A hepatitis stochastic epidemic model with acute and chronic stages

AbstractThe article is based on the study of hepatitis transmission dynamics using a stochastic epidemic model. We discuss the stochastic perturbations of our proposed model by considering the effect of environmental fluctuation and distribute the transmission rate in the form of white noise. Taking into account the Lyapunov function theory, the uniqueness and existence of the global positive solution are proven. Some sufficient conditions for the extinction and persistence in the mean are established. The numerical simulations are given to verify the main theoretical findings.

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Study on a susceptible–infected–vaccinated model with delay and proportional vaccination

International Journal of Biomathematics ◽

10.1142/s1793524518501024 ◽

2018 ◽

Vol 11 (08) ◽

pp. 1850102 ◽

Cited By ~ 1

Author(s):

Shuqi Gan ◽

Fengying Wei

Keyword(s):

Positive Solution ◽

Epidemic Model ◽

Sufficient Conditions ◽

Sufficient Condition ◽

Stochastic Epidemic ◽

Persistence In The Mean ◽

Global Positive Solution ◽

The Mean ◽

Stochastic Epidemic Model

A susceptible–infected–vaccinated epidemic model with proportional vaccination and generalized nonlinear rate is formulated and investigated in the paper. We show that the stochastic epidemic model admits a unique and global positive solution with probability one when constructing a proper [Formula: see text]-function therewith. Then a sufficient condition that guarantees the disappearances of diseases is derived when the indicator [Formula: see text]. Further, if [Formula: see text], then we obtain that the solution is weakly permanent with probability one. We also derived the sufficient conditions of the persistence in the mean for the susceptible and infected when another indicator [Formula: see text].

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DYNAMIC ANALYSIS OF AN SIR MODEL WITH STOCHASTIC PERTURBATIONS

International Journal of Biomathematics ◽

10.1142/s1793524513500411 ◽

2013 ◽

Vol 06 (06) ◽

pp. 1350041

Author(s):

ZHENJIE LIU ◽

JINLIANG WANG ◽

YALAN XU ◽

GUOQIANG LI

Keyword(s):

Epidemic Model ◽

Lyapunov Functions ◽

Sir Model ◽

Sir Epidemic Model ◽

Stochastic Perturbations ◽

Sir Epidemic ◽

Stochastic Epidemic ◽

Differential Infectivity ◽

Global Positive Solution ◽

Stochastic Epidemic Model

In this paper, we present a differential infectivity SIR epidemic model with modified saturation incidences and stochastic perturbations. We show that the stochastic epidemic model has a unique global positive solution, and we utilize stochastic Lyapunov functions to show the asymptotic behavior of the solution.

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Stochastic analysis of a SIRI epidemic model with double saturated rates and relapse

Journal of Applied Mathematics and Computing ◽

10.1007/s12190-021-01646-2 ◽

2021 ◽

Author(s):

Yan Zhang ◽

Shujing Gao ◽

Shihua Chen

Keyword(s):

Epidemic Model ◽

Sufficient Conditions ◽

Natural World ◽

Incidence Rates ◽

Environmental Fluctuation ◽

Stochastic Perturbations ◽

Saturated Incidence ◽

Global Positive Solution ◽

Random Fluctuations ◽

Crucial Part

AbstractInfectious diseases have for centuries been the leading causes of death and disability worldwide and the environmental fluctuation is a crucial part of an ecosystem in the natural world. In this paper, we proposed and discussed a stochastic SIRI epidemic model incorporating double saturated incidence rates and relapse. The dynamical properties of the model were analyzed. The existence and uniqueness of a global positive solution were proven. Sufficient conditions were derived to guarantee the extinction and persistence in mean of the epidemic model. Additionally, ergodic stationary distribution of the stochastic SIRI model was discussed. Our results indicated that the intensity of relapse and stochastic perturbations greatly affected the dynamics of epidemic systems and if the random fluctuations were large enough, the disease could be accelerated to extinction while the stronger relapse rate were detrimental to the control of the disease.

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Fractal–fractional and stochastic analysis of norovirus transmission epidemic model with vaccination effects

Scientific Reports ◽

10.1038/s41598-021-03732-8 ◽

2021 ◽

Vol 11 (1) ◽

Author(s):

Ting Cui ◽

Peijiang Liu ◽

Anwarud Din

Keyword(s):

Epidemic Model ◽

Fixed Point Theory ◽

Sufficient Conditions ◽

Stochastic Perturbation ◽

Point Theory ◽

Fractional Dynamics ◽

Contagious Diseases ◽

Proposed Model ◽

Global Positive Solution ◽

Definition Of

AbstractIn this paper, we investigate an norovirus (NoV) epidemic model with stochastic perturbation and the new definition of a nonlocal fractal–fractional derivative in the Atangana–Baleanu–Caputo (ABC) sense. First we present some basic properties including equilibria and the basic reproduction number of the model. Further, we analyze that the proposed stochastic system has a unique global positive solution. Next, the sufficient conditions of the extinction and the existence of a stationary probability measure for the disease are established. Furthermore, the fractal–fractional dynamics of the proposed model under Atangana–Baleanu–Caputo (ABC) derivative of fractional order “$${p}$$ p ” and fractal dimension “$${q}$$ q ” have also been addressed. Besides, coupling the non-linear functional analysis with fixed point theory, the qualitative analysis of the proposed model has been performed. The numerical simulations are carried out to demonstrate the analytical results. It is believed that this study will comprehensively strengthen the theoretical basis for comprehending the dynamics of the worldwide contagious diseases.

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A Stochastic Switched Epidemic Model with Two Epidemic Diseases

Complexity ◽

10.1155/2021/5560538 ◽

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.

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A generalized stochastic competitive system with Ornstein–Uhlenbeck process

International Journal of Biomathematics ◽

10.1142/s1793524521500017 ◽

2020 ◽

pp. 2150001

Author(s):

Baodan Tian ◽

Liu Yang ◽

Xingzhi Chen ◽

Yong Zhang

Keyword(s):

Dynamical Behavior ◽

Sufficient Conditions ◽

Competitive System ◽

Uhlenbeck Process ◽

Stochastic Perturbations ◽

Stochastic Permanence ◽

Persistence In The Mean ◽

Ornstein Uhlenbeck Process ◽

Global Positive Solution ◽

The Mean

A generalized competitive system with stochastic perturbations is proposed in this paper, in which the stochastic disturbances are described by the famous Ornstein–Uhlenbeck process. By theories of stochastic differential equations, such as comparison theorem, Itô’s integration formula, Chebyshev’s inequality, martingale’s properties, etc., the existence and the uniqueness of global positive solution of the system are obtained. Then sufficient conditions for the extinction of the species almost surely, persistence in the mean and the stochastic permanence for the system are derived, respectively. Finally, by a series of numerical examples, the feasibility and correctness of the theoretical analysis results are verified intuitively. Moreover, the effects of the intensity of the stochastic perturbations and the speed of the reverse in the Ornstein–Uhlenbeck process to the dynamical behavior of the system are also discussed.

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