Analysis of epidemic spreading of an SIRS model in complex heterogeneous networks

Li, Chun-Hsien; Tsai, Chiung Chiou; Yang, Shao-Ming

doi:10.1016/j.cnsns.2013.08.033

Cited by 143 publications

(66 citation statements)

References 28 publications

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“…Stability analysis is an important tool to understand the spreading dynamics of epidemic models on complex networks. Recently, there have been many studies concerning the stability and asymptotic behavior of epidemic models on complex networks [15][16][17][18][19][20][21][22][23].…”

Section: Introductionmentioning

confidence: 99%

Global stability of an SIS epidemic model with feedback mechanism on networks

Wei

Zhou

2018

Adv Differ Equ

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We study the global stability of endemic equilibrium of an SIS epidemic model with feedback mechanism on networks. The model was proposed by J. Zhang and J. Sun (Physica A 394:24-32, 2014), who obtained the local asymptotic stability of endemic equilibrium. Our main purpose is to show that if the feedback parameter is sufficiently large or if the basic reproductive number belongs to the interval (1, 2], then the endemic equilibrium is globally asymptotically stable. We also present numerical simulations to illustrate the theoretical results.

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Section: Introductionmentioning

confidence: 99%

Global stability of an SIS epidemic model with feedback mechanism on networks

Wei

Zhou

2018

Adv Differ Equ

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“…Here, N(t) = S(t) + I(t) + R(t) represents all individuals, λ is the rate of transmission per contact, d represents the diseased death rate and also represents the rate of recruitment of individuals, ν represents the rate at which recovered individuals lose immunity and return to the susceptible individuals, r is the recovery rate of the infected individuals. Many researchers have studied several different SIRS epidemic models in the literature [21][22][23][24][25]. In epidemiological models, many different types of incidence rate play an important role.…”

Section: = Dn(t) -Ds(t) -λS(t)i(t) + νR(t) Di(t) Dt = λS(t)i(t) -(D mentioning

confidence: 99%

“…Let us assume that all individuals are divided into three compartments: S(t) represents susceptible individuals who are susceptible to the disease; I(t) represents infected individuals who are infected by the disease; and R(t) represents recovered individuals who hold temporary immunity acquired from a disease, namely, after recovery, individuals lose immunity and move into the susceptible individuals. This is called SIRS model [21]. In most epidemic models, the bilinear incidence rate λS(t)I(t) is extensively used.…”

Section: Introductionmentioning

confidence: 99%

Application of stochastic inequalities to global analysis of a nonlinear stochastic SIRS epidemic model with saturated treatment function

2018

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In this paper, we propose a new nonlinear stochastic SIRS epidemic model with standard incidence rate and saturated treatment function. The main purpose of this paper is to investigate the threshold dynamics of the nonlinear stochastic SIRS epidemic model by making use of stochastic inequality techniques. By using Lyapunov methods and Itô's formula, we first prove the existence and uniqueness of a global positive solution for the corresponding limiting system. Furthermore, we obtain sufficient conditions for the extinction and persistence in mean of the nonlinear stochastic SIRS epidemic model by using the techniques of a series of stochastic inequalities. Finally, we provide some numerical simulations to illustrate the performance of our theoretical findings.

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“…In the early research, epidemic model on scale-free networks. Refs [7] [8] [9] studied the spreading of infections on scale-free networks; these papers found the epidemic threshold on scale-free networks and proved the stability of equilibriums. In order to efficiently control the outbreak of infectious diseases, Chen and Sun [10] firstly succeeded in studying optimal control of an SIRS (susceptible-infected-recovered-susceptible) epidemic model on scale-free networks.…”

Section: Introductionmentioning

confidence: 99%

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

Liu¹,

Li²,

Wang³

et al. 2017

OALib

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In this paper, a modified SIS (susceptible-infected-susceptible) model with infective medium and feedback mechanism on scale-free networks is presented. The model is suited to describe some epidemic spreading which are not only transmitting by medium but also spreading between individuals by direct contacts. Considering biological relevance and people's subjective consciousness, we introduce medium and feedback to describe the epidemic spreading. By mathematical analysis, we obtain the epidemic threshold and equilibriums. Simulation shows that the medium parameter can change the threshold, and the bigger it is, the easier epidemic breaks. Feedback parameter cannot change the basic reproductive number, but it can reduce the endemic level and weaken the epidemic spreading.

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Analysis of epidemic spreading of an SIRS model in complex heterogeneous networks

Cited by 143 publications

References 28 publications

Global stability of an SIS epidemic model with feedback mechanism on networks

Global stability of an SIS epidemic model with feedback mechanism on networks

Application of stochastic inequalities to global analysis of a nonlinear stochastic SIRS epidemic model with saturated treatment function

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

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