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Networks and Heterogeneous Media (NHM)
 

Archimedean copula and contagion modeling in epidemiology

Pages: 149 - 170, Volume 8, Issue 1, March 2013      doi:10.3934/nhm.2013.8.149

 
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Jacques Demongeot - FRE 3405, AGIM (AGeing Imaging Modeling), CNRS-UJF-EPHE-UPMF, University J. Fourier of Grenoble, Faculty of Medicine of Grenoble, 38700 La Tronche, France (email)
Mohamad Ghassani - FRE 3405, AGIM (AGeing Imaging Modeling), CNRS-UJF-EPHE-UPMF, Université Pierre Mendès France, UFR SHS, BP.47, 38040 Grenoble Cedex 09, Faculty of Medicine of Grenoble, 38700 La Tronche, France (email)
Mustapha Rachdi - FRE 3405, AGIM (AGeing Imaging Modeling), CNRS-UJF-EPHE-UPMF, Université Pierre Mendès France, UFR SHS, BP.47, 38040 Grenoble Cedex 09, Faculty of Medicine of Grenoble, 38700 La Tronche, France (email)
Idir Ouassou - FRE 3405, AGIM (AGeing Imaging Modeling), CNRS-UJF-EPHE-UPMF, Faculty of Medicine of Grenoble, 38700 La Tronche, France (email)
Carla Taramasco - FRE 3405, AGIM (AGeing Imaging Modeling), CNRS-UJF-EPHE-UPMF, Faculty of Medicine of Grenoble, 38700 La Tronche, France (email)

Abstract: The aim of this paper is first to find interactions between compartments of hosts in the Ross-Macdonald Malaria transmission system. So, to make clearer this association we introduce the concordance measure and then the Kendall's tau and Spearman's rho. Moreover, since the population compartments are dependent, we compute their conditional distribution function using the Archimedean copula. Secondly, we get the vector population partition into several dependent parts conditionally to the fecundity and to the transmission parameters and we show that we can divide the vector population by using $p$-th quantiles and test the independence between the subpopulations of susceptibles and infecteds. Third, we calculate the $p$-th quantiles with the Poisson distribution. Fourth, we introduce the proportional risk model of Cox in the Ross-Macdonald model with the copula approach to find the relationship between survival functions of compartments.

Keywords:  Archimedean copula, quantile, malaria, transmission system, measure of concordance.
Mathematics Subject Classification:  34, 60, 62, 92.

Received: April 2012;      Revised: February 2013;      Available Online: April 2013.

 References