Global analysis of an SIS model with an infective vector on complex networks

Wang, Yi; Jin, Zhen; Yang, Zimo; Zhang, Zi-Ke; Zhou, Tao; Sun, Gui‐Quan

doi:10.1016/j.nonrwa.2011.07.033

Cited by 139 publications

(74 citation statements)

References 35 publications

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“…Research used in the modeling was done in clinical, medical and other fields related with Entamoeba histolytica. In referral classical epidemiological models, the population targeted by the study is classified into epidemiological classes or compartments [18][19][20][21]. For Amoebiasis, the population is subdivided into five epidemiological classes or states: susceptible, exposed, infectious, carriers and removal or recovered.…”

Section: Related Workmentioning

confidence: 99%

“…By Equation (8), the domain of the initial value problem (7) is closed, and hence, it is a compact set. Let us mimic the method developed in [18] by considering the boundary of the domain as the union of its subsets expressed as ∂Ω = ∂Ω 1 ∪ ∂Ω 2 where: …”

Section: Theorem 1 ω Is Positively Invariant Under the Initial Valuementioning

confidence: 99%

“…It is clear that the inequality holds only if R 0 < 1, as in this case, β σ+µ > 1 and k 2 > k 3 As far as the condition (42) is concerned, by developing the left side of the corresponding inequality and using (18) and (19) by the fact that µ is much smaller than σ, we have:…”

Section: Stability Of the Endemic Equilibriummentioning

confidence: 99%

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Dynamics of Amoebiasis Transmission: Stability and Sensitivity Analysis

2017

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Abstract:Compartmental epidemic models are intriguing in the sense that the generic model may explain different kinds of infectious diseases with minor modifications. However, there may exist some ailments that may not fit the generic capsule. Amoebiasis is one such example where transmission through the population demands a more detailed and sophisticated approach, both mathematical and numerical. The manuscript engages in a deep analytical study of the compartmental epidemic model; susceptible-exposed-infectious-carrier-recovered-susceptible (SEICRS), formulated for Amoebiasis. We have shown that the model allows the single disease-free equilibrium (DFE) state if R 0 , the basic reproduction number, is less than unity and the unique endemic equilibrium (EE) state if R 0 is greater than unity. Furthermore, the basic reproduction number depends uniquely on the input parameters and constitutes a key threshold indicator to portray the general trends of the dynamics of Amoebiasis transmission. We have also shown that R 0 is highly sensitive to the changes in values of the direct transmission rate in contrast to the change in values of the rate of transfer from latent infection to the infectious state. Using the Routh-Hurwitz criterion and Lyapunov direct method, we have proven the conditions for the disease-free equilibrium and the endemic equilibrium states to be locally and globally asymptotically stable. In other words, the conditions for Amoebiasis "die-out" and "infection propagation" are presented.

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Section: Related Workmentioning

confidence: 99%

Section: Theorem 1 ω Is Positively Invariant Under the Initial Valuementioning

confidence: 99%

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Dynamics of Amoebiasis Transmission: Stability and Sensitivity Analysis

2017

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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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“…The purpose of this modification is to have better understanding and prediction of epidemic patterns and intervention measures. For more details see [4][5][6].…”

Section: Introductionmentioning

confidence: 99%

A Fractional-Order Epidemic Model for Bovine Babesiosis Disease and Tick Populations

Santos¹,

Cardoso²,

Monteiro³

et al. 2015

Abstract and Applied Analysis

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This paper shows that the epidemic model, previously proposed under ordinary differential equation theory, can be generalized to fractional order on a consistent framework of biological behavior. The domain set for the model in which all variables are restricted is established. Moreover, the existence and stability of equilibrium points are studied. We present the proof that endemic equilibrium point when reproduction number 0 > 1 is locally asymptotically stable. This result is achieved using the linearization theorem for fractional differential equations. The global asymptotic stability of disease-free point, when 0 < 1, is also proven by comparison theory for fractional differential equations. The numeric simulations for different scenarios are carried out and data obtained are in good agreement with theoretical results, showing important insight about the use of the fractional coupled differential equations set to model babesiosis disease and tick populations.

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Global analysis of an SIS model with an infective vector on complex networks

Cited by 139 publications

References 35 publications

Dynamics of Amoebiasis Transmission: Stability and Sensitivity Analysis

Dynamics of Amoebiasis Transmission: Stability and Sensitivity Analysis

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

A Fractional-Order Epidemic Model for Bovine Babesiosis Disease and Tick Populations

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