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Communications on Pure and Applied Analysis (CPAA)
 

Demography in epidemics modelling

Pages: 61 - 82, Volume 11, Issue 1, January 2012      doi:10.3934/cpaa.2012.11.61

 
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Jacques Demongeot - AGIM Laboratory, FRE 3405 UJF-CNRS, TIMB Team, University J. Fourier of Grenoble (UJF), Faculty of Medicine, 38700 La Tronche, France (email)
Jean Gaudart - LERTIM, EA 3283, Aix-Marseille University, Faculty of Medicine, 27 Bd Jean Moulin, 13385 Marseille Cedex 5, France (email)
Julie Mintsa - AGIM Laboratory, FRE 3405 CNRS, TIMB Team, University P. Mendès-France of Grenoble (UPMF), Faculty of Medicine, 38700 La Tronche, France (email)
Mustapha Rachdi - AGIM Laboratory, FRE 3405 CNRS, TIMB Team, University P. Mendès-France of Grenoble (UPMF), Faculty of Medicine, 38700 La Tronche, France (email)

Abstract: Classical models of epidemics by Ross and McKendrick have to be revisited in order to take into account the demography (fecundity, mortality and migration) both of host and vector populations and also the diffusion and mutation of infectious agents. The classical models are supposing the populations involved in the infectious disease to be constant during the epidemic wave, but the presently observed pandemics show that the duration of their spread during months or years imposes to take into account the host and vector population changes, and also the transient or permanent migration and diffusion of hosts (susceptible or infected), as well as those of vectors and infectious agents. One example is presented concerning the malaria in Mali.

Keywords:  Epidemic modelling, contagious diseases, endemic state, demographic dynamics, reaction-diffusion, zero diffusion set.
Mathematics Subject Classification:  Primary: 35A18, 35B35, 35B36, 35B40, 35K57; Secondary: 92B05, 92D30.

Received: February 2010;      Revised: January 2011;      Published: September 2011.

 References