Julien Arino

Organization: INRIA

Research Unit: Sophia Antipolis

E-mail:

Present status

After spending two years as a postdoctoral fellow in the Department of Mathematics and Statistics of the University of Victoria (British Colombia, Canada), I will be starting in January 2003 a new two years postoc, in the department of Mathematics at McMaster University.

Research activities

My domain of interest is mathematical population dynamics. My work in Victoria is carried out in collaboration with Pauline van den Driessche, and deals with the formulation and the analysis of mathematical models of disease transmission. More precisely, I am interested in the following problems:

Effect of the vaccination policy and of vaccine efficacy on epidemic dynamics.
Dynamics of disease propagation in a network of cities.
Dynamics of a spatial multispecies epidemic model.
Use of compound matrices in a model exhibiting multistability.

The models under consideration are formulated using ordinary, delay and integral differential equations. My work during my Ph.D. dealt with mathematical modelling of phytoplankton growth in the chemostat. More specifically, I was interested in the structuration of such models. The models that were used are either ordinary differential equations or difference equations (time discrete equations).

Publications

J. Arino, J.-L. Gouzé and A. Sciandra. A discrete, size-structured model of phytoplankton growth in the chemostat. Introduction of non constant cell division. Inria Research Report 3963, 2000.
J. Arino. Modélisation structurée de la croissance du phytoplancton en chemostat. Thèse de l'Université Grenoble 1, 2001.
J. Arino and J.-L. Gouzé. A size-structured, non conservative ODE model of the chemostat. Mathematical Biosciences, 177&178:127-145, 2002.
J. Arino, J.-L. Gouzé and A. Sciandra. A discrete, size-structured model of phytoplankton growth in the chemostat. Introduction of inhomogeneous cell division size. Journal of Mathematical Biology, 45(4):313-336. PDF Version ou Springer-Verlag DOI.

Ongoing work

J. Arino, K.L. Cooke, P. van den Driessche and J. Velasco-Hernández. An epidemiology model that includes vaccination and waning. Submitted.
J. Arino, C.C. McCluskey and P. van den Driessche. Global results for an epidemic model with vaccination that exhibits backward bifurcation. Submitted.
J. Arino and P. van den Driessche. A multi-city epidemic model. Submitted.

Teaching

February-March 2000: Statistics course. Magistère de Pharmacologie (coop program in pharmacology), University of Nice - Sophia Antipolis.
September-December 2001. Math 151, Discrete Mathematics. University of Victoria.
January-April 2002. Math 201, Introduction to Differential Equations. University of Victoria.
March 2002. Course about the chemostat, part of Math 560, Mathematical Models. University of Victoria.
January-April 2003. Math 1NN3, Calculus for Engineering II. McMaster University.

Conferences

April 1999. Un modèle discret de chemostat structuré. Comparaison avec des résultats expérimentaux. Annual meeting of the GdR CoRev (1107), CIRM Luminy, Marseille, France.
June 1999. A structured, discrete model of phytoplankton growth in the chemostat. Comparison with experiments. European Summer School Mathematics of Cell Physiology and Proliferation, Termoli, Italy.
July 1999. Size structured models for the chemostat; comparison with experiments. 3^rd International Conference Theory and Mathematics in Medicine and Biology (TMBM'99), Amsterdam, Netherlands.
May 2000. Un modèle structuré discret de croissance dans le chemostat. Division cellulaire non égale. Annual meeting of the GdR CoReV, INA Paris-Grignon.
August 2000. A Size-Structured, Non Conservative ODE Model of the Chemostat. DESTOBIO 2000 Conference, Purdue University, West Lafayette, IN, USA.
May 2001. MITACS AGM, McGill University, Montréal, Quebec, Canada. Poster Reproduction numbers for compartmental models of disease transmission. First prize.
May 2002. MITACS Biomedical theme meeting and AGM, UBC, Vancouver, B.C., Canada. Poster and presentation of A multicity epidemic model.
June 2002. DIMACS International Conference on Computation and Mathematical Epidemiology, Rutgers University, NJ, USA. Poster A multicity epidemic model.
July 2002. Mathematical Modeling & Computing in Biology and Medicine Conference, Milan, Italie. Vaccination and waning in a model of infectious disease transmission.
September 2002. Marrakech School on Delay differential equations and applications. Time delays in epidemic models: modeling and numerical considerations.

Seminars

On several occasions, I had the occasion of presenting some aspects of my work, during seminars of the Comore team.
October 1999. Modèles structurés de croissance du phytoplancton en chemostat. Un modèle en temps discret. INRIA Sophia Antipolis doctoral days.
October 2000. Modèles structurés d'un ecosystème marin de laboratoire. INRIA Sophia Antipolis doctoral days.
February 2001. Graduate Seminar, University of Victoria. Modelling of the growth of micro-organisms in a laboratory ecosystem. Description of cellular size and cellular division.
February-March 2001. Dynamics Seminar, University of Victoria. Size-structured population models of phytoplankton growth in the chemostat. I. Biological and Mathematical background. and II. A discrete-time system describing cellular death & A continuous time system with cellular death and maintenance.
September 2002. UR GEODES, IRD Bondy, France. Le nombre de reproduction élémentaire: deux exemples.
October 2002. Graduate Seminar, University of Victoria. A multicity epidemic model.
October 2002. Biophysics Seminar, University of Alberta. Time delays in epidemic models: modeling and numerical considerations.

Various activities

I take care of the site EuroMedBiomath, web portal of the homonymous association. This site maintains a list of biomathematics related events and sites. I also take care of the web side of schools co-organized by the association: Siguenza school (2001), Marrakech school on delay differential equations (2002) and Siguenza school on mathematical ecology (2003).

Thesis

I defended my thesis on January 12, 2001. My Ph.D. supervisor was Jean-Luc Gouzé. I was a student of the doctoral school Instruments and Models in Medicine and Biology (MIMB) of the Joseph Fourier University in Grenoble.

Thesis summary

This thesis deals with the formulation and analysis of structured models of growth in a chemostat, an experimental device used for the culture of micro-organisms in idealized conditions. More specifically, we will be concerned with the description of the size of phytoplanktonic organisms. In a first part, we give some biological indications concerning phytoplankton, then describe the experimental apparatus and finally introduce the mathematical models used for an elementary description of the chemostat.
The second and main part of this thesis begins by an introduction to structured population models, with emphasis on cellular division description. Then time discrete models describing in a detailed way cellular division are studied, followed by ordinary differential equations systems verifying the mass conservation principle, and finally by a class of models that do not verify this property.
We end this thesis by considering possible applications to other contexts or populations of the type of models developped herein.

Download the thesis (in French): pdf or ps version.

J.A.

Last modified: Sun Nov 24 00:03:46 Pacific Standard Time 2002