Stationary distribution and probability density function of a stochastic SVIS epidemic model with standard incidence and vaccination strategies

Zhou, Baoquan; Jiang, Daqing; Dai, Yucong; Hayat, Tasawar; Alsaedi, Ahmed

doi:10.1016/j.chaos.2020.110601

Cited by 32 publications

(11 citation statements)

References 42 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Combining the Routh‐Hurwitz stability criterion 46 and Zhou et al, 47 a solving theory of a special algebraic equation is shown in the following Lemma .…”

Section: Models Notations and Necessary Lemmasmentioning

confidence: 98%

Ergodic property, extinction, and density function of an SIRI epidemic model with nonlinear incidence rate and high‐order stochastic perturbations

Zhou

Jiang

Dai

et al. 2021

Math Methods in App Sciences

Self Cite

View full text Add to dashboard Cite

In this paper, we investigate an SIRI epidemic model with nonlinear incidence rate and high‐order stochastic perturbation. First, we obtain a stochastic threshold scriptR0P related to the basic reproduction number scriptR0. A key contribution of our paper is to derive the existence and uniqueness of an ergodic stationary distribution of the stochastic model if scriptR0P>1. Next, by solving the corresponding Fokker‐Planck equation, the exact expression of probability density function of the stochastic model is obtained. Moreover, we establish the sufficient condition scriptR0Q<1 for disease extinction in a long term. Finally, several empirical examples and numerical simulations are provided to verify the above theoretical results.

show abstract

“…Combining the Routh‐Hurwitz stability criterion 46 and Zhou et al, 47 a solving theory of a special algebraic equation is shown in the following Lemma .…”

Section: Models Notations and Necessary Lemmasmentioning

confidence: 98%

Ergodic property, extinction, and density function of an SIRI epidemic model with nonlinear incidence rate and high‐order stochastic perturbations

Zhou

Jiang

Dai

et al. 2021

Math Methods in App Sciences

Self Cite

View full text Add to dashboard Cite

show abstract

“…This population is divided into susceptible vaccinated infected populations at any instant In this study, the susceptible individuals obey the rule of logistic growth model which is the growth process of species in natural way (Jiang et al 2007 ; Arino et al 2006 ; Xu et al 2015 ). We formulate a deterministic SVIS epidemic system (Zhou et al 2020 , 2021 ) with saturated incidence and vaccination strategies, which is given as where and are all positive constants. The parameter is the intrinsic growth rate of susceptible individuals, and depicts the carrying capacity of The term is more sensitive than the bilinear incidence rate in epidemiological study (Zhu et al 2020 ; Xu et al 2016 ; Batabyal and Batabyal 2021 ; Chong et al 2014 ).…”

Section: Model Calibration and Dynamical Behaviormentioning

confidence: 99%

“…The existence of ergodic stationary distribution and the probability density function of the SVIS epidemic model were studied by Zhou et al ( 2020 ). Zhou et al ( 2021 ) solved the general three-dimensional Fokker–Planck equation. The existence of stationary distribution and ergodicity of the system has been discussed.…”

Section: Introductionmentioning

confidence: 99%

Stationary distribution and density function analysis of SVIS epidemic model with saturated incidence and vaccination under stochastic environments

Mahato

Das

et al. 2023

Theory Biosci.

View full text Add to dashboard Cite

In this article, we study the dynamical properties of susceptible-vaccinated-infected-susceptible (SVIS) epidemic system with saturated incidence rate and vaccination strategies. By constructing the suitable Lyapunov function, we examine the existence and uniqueness of the stochastic system. With the help of Khas’minskii theory, we set up a critical value with respect to the basic reproduction number of the deterministic system. A unique ergodic stationary distribution is investigated under the condition of . In the epidemiological study, the ergodic stationary distribution represents that the disease will persist for long-term behavior. We focus for developing the general three-dimensional Fokker–Planck equation using appropriate solving theories. Around the quasi-endemic equilibrium, the probability density function of the stochastic system is analyzed which is the main theme of our study. Under , both the existence of ergodic stationary distribution and density function can elicit all the dynamical behavior of the disease persistence. The condition of disease extinction of the system is derived. For supporting theoretical study, we discuss the numerical results and the sensitivities of the biological parameters. Results and conclusions are highlighted.

show abstract

“…is a positive definite matrix on the basis of Zhou et al 28, Lemma 2.3, and c 1 > 0 is the minimum eigenvalue of matrix Θ0 .…”

Section: Dynamical Analysis and Density Function For The Model With B...mentioning

confidence: 99%

Dynamical behavior and density function analysis of a stochastic HIV/AIDS model with general incidence rate

Zhang

Yang

Wang

2022

Math Methods in App Sciences

View full text Add to dashboard Cite

In this paper, we mainly present the dynamic properties of a stochastic SICA model with general incidence rate. Through rigorous analysis and reasoning of the stochastic model, we obtain that the solution of the model is global, positive, and unique. By constructing the threshold value R s 0 , which includes the influence of white noise, we obtain a sufficient condition for the ergodicity of this model. Furthermore, we show that the model has a unique ergodic stationary distribution while R s 0 > 1 by adopting a novel method. The extinction of the system is also established. Besides, the expression of probability density function of the stochastic model with bilinear incidence rate around the unique stable positive equilibrium of the deterministic model is derived. Finally, numerical simulations are presented to illustrate the theoretical results.

show abstract

Stationary distribution and probability density function of a stochastic SVIS epidemic model with standard incidence and vaccination strategies

Cited by 32 publications

References 42 publications

Ergodic property, extinction, and density function of an SIRI epidemic model with nonlinear incidence rate and high‐order stochastic perturbations

Ergodic property, extinction, and density function of an SIRI epidemic model with nonlinear incidence rate and high‐order stochastic perturbations

Stationary distribution and density function analysis of SVIS epidemic model with saturated incidence and vaccination under stochastic environments

Dynamical behavior and density function analysis of a stochastic HIV/AIDS model with general incidence rate

Contact Info

Product

Resources

About