaviour of a Stochastic SIVR Epidemic Model with Imperfect Vaccine

2018 ◽  
Vol 2018 ◽  
pp. 1-11 ◽  
Author(s):  
Driss Kiouach ◽  
Lahcen Boulaasair
Keyword(s):  
Numerical Simulations ◽  
Stationary Distribution ◽  
Epidemic Model ◽  
Critical Condition ◽  
Dynamic Behaviour ◽  
Sufficient Conditions ◽  
Analytical Results ◽  
The Mean

We consider a stochastic SIVR (susceptible-infected-vaccinated-recovered) epidemic model with imperfect vaccine. First, we obtain critical condition under which the disease is persistent in the mean. Second, we establish sufficient conditions for the existence of an ergodic stationary distribution to the model. Third, we study the extinction of the disease. Finally, numerical simulations are given to support the analytical results.

scholarly journals A Stochastic Switched Epidemic Model with Two Epidemic Diseases

Complexity ◽  
2021 ◽  
Vol 2021 ◽  
pp. 1-13
Author(s):  
Amine El Koufi ◽  
Abdelkrim Bennar ◽  
Noura Yousfi
Keyword(s):  
White Noise ◽  
Numerical Simulations ◽  
Epidemic Model ◽  
Sufficient Conditions ◽  
Markovian Switching ◽  
Analytical Results ◽  
Stochastic Epidemic ◽  
Telegraph Noise ◽  
Stochastic Epidemic Model ◽  
Epidemic Diseases

In this paper, we study a stochastic epidemic model with double epidemics which includes white noise and telegraph noise modeled by Markovian switching. Sufficient conditions for the extinction and persistence of the diseases are established. In the end, some numerical simulations are presented to demonstrate our analytical results.

scholarly journals Extinction and Stationary Distribution of a Stochastic SIRS Epidemic Model Incorporating Media Coverage

2019 ◽  
pp. 1-19
Author(s):  
Eric N'zi ◽  
Modeste N'zi
Keyword(s):  
Numerical Simulations ◽  
Stationary Distribution ◽  
Epidemic Model ◽  
Media Coverage ◽  
Sufficient Conditions ◽  
Stochastic Perturbation ◽  
Demographic Stochasticity ◽  
Sirs Epidemic Model ◽  
The Media ◽  
Well Posed

In this paper, we include stochastic perturbation into SIRS epidemic model incorporating media coverage and study their dynamics. Our model is obtained by taking into account both for demographic stochasticity and environmental fluctuations on contact rate before alert media β1. First, we show that the model is biologically well-posed by proving the global existence, positivity and boundedness of solution . Then, sufficient conditions for the extinction of infectious diseaseis proved. We also established sufficient conditions for the existence of an ergodic stationary distribution to the model. Finally, the theoretical results are illustrated by numerical simulations; in addition we show that the media coverage can reduce the peak of infective individuals via numerical simulations.

scholarly journals The Dynamics of a Stochastic SEITRmodel for Tuberculosis with Incomplete Treatment

2021 ◽  
Author(s):  
Xiaodong Wang ◽  
Chunxia Wang ◽  
k wang
Keyword(s):  
Numerical Simulations ◽  
Stationary Distribution ◽  
Sufficient Conditions ◽  
Numerical Results ◽  
Transmission Dynamics ◽  
Environmental Perturbations ◽  
Analytical Results

Abstract In this paper, a stochastic SEITR model is formulated to describe the transmission dynamics of tuberculosis with incompletely treated. Sufficient conditions for the existence of a stationary distribution and extinction are obtained. In addition, numerical simulations are given to illustrate these analytical results. Theoretical and numerical results show that large environmental perturbations can inhibit the spread of tuberculosis.

Modeling a stochastic avian influenza model under regime switching and with human-to-human transmission

2020 ◽  
Vol 13 (07) ◽  
pp. 2050064
Author(s):  
Zhenfeng Shi ◽  
Xinhong Zhang
Keyword(s):  
Avian Influenza ◽  
Numerical Simulations ◽  
Stationary Distribution ◽  
Stochastic System ◽  
Regime Switching ◽  
Lyapunov Functions ◽  
Sufficient Conditions ◽  
Analytical Results

In this paper, we investigate the stochastic avian influenza model with human-to-human transmission, which is disturbed by both white and telegraph noises. First, we show that the solution of the stochastic system is positive and global. Furthermore, by using stochastic Lyapunov functions, we establish sufficient conditions for the existence of a unique ergodic stationary distribution. Then we obtain the conditions for extinction. Finally, numerical simulations are employed to demonstrate the analytical results.

Dynamics of a stochastic heroin epidemic model with bilinear incidence and varying population size

2019 ◽  
Vol 12 (01) ◽  
pp. 1950005 ◽  
Author(s):  
Shitao Liu ◽  
Liang Zhang ◽  
Xiao-Bing Zhang ◽  
Aibing Li
Keyword(s):  
Numerical Simulations ◽  
Population Size ◽  
Stationary Distribution ◽  
Epidemic Model ◽  
Lyapunov Functions ◽  
Drug Abusers ◽  
Analytical Results ◽  
Varying Population ◽  
Better Than

We investigate a stochastic heroin epidemic model with bilinear incidence and varying population size. Sufficient criteria for the extinction of the drug abusers and the existence of ergodic stationary distribution for the model are established by constructing suitable stochastic Lyapunov functions. By analyzing the sensitivity of the threshold of spread, we obtain that prevention is better than cure. Numerical simulations are carried out to confirm the analytical results.

scholarly journals Dynamics of a stochastic SIQR epidemic model with saturated incidence rate

Filomat ◽  
2018 ◽  
Vol 32 (15) ◽  
pp. 5239-5253 ◽  
Author(s):  
Li-Li Wang ◽  
Nan-Jing Huang ◽  
Donal O’Regan
Keyword(s):  
Numerical Simulations ◽  
Positive Solution ◽  
Incidence Rate ◽  
Epidemic Model ◽  
Lyapunov Functions ◽  
Sufficient Conditions ◽  
Saturated Incidence Rate ◽  
Saturated Incidence ◽  
Global Positive Solution ◽  
The Mean

The purpose of this paper is to propose and investigate a stochastic SIQR epidemic model with saturated incidence rate. Firstly, we give some conditions to guarantee the stochastic SIQR epidemic model has a unique global positive solution. Then we verify that the disease in this model will die out exponentially if Rs 0 < 1, while the disease will be persistent in the mean if Rs 0 > 1. Moreover, by constructing suitable Lyapunov functions, we establish some sufficient conditions for the existence of an ergodic stationary distribution for the model. Finally, we provide some numerical simulations to illustrate the analytical results.

scholarly journals Ergodic Stationary Distribution of a Stochastic Hepatitis B Epidemic Model with Interval-Valued Parameters and Compensated Poisson Process

2020 ◽  
Vol 2020 ◽  
pp. 1-12
Author(s):  
Driss Kiouach ◽  
Yassine Sabbar
Keyword(s):  
Hepatitis B ◽  
Poisson Process ◽  
Numerical Simulations ◽  
Positive Solution ◽  
Stationary Distribution ◽  
Epidemic Model ◽  
Environmental Disturbances ◽  
Analytical Results ◽  
Global Positive Solution ◽  
Interval Valued

Hepatitis B epidemic was and is still a rich subject that sparks the interest of epidemiological researchers. The dynamics of this epidemic is often modeled by a system with constant parameters. In reality, the parameters associated with the Hepatitis B model are not certain, but the interval in which it belongs to can readily be determined. Our paper focuses on an imprecise Hepatitis B model perturbed by Lévy noise due to unexpected environmental disturbances. This model has a global positive solution. Under an appropriate assumption, we prove the existence of a unique ergodic stationary distribution by using the mutually exclusive possibilities lemma demonstrated by Stettner in 1986. Our main effort is to establish an almost perfect condition for the existence of the stationary distribution. Numerical simulations are introduced to illustrate the analytical results.

A stochastic threshold of a delayed epidemic model incorporating Lévy processes with harmonic mean and vaccination

2020 ◽  
Vol 13 (07) ◽  
pp. 2050069 ◽  
Author(s):  
Mohamed El Fatini ◽  
Idriss Sekkak ◽  
Aziz Laaribi ◽  
Roger Pettersson ◽  
Kai Wang
Keyword(s):  
Numerical Simulations ◽  
Epidemic Model ◽  
Harmonic Mean ◽  
Lévy Noise ◽  
Model Parameters ◽  
Well Posedness ◽  
Nonlinear Incidence ◽  
Model Driven ◽  
Analytical Results ◽  
Tuberculosis Disease

The aim of this paper is to investigate a stochastic threshold for a delayed epidemic model driven by Lévy noise with a nonlinear incidence and vaccination. Mainly, we derive a stochastic threshold [Formula: see text] which depends on model parameters and stochastic coefficients for a better understanding of the dynamical spreading of the disease. First, we prove the well posedness of the model. Then, we study the extinction and the persistence of the disease according to the values of [Formula: see text]. Furthermore, using different scenarios of Tuberculosis disease in Morocco, we perform some numerical simulations to support the analytical results.

The stationary distribution and ergodicity of a stochastic mutualism model

2018 ◽  
Vol 68 (3) ◽  
pp. 685-690 ◽  
Author(s):  
Jingliang Lv ◽  
Sirun Liu ◽  
Heng Liu
Keyword(s):  
Stochastic Model ◽  
Stationary Distribution ◽  
Sufficient Conditions ◽  
Ergodic Property ◽  
Model Simulations ◽  
Analytical Results ◽  
Stationary Distribution And Ergodicity ◽  
Mutualism Model ◽  
Mutualism System

Abstract This paper is concerned with a stochastic mutualism system with toxicant substances and saturation terms. We obtain the sufficient conditions for the existence of a unique stationary distribution to the equation and it has an ergodic property. It is interesting and surprising that toxicant substances have no effect on the stationary distribution of the stochastic model. Simulations are also carried out to confirm our analytical results.

scholarly journals Stationary Distribution and Extinction in a Stochastic SIQR Epidemic Model Incorporating Media Coverage and Markovian Switching

Symmetry ◽  
2021 ◽  
Vol 13 (7) ◽  
pp. 1122
Author(s):  
Yanlin Ding ◽  
Jianjun Jiao ◽  
Qianhong Zhang ◽  
Yongxin Zhang ◽  
Xinzhi Ren
Keyword(s):  
Numerical Simulation ◽  
Lyapunov Function ◽  
Stationary Distribution ◽  
Dynamic Characteristics ◽  
Epidemic Model ◽  
Regime Switching ◽  
Media Coverage ◽  
Sufficient Conditions ◽  
Unique Positive Solution ◽  
Theoretical Results

This paper is concerned with the dynamic characteristics of the SIQR model with media coverage and regime switching. Firstly, the existence of the unique positive solution of the proposed system is investigated. Secondly, by constructing a suitable random Lyapunov function, some sufficient conditions for the existence of a stationary distribution is obtained. Meanwhile, the conditions for extinction is also given. Finally, some numerical simulation examples are carried out to demonstrate the effectiveness of theoretical results.

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