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Random Modelling of Contagious Diseases

Acta Biotheoretica volume 61, pages 141–172 (2013)Cite this article

Abstract

Modelling contagious diseases needs to include a mechanistic knowledge about contacts between hosts and pathogens as specific as possible, e.g., by incorporating in the model information about social networks through which the disease spreads. The unknown part concerning the contact mechanism can be modelled using a stochastic approach. For that purpose, we revisit SIR models by introducing first a microscopic stochastic version of the contacts between individuals of different populations (namely Susceptible, Infective and Recovering), then by adding a random perturbation in the vicinity of the endemic fixed point of the SIR model and eventually by introducing the definition of various types of random social networks. We propose as example of application to contagious diseases the HIV, and we show that a micro-simulation of individual based modelling (IBM) type can reproduce the current stable incidence of the HIV epidemic in a population of HIV-positive men having sex with men (MSM).

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Affiliations

  1. AGIM, FRE, CNRS 3405, Faculty of Medicine of Grenoble, University J. Fourier, 38700, La Tronche, France

    J. Demongeot, O. Hansen, H. Hessami, A. S. Jannot, J. Mintsa, M. Rachdi & C. Taramasco

  2. Escuela de Ingeniería Civil Informática, Universidad de Valparaiso, Avenida Gran Bretaña 1111, Valparaiso, Chile

    C. Taramasco

  3. ISCPIF, Complex Systems Institute of Paris Ile de France, 57-59 rue Lhommond, 75005, Paris, France

    C. Taramasco

  4. Universidad de Valparaiso, Avenida Gran Bretaña 1111, Valparaiso, Chile

    J. Demongeot & C. Taramasco

  5. University Pierre Mendès-France, BP 47, 38040, Grenoble Cedex 9, France

    M. Rachdi

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  1. J. Demongeot
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  2. O. Hansen
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  3. H. Hessami
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Annex

Annex

Fig. 12
figure 12

Diagram describing the different status an individual male single or in couple having sex with other men (MSM) could successively go through during HIV spread in a MSM population

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Demongeot, J., Hansen, O., Hessami, H. et al. Random Modelling of Contagious Diseases. Acta Biotheor 61, 141–172 (2013). https://doi.org/10.1007/s10441-013-9176-6

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  • DOI: https://doi.org/10.1007/s10441-013-9176-6

Keywords

  • Social networks
  • Contagious diseases
  • Stochastic epidemic modelling
  • HIV