Small World Effect in an Epidemiological Model

Kuperman, M. N.; Abramson, Guillermo

doi:10.1103/physrevlett.86.2909

Cited by 486 publications

(423 citation statements)

References 19 publications

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“…Then, with a probability p, each of the KZ4kZ12 nearest neighbours of each of the edges in the lattice is randomly rewired to an arbitrary node, not permitting duplications. These rewired connections, or short cuts (Watts & Strogatz 1998;Kuperman & Abramson 2001), may extend to far regions of the network.…”

Section: The Network Sirs Modelmentioning

confidence: 99%

Spatio-temporal waves and targeted vaccination in recurrent epidemic network models

Litvak-Hinenzon

Stone

2008

J. R. Soc. Interface.

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The success of an infectious disease to invade a population is strongly controlled by the population's specific connectivity structure. Here, a network model is presented as an aid in understanding the role of social behaviour and heterogeneous connectivity in determining the spatio-temporal patterns of disease dynamics. We explore the controversial origins of longterm recurrent oscillations believed to be characteristic of diseases that have a period of temporary immunity after infection. In particular, we focus on sexually transmitted diseases such as syphilis, where this controversy is currently under review. Although temporary immunity plays a key role, it is found that, in realistic small-world networks, the social and sexual behaviour of individuals also has a great influence in generating long-term cycles. The model generates circular waves of infection with unusual spatial dynamics that depend on focal areas that act as pacemakers in the population. Eradication of the disease can be efficiently achieved by eliminating the pacemakers with a targeted vaccination scheme. A simple difference equation model is derived, which captures the infection dynamics of the network model and gives insights into their origins and their eradication through vaccination. Illustrative videos may be found in the electronic supplementary material.

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Section: The Network Sirs Modelmentioning

confidence: 99%

Spatio-temporal waves and targeted vaccination in recurrent epidemic network models

Litvak-Hinenzon

Stone

2008

J. R. Soc. Interface.

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“…18 La dinámica de la transmisión de las enfermedades infecciosas se representa a través de los principales modelos epidemiológicos: susceptible-infeccioso (S-I), susceptible-infeccioso-susceptible (S-I-S), susceptibleinfeccioso-removido (S-I-R) y susceptible-infecciosoremovido-susceptible (S-I-R-S). 5,19 El modelo más común es el S-I-R, que se utiliza en enfermedades infecciosas de ciclo corto en las que se adquiere inmunidad permanente después de padecer la infección, 20 como ocurre con la rubéola, el sarampión, la varicela, las infecciones virales y el dengue.…”

Section: Modelo Estocástico De La Transmisión De Enfermedades Infecciunclassified

“…En una red regular se representan los contactos dentro de las familias, los vértices son las N personas de la población y cada uno se conecta a través de k ligas; 24 éstas representan los contactos entre ellos y una infección sólo se puede diseminar a través de las ligas 19 que unen a cada vértice con sus k/2 vértices vecinos localizados a los lados.…”

Section: Modelo Estocástico De La Transmisión De Enfermedades Infecciunclassified

“…La primera consiste en el promedio mínimo de las ligas necesarias para conectar aleatoriamente a cualquier par de vértices, lo que se conoce como el tamaño de la red (L). 19,37 La segunda propiedad es el coeficiente de agrupación (C), que expresa la proporción de interacciones que realizan entre sí los vértices unidos a uno en particular. 37 Una red es eficiente cuando L es pequeño, aproximadamente menor o igual a 4; esto indica que se necesitan en promedio cuatro ligas para unir de manera aleatoria cualquier par de vértices, aunque se han encontrado redes con valores que fluctúan entre 4 y 9.…”

Section: Modelo Estocástico De La Transmisión De Enfermedades Infecciunclassified

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Modelo estocástico de la transmisión de enfermedades infecciosas

Ruiz-Ramírez

Hernández-Rodríguez

2009

Salud pública Méx

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ResumenObjetivo. Proponer un modelo estocástico que muestre la forma en que afecta la estructura de la población al tamaño de la epidemia de las enfermedades infecciosas. Material y métodos. Este estudio se realizó en la Universidad de Colima en el año 2004. Se utilizó la topología de red del mundo pequeño generalizada para representar los contactos ocurridos dentro y entre familias; para ello se realizaron dos programas en MATLAB para calcular la eficiencia de la red; también se requirió la elaboración de un programa en el lenguaje C, que representa el modelo estocástico susceptible-infecciosoremovido, y se obtuvieron resultados simultáneos del número de personas infectadas. Resultados. El incremento del núme-ro de familias conectadas por los sitios de reunión modificó el tamaño de las enfermedades infecciosas en una proporción de casi 400%. Discusión. La estructura de la población influye en la propagación rápida de las enfermedades infecciosas y puede alcanzar efectos epidémicos. AbstractObjective. Propose a mathematic model that shows how population structure affects the size of infectious disease epidemics. Material and Methods. This study was conducted during 2004 at the University of Colima. It used generalized small-world network topology to represent contacts that occurred within and between families. To that end, two programs in MATLAB were conducted to calculate the efficiency of the network. The development of a program in the C programming language was also required, that represents the stochastic susceptible-infectious-removed model, and simultaneous results were obtained for the number of infected people. Results. An increased number of families connected by meeting sites impacted the size of the infectious diseases by roughly 400%. Discussion. Population structure influences the rapid spread of infectious diseases, reaching epidemic effects.

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“…Inspired by the metapopulation epidemic model, the territorial epidemic model and the networked epidemic model in refs [64,65,66,67,68,70,71,72], in the present model, we incorporate a multi-layer network, which consists of a regular network with segregated spatial domains and a random network representing individual-based linkage, into the SIS model. The coupled dynamics of random walk and pre-arranged linkage is investigated.…”

Section: Introductionmentioning

confidence: 99%

Coupled effects of local movement and global interaction on contagion

Liu

Chen

et al. 2015

Physica A: Statistical Mechanics and its Applications

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By incorporating segregated spatial domain and individual-based linkage into the SIS (susceptible-infected-susceptible) model, we propose a generalized epidemic model which can change from the territorial epidemic model to the networked epidemic model. The role of the individual-based linkage between different spatial domains is investigated. As we adjust the timescale parameter τ from 0 to unity, which represents the degree of activation of the individual-based linkage, three regions are found. Within the region of 0 < τ < 0.02, the epidemic is determined by local movement and is sensitive to the timescale τ . Within the region of 0.02 < τ < 0.5, the epidemic is insensitive to the timescale τ . Within the region of 0.5 < τ < 1, the outbreak of the epidemic is determined by the structure of the individualbased linkage. As we keep an eye on the first region, the role of activating the individual-based linkage in the present model is similar to the role of the shortcuts in the two-dimensional small world network. Only activating a small number of the individual-based linkage can prompt the outbreak of the epidemic globally. The role of narrowing segregated spatial domain and reducing mobility in epidemic control is checked. These two measures are found to be conducive to curbing the spread of infectious disease only when the global interaction is suppressed. A log-log relation between the change in the number of infected individuals and the timescale τ is found.By calculating the epidemic threshold and the mean first encounter time, we heuristically analyze the microscopic characteristics of the propagation of the epidemic in the present model.

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Small World Effect in an Epidemiological Model

Cited by 486 publications

References 19 publications

Spatio-temporal waves and targeted vaccination in recurrent epidemic network models

Spatio-temporal waves and targeted vaccination in recurrent epidemic network models

Modelo estocástico de la transmisión de enfermedades infecciosas

Coupled effects of local movement and global interaction on contagion

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