A new SEIR epidemic model with applications to the theory of eradication and control of diseases, and to the calculation of

Huang, Sen-Zhong

doi:10.1016/j.mbs.2008.06.005

Cited by 45 publications

(34 citation statements)

References 48 publications

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“…Huang [45] defined four reproductive numbers associated with four types of transmission patterns, each depending on z, the ratio of the mean infectious period to the mean latent period. These four reproduction numbers are the following:…”

Section: Alternatives To Rmentioning

confidence: 99%

The Failure of R₀

Blakeley

Smith

2011

Computational and Mathematical Methods in Medicine

187

158

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The basic reproductive ratio, R 0, is one of the fundamental concepts in mathematical biology. It is a threshold parameter, intended to quantify the spread of disease by estimating the average number of secondary infections in a wholly susceptible population, giving an indication of the invasion strength of an epidemic: if R 0 < 1, the disease dies out, whereas if R 0 > 1, the disease persists. R 0 has been widely used as a measure of disease strength to estimate the effectiveness of control measures and to form the backbone of disease-management policy. However, in almost every aspect that matters, R 0 is flawed. Diseases can persist with R 0 < 1, while diseases with R 0 > 1 can die out. We show that the same model of malaria gives many different values of R 0, depending on the method used, with the sole common property that they have a threshold at 1. We also survey estimated values of R 0 for a variety of diseases, and examine some of the alternatives that have been proposed. If R 0 is to be used, it must be accompanied by caveats about the method of calculation, underlying model assumptions and evidence that it is actually a threshold. Otherwise, the concept is meaningless.

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Section: Alternatives To Rmentioning

confidence: 99%

The Failure of R₀

Blakeley

Smith

2011

Computational and Mathematical Methods in Medicine

187

158

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“…Shulgin et al (1998) used a SIR model based in ODE to determine, in terms of R 0 , the minimum percentage p of susceptible individuals that must be vaccinated to eradicate a contagious disease; they found p = (R 0 − 1)/R 0 . This expression was also derived by Huang (2008) from a SEIR model (where E represents the exposed (latent) group), who applied it for calculating the critical vaccination level associated to 21 wellknown infectious diseases. A similar expression was obtained by Farrington (2003) considering the vaccine efficacy.…”

Section: Discussionmentioning

confidence: 99%

On the basic reproduction number and the topological properties of the contact network: An epidemiological study in mainly locally connected cellular automata

Schimit

Monteiro

2009

Ecological Modelling

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a b s t r a c tWe study the spreading of contagious diseases in a population of constant size using susceptible-infectiverecovered (SIR) models described in terms of ordinary differential equations (ODEs) and probabilistic cellular automata (PCA). In the PCA model, each individual (represented by a cell in the lattice) is mainly locally connected to others. We investigate how the topological properties of the random network representing contacts among individuals influence the transient behavior and the permanent regime of the epidemiological system described by ODE and PCA. Our main conclusions are: (1) the basic reproduction number (commonly called R 0 ) related to a disease propagation in a population cannot be uniquely determined from some features of transient behavior of the infective group; (2) R 0 cannot be associated to a unique combination of clustering coefficient and average shortest path length characterizing the contact network. We discuss how these results can embarrass the specification of control strategies for combating disease propagations.

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“…One of the most fundamental issues when studying stability is the determination of the so-called reproduction number of the model, 0 . This number is defined as the expected number of secondary cases generated by one typical primary case in an entirely susceptible and sufficiently large population [16]. The reproduction number usually determines the stability of the equilibrium points when they exist.…”

Section: Introductionmentioning

confidence: 99%

Robust Sliding Control of SEIR Epidemic Models

Ibeas

Sen

Alonso‐Quesada

2014

Mathematical Problems in Engineering

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This paper is aimed at designing a robust vaccination strategy capable of eradicating an infectious disease from a population regardless of the potential uncertainty in the parameters defining the disease. For this purpose, a control theoretic approach based on a sliding-mode control law is used. Initially, the controller is designed assuming certain knowledge of an upper-bound of the uncertainty signal. Afterwards, this condition is removed while an adaptive sliding control system is designed. The closed-loop properties are proved mathematically in the nonadaptive and adaptive cases. Furthermore, the usual sign function appearing in the sliding-mode control is substituted by the saturation function in order to prevent chattering. In addition, the properties achieved by the closed-loop system under this variation are also stated and proved analytically. The closed-loop system is able to attain the control objective regardless of the parametric uncertainties of the model and the lack ofa prioriknowledge on the system.

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A new SEIR epidemic model with applications to the theory of eradication and control of diseases, and to the calculation of

Cited by 45 publications

References 48 publications

The Failure of R₀

The Failure of R₀

On the basic reproduction number and the topological properties of the contact network: An epidemiological study in mainly locally connected cellular automata

Robust Sliding Control of SEIR Epidemic Models

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A new SEIR epidemic model with applications to the theory of eradication and control of diseases, and to the calculation of

Cited by 45 publications

References 48 publications

The Failure of R0

The Failure of R0

On the basic reproduction number and the topological properties of the contact network: An epidemiological study in mainly locally connected cellular automata

Robust Sliding Control of SEIR Epidemic Models

Contact Info

Product

Resources

About

The Failure of R₀

The Failure of R₀