Dynamics of a network-based SIS epidemic model with nonmonotone incidence rate

Li, Chun-Hsien

doi:10.1016/j.physa.2015.02.023

Cited by 35 publications

(35 citation statements)

References 25 publications

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“…Clearly, the feedback mechanism can affect the contacts among people. To investigate the efficiency of feedback mechanism, new models based on the SIS model were established [1,[24][25][26]. Under the assumption that all individuals understand the instant situation of the propagation and can estimate the possibility of contacting with infected individuals, Zhang and Sun [1] proposed the following model with a feedback mechanism:…”

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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“…Inspired by the works of [3] and [6], in this paper we propose the following SIRS epidemic model with vaccination and the nonmonotone incidence rate as follows,…”

Section: Introductionmentioning

confidence: 99%

Global stability of a network-based SIRS epidemic model with nonmonotone incidence rate

Liu¹,

Wei²,

Zhang³

2019

Physica A: Statistical Mechanics and its Applications

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This paper studies the dynamics of a network-based SIRS epidemic model with vaccination and a nonmonotone incidence rate. This type of nonlinear incidence can be used to describe the psychological or inhibitory effect from the behavioral change of the susceptible individuals when the number of infective individuals on heterogeneous networks is getting larger. Using the analytical method, epidemic threshold R 0 is obtained. When R 0 is less than one, we prove the disease-free equilibrium is globally asymptotically stable and the disease dies out, while R 0 is greater than one, there exists a unique endemic equilibrium. By constructing a suitable Lyapunov function, we also prove the endemic equilibrium is globally asymptotically stable if the inhibitory factor α is sufficiently large. Numerical experiments are also given to support the theoretical results. It is shown both theoretically and numerically a larger α can accelerate the extinction of the disease and reduce the level of disease.

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“…However, in reality, each individual has limited contact with those who can spread disease. For better handling the effects of contact heterogeneity, the disease transmission should be modeled over complex heterogenous networks [11,27]. On networks, nodes stand for individuals and an edge connecting two nodes describes the interaction between individuals, in which the infection may spread.…”

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confidence: 99%

“…In this way, the node with more edges has a higher possibility of being infected. Recently, considerable concern has 724 SHOUYING HUANG AND JIFA JIANG arisen over the study of epidemic models on complex heterogeneous networks (see [2,3,5,7,8], [11]− [14], [16,17], [19]− [27])…”

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confidence: 99%

“…ϕ(k) represents the infectivity of a node with degree k, i.e., ϕ(k) denotes the average number of occupied edges from which a node with degree k can transmit the disease [8]. This means that ϕ(k) ≤ k. It should be noted that various types of the infectivity ϕ(k) have been studied, such as ϕ(k) = k [11,12,14,17,20,27]; ϕ(k) = A [21]; ϕ(k) = min{A, σk}, 0 < σ ≤ 1 [3]; ϕ(k) = k σ [2] and ϕ(k) = ak σ /(1 + νk σ ), a > 0, ν ≥ 0 [22]. That is, the function ϕ(i) in (2) can take any of the above forms according to the degree of real networks.…”

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confidence: 99%

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Global stability of a network-based sis epidemic model with a general nonlinear incidence rate

Huang

Jiang

2016

MBE

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In this paper, we develop and analyze an SIS epidemic model with a general nonlinear incidence rate, as well as degree-dependent birth and natural death, on heterogeneous networks. We analytically derive the epidemic threshold R0 which completely governs the disease dynamics: when R0 < 1, the disease-free equilibrium is globally asymptotically stable, i.e., the disease will die out; when R0 > 1, the disease is permanent. It is interesting that the threshold value R0 bears no relation to the functional form of the nonlinear incidence rate and degree-dependent birth. Furthermore, by applying an iteration scheme and the theory of cooperative system respectively, we obtain sufficient conditions under which the endemic equilibrium is globally asymptotically stable. Our results improve and generalize some known results. To illustrate the theoretical results, the corresponding numerical simulations are also given.

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Dynamics of a network-based SIS epidemic model with nonmonotone incidence rate

Cited by 35 publications

References 25 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

Global stability of a network-based SIRS epidemic model with nonmonotone incidence rate

Global stability of a network-based sis epidemic model with a general nonlinear incidence rate

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