Archimedean copula and contagion modeling in epidemiology

Jacques Demongeot; Mohamad Ghassani; Mustapha Rachdi; Idir Ouassou; Carla Taramasco; Jacques Demongeot; Mohamad Ghassani; Mustapha Rachdi; Idir Ouassou; Carla Taramasco

doi:10.3934/nhm.2013.8.149

Networks and Heterogeneous Media

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

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Archimedean copula and contagion modeling in epidemiology

1.
FRE 3405, AGIM (AGeing Imaging Modeling), CNRS-UJF-EPHE-UPMF, University J. Fourier of Grenoble, Faculty of Medicine of Grenoble, 38700 La Tronche
2.
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
3.
FRE 3405, AGIM (AGeing Imaging Modeling), CNRS-UJF-EPHE-UPMF, Faculty of Medicine of Grenoble, 38700 La Tronche

Received: 01 April 2012 Revised: 01 February 2013
34, 60, 62, 92.

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.
- Archimedean copula,
- quantile,
- malaria,
- transmission system,
- measure of concordance
Citation: Jacques Demongeot, Mohamad Ghassani, Mustapha Rachdi, Idir Ouassou, Carla Taramasco. Archimedean copula and contagion modeling in epidemiology[J]. Networks and Heterogeneous Media, 2013, 8(1): 149-170. doi: 10.3934/nhm.2013.8.149

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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.

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