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.

scholarly journals Analysis of a Dengue Disease Model with Nonlinear Incidence

2013 ◽  
Vol 2013 ◽  
pp. 1-10 ◽  
Author(s):  
Shu-Min Guo ◽  
Xue-Zhi Li ◽  
Mini Ghosh
Keyword(s):  
Numerical Simulations ◽  
Epidemic Model ◽  
Disease Model ◽  
Geometric Approach ◽  
Backward Bifurcation ◽  
Nonlinear Incidence ◽  
Dengue Disease ◽  
Proposed Model ◽  
The Stability

A dengue disease epidemic model with nonlinear incidence is formulated and analyzed. The equilibria and threshold of the model are found. The stability of the system is analyzed through a geometric approach to stability. The proposed model also exhibits backward bifurcation under suitable conditions on parameters. Our results imply that a nonlinear incidence produces rich dynamics and they should be studied carefully in order to analyze the spread of disease more accurately. Finally, numerical simulations are presented to illustrate the analytical findings.

A stochastic vaccinated epidemic model incorporating Lévy processes with a general awareness-induced incidence

2021 ◽  
pp. 2150044
Author(s):  
Khadija Akdim ◽  
Adil Ez-Zetouni ◽  
Mehdi Zahid
Keyword(s):  
Numerical Simulations ◽  
Positive Solution ◽  
Dynamic Behavior ◽  
Epidemic Model ◽  
Equilibrium Points ◽  
Sufficient Conditions ◽  
Lévy Noise ◽  
Global Positive Solution ◽  
Levy Noise ◽  
Disease Free

In this paper, we investigate a stochastic vaccinated epidemic model with a general awareness-induced incidence perturbed by Lévy noise. First, we show that this model has a unique global positive solution. Therefore, we establish the dynamic behavior of the solution around both disease-free and endemic equilibrium points. Furthermore, when [Formula: see text], we give sufficient conditions for the existence of an ergodic stationary distribution to the model when the jump part in the Lévy noise is null. Finally, we present some examples to illustrate the analytical results by numerical simulations.

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 Dynamics of the burning model

2005 ◽  
Vol 12 (5) ◽  
pp. 717-723 ◽  
Author(s):  
M. Gedalin ◽  
M. Bregman ◽  
M. Balikhin ◽  
D. Coca ◽  
G. Consolini ◽  
...  
Keyword(s):  
Numerical Simulations ◽  
Crucial Role ◽  
Active Sites ◽  
Continuous System ◽  
Life Time ◽  
Model Parameters ◽  
Analytical Treatment ◽  
Analytical Results ◽  
Local Threshold ◽  
Burning Model

Abstract. We propose a new avalanching model which is characterized by a) a local threshold in the transition from passive to active states, b) finite life time of active sites, and c) is dissipative. This model seems to be more appropriate for the description of a continuous system where localized reconnection plays a crucial role. The model allows for an analytical treatment. We establish the shape of the distribution of cluster sizes and the relation of the observables to the model parameters. The results are illustrated with numerical simulations which 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.

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 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.

scholarly journals Threshold dynamics for a class of stochastic SIRS epidemic models with nonlinear incidence and Markovian switching

2021 ◽  
Author(s):  
Amine EL Koufi ◽  
Abdelkrim Bennar ◽  
Noura Yousfi ◽  
M Pitchaimani
Keyword(s):  
Numerical Simulations ◽  
Stochastic System ◽  
Epidemic Model ◽  
Stochastic Calculus ◽  
Markovian Switching ◽  
Threshold Dynamics ◽  
Nonlinear Incidence ◽  
Sirs Epidemic Model ◽  
Stochastic Sirs Epidemic Model ◽  
Theoretical Results

In this paper, we consider a stochastic SIRS epidemic model with nonlinear incidence and Markovian switching. By using the stochastic calculus background, we establish that the stochastic threshold R_{ swt}  can be used to determine the compartment dynamics of the stochastic system. Some examples and numerical simulations are presented to confirm the theoretical results established in this paper.

Sign in / Sign up

Export Citation Format

Share Document