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Journal ArticleDOI

A Probabilistic Individual-based Model for Infectious Diseases Outbreaks

15 Jul 2013-Vol. 63, Iss: 3
TL;DR: The authors give a short state of the art of compartmental models, summarise one of the most know individual models, and describe both a generalization and a simulation algorithm.
Abstract: The mathematical modelling of infectious diseases is a large research area with a wide literature In the recent past, most of the scientific contributions focused on compartmental models However, the increasing computing power is pushing towards the development of individual models that consider the disease transmission and evolution at a very fine-grained level In the paper, the authors give a short state of the art of compartmental models, summarise one of the most know individual models, and describe both a generalization and a simulation algorithm
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TL;DR: The compartmental models and their application is one book that the authors really recommend you to read, to get more solutions in solving this problem.
Abstract: A solution to get the problem off, have you found it? Really? What kind of solution do you resolve the problem? From what sources? Well, there are so many questions that we utter every day. No matter how you will get the solution, it will mean better. You can take the reference from some books. And the compartmental models and their application is one book that we really recommend you to read, to get more solutions in solving this problem.

163 citations

References
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Journal ArticleDOI
TL;DR: Threshold theorems involving the basic reproduction number, the contact number, and the replacement number $R$ are reviewed for classic SIR epidemic and endemic models and results with new expressions for $R_{0}$ are obtained for MSEIR and SEIR endemic models with either continuous age or age groups.
Abstract: Many models for the spread of infectious diseases in populations have been analyzed mathematically and applied to specific diseases. Threshold theorems involving the basic reproduction number $R_{0}$, the contact number $\sigma$, and the replacement number $R$ are reviewed for the classic SIR epidemic and endemic models. Similar results with new expressions for $R_{0}$ are obtained for MSEIR and SEIR endemic models with either continuous age or age groups. Values of $R_{0}$ and $\sigma$ are estimated for various diseases including measles in Niger and pertussis in the United States. Previous models with age structure, heterogeneity, and spatial structure are surveyed.

5,915 citations


"A Probabilistic Individual-based Mo..." refers background in this paper

  • ...In such a context, the mathematical modelling of infectious diseases has a long tradition [10, 12]....

    [...]

Journal ArticleDOI
13 May 2004-Nature
TL;DR: The results suggest that outbreaks can be contained by a strategy of targeted vaccination combined with early detection without resorting to mass vaccination of a population.
Abstract: Here we present a highly resolved agent-based simulation tool (EpiSims), which combines realistic estimates of population mobility,based on census and land-use data, with parameterized models for simulating the progress of a disease within a host and of transmission between hosts10. The simulation generates a largescale,dynamic contact graph that replaces the differential equations of the classic approach. EpiSims is based on the Transportation Analysis and Simulation System (TRANSIMS) developed at Los Alamos National Laboratory, which produces estimates of social networks based on the assumption that the transportation infrastructure constrains people’s choices about where and when to perform activities11. TRANSIMS creates a synthetic population endowed with demographics such as age and income, consistent with joint distributions in census data. It then estimates positions and activities of all travellers on a second-by-second basis. For more information on TRANSIMS and its availability, see Supplementary Information. The resulting social network is the best extant estimate of the physical contact patterns among large groups of people—alternative methodologies are limited to physical contacts among hundreds of people or non-physical contacts (such as e-mail or citations) among large groups.

2,095 citations


"A Probabilistic Individual-based Mo..." refers background in this paper

  • ...Currently, different approaches exist: compartmental models based on differential equations [8, 9], ad-hoc models for the contact process [11, 1], or individual-based models [7, 4, 14]....

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  • ..., the Eubank model [7]), and delves into a recent extension [14] by presenting a further generalisation and diverse stopping criteria....

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  • ...One of the most known individual-based models is the one proposed by Eubank at al [7]....

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Journal ArticleDOI
TL;DR: By modelling the correlations between individuals, this work is able to understand the role of spatial heterogeneity in invasion dynamics without the need for large–scale computer simulations.
Abstract: Predicting the likely success of invasions is vitally important in ecology and especially epidemiology. Whether an organism can successfully invade and persist in the short–term is highly dependent on the spatial correlations that develop in the early stages of invasion. By modelling the correlations between individuals, we are able to understand the role of spatial heterogeneity in invasion dynamics without the need for large–scale computer simulations. Here, a natural methodology is developed for modelling the behaviour of individuals in a fixed network. This formulation is applied to the spread of a disease through a structured network to determine invasion thresholds and some statistical properties of a single epidemic.

831 citations


"A Probabilistic Individual-based Mo..." refers background in this paper

  • ...Currently, different approaches exist: compartmental models based on differential equations [8, 9], ad-hoc models for the contact process [11, 1], or individual-based models [7, 4, 14]....

    [...]

Journal ArticleDOI
TL;DR: An intuitive introduction to the process of disease transmission is provided, how this stochastic process can be represented mathematically and how this mathematical representation can be used to analyse the emergent dynamics of observed epidemics.
Abstract: The dynamics of infectious diseases are complex, so developing models that can capture key features of the spread of infection is important. Grassly and Fraser provide an introduction to the mathematical analysis and modelling of disease transmission, which, in addition to informing public health disease control measures, is also important for understanding pathogen evolution and ecology.

634 citations


"A Probabilistic Individual-based Mo..." refers background in this paper

  • ...Currently, different approaches exist: compartmental models based on differential equations [8, 9], ad-hoc models for the contact process [11, 1], or individual-based models [7, 4, 14]....

    [...]

Book
01 Oct 1983

469 citations