T. Bächler, V. Gerdt, M. Lange-hegermann, and D. Robertz, Algorithmic Thomas decomposition of algebraic and differential systems, Journal of Symbolic Computation, vol.47, issue.10, pp.1233-1266, 2012.
DOI : 10.1016/j.jsc.2011.12.043

V. V. Bavula, The algebra of integro-differential operators on a polynomial algebra, Journal of the London Mathematical Society, vol.83, issue.2, pp.517-543, 2011.
DOI : 10.1112/jlms/jdq081

V. V. Bavula, The algebra of integro-differential operators on an affine line and its modules, Journal of Pure and Applied Algebra, vol.217, issue.3, pp.495-529, 2013.
DOI : 10.1016/j.jpaa.2012.06.024

V. V. Bavula, The Algebra of Polynomial Integro-Differential Operators is a Holonomic Bimodule over the Subalgebra of Polynomial Differential Operators, Algebras and Representation Theory, vol.4, issue.4, pp.275-288, 2014.
DOI : 10.1007/978-3-642-66066-5

F. Boulier and F. Lemaire, A Normal Form Algorithm for Regular Differential Chains, Mathematics in Computer Science, vol.23, issue.4,5, pp.185-201, 2010.
DOI : 10.1090/S0002-9939-1969-0248122-5
URL : https://hal.archives-ouvertes.fr/hal-00824964

F. Boulier, A. Korporal, F. Lemaire, W. Perruquetti, A. Poteaux et al., An Algorithm for Converting Nonlinear Differential Equations to Integral Equations with an Application to Parameter Estimation from Noisy Data, Proceedings of Computer Algebra and Scientific Computing (CASC) 2014, pp.28-43, 2014.
DOI : 10.1007/978-3-319-10515-4_3
URL : https://hal.archives-ouvertes.fr/hal-01114187

F. Boulier, J. Lallemand, F. Lemaire, G. Regensburger, and M. Rosenkranz, Additive normal forms and integration of differential fractions, Journal of Symbolic Computation, vol.77, pp.16-38, 2016.
DOI : 10.1016/j.jsc.2016.01.002
URL : https://hal.archives-ouvertes.fr/hal-01245378

F. Boulier, D. Lazard, F. Ollivier, and M. Petitot, Representation for the radical of a finitely generated differential ideal, Proceedings of the 1995 international symposium on Symbolic and algebraic computation , ISSAC '95, pp.158-166
DOI : 10.1145/220346.220367
URL : https://hal.archives-ouvertes.fr/hal-00138020

F. Boulier, D. Lazard, F. Ollivier, and M. Petitot, Computing representations for radicals of finitely generated differential ideals Applicable Algebra in Engineering, Communication and Computing, vol.20, issue.1, pp.73-121, 1997.

F. Boulier, F. Lemaire, and M. Moreno-maza, Computing differential characteristic sets by change of ordering, Journal of Symbolic Computation, vol.45, issue.1, pp.124-149, 2010.
DOI : 10.1016/j.jsc.2009.09.004
URL : https://hal.archives-ouvertes.fr/hal-00141095

F. Boulier, F. Lemaire, M. Moreno-maza, and A. Poteaux, An Equivalence Theorem For Regular Differential Chains, Journal of Symbolic Computation, 2018.
DOI : 10.1016/j.jsc.2018.04.011
URL : https://hal.archives-ouvertes.fr/hal-01391768

F. Boulier, F. Lemaire, M. Rosenkranz, R. Ushirobira, and N. Verdì-ere, On Symbolic Approaches to Integro-Differential Equations Advances in Delays and Dynamics, 2017.

H. Brunner and P. J. Van-der-hoeven, The numerical solution of Volterra equations, 1986.

L. Denis-vidal, G. Joly-blanchard, and C. Noiret, System Identifiability (Symbolic Computation) and Parameter Estimation (Numerical Computation), Numerical Algorithms, vol.34, issue.2-4, pp.282-292, 2003.
DOI : 10.1023/B:NUMA.0000005366.05704.88

X. Gao and L. Guo, Constructions of Free Commutative Integro-Differential Algebras, Algebraic and Algorithmic Aspects of Differential and Integral Operators, pp.1-22, 2014.
DOI : 10.1007/978-3-642-54479-8_1

L. Guo, G. Regensburger, and M. Rosenkranz, On integro-differential algebras, Journal of Pure and Applied Algebra, vol.218, issue.3, pp.456-473, 2014.
DOI : 10.1016/j.jpaa.2013.06.015
URL : http://arxiv.org/pdf/1212.0266.pdf

E. Hairer, S. P. Norsett, and G. Wanner, Solving ordinary differential equations I. Nonstiff problems, Series in Computational Mathematics, 1993.
DOI : 10.1007/978-3-662-12607-3

A. J. Jerri, Introduction to Integral Equations with Applications, Monographs and Textbooks in Pure and Applied Mathematics, 1985.

J. Keener and J. Sneyd, Mathematical Physiology I: Cellular Physiology, Interdisciplinary Applied Mathematics, vol.8, 2010.

E. R. Kolchin, Differential Algebra and Algebraic Groups, 1973.

L. Ljung and S. T. Glad, On global identifiability for arbitrary model parametrizations, Automatica, vol.30, issue.2, pp.265-276, 1994.
DOI : 10.1016/0005-1098(94)90029-9

E. L. Mansfield, Differential Gröbner Bases, 1991.

D. Moulay, N. Verdì-ere, and L. Denis-vidal, Identifiability of parameters in an epidemiologic model modeling the transmission of the Chikungunya, Proceedings of the 9` eme Conférence Internationale de Modélisation, 2012.

F. Ollivier, Leprobì eme de l'identifiabilité structurelle globale : approche théorique, méthodes effectives et bornes de complexité, 1990.

J. Paulsson and J. Elf, Stochastic Modeling of Intracellular Kinetics System Modeling in Cellular Biology: From Concepts to Nuts and Bolts, pp.149-175, 2006.

A. Pavé, Modeling living systems, from cell to ecosystem, 2012.

A. Quadrat and G. Regensburger, Polynomial Solutions and Annihilators of Ordinary Integro-Differential Operators* *G.R. was supported by the Austrian Science Fund (FWF): J 3030-N18., IFAC Proceedings Volumes, vol.46, issue.2, pp.308-313, 2013.
DOI : 10.3182/20130204-3-FR-2033.00133

G. J. Reid, A. D. Wittkopf, and A. Boulton, Reduction of systems of nonlinear partial differential equations to simplified involutive forms, European Journal of Applied Mathematics, vol.18, issue.06, pp.635-666, 1996.
DOI : 10.1088/0951-7715/7/3/012

J. F. Ritt, Differential Algebra, 1950.
DOI : 10.1090/coll/033

M. Rosenkranz and G. Regensburger, Integro-differential polynomials and operators, Proceedings of the twenty-first international symposium on Symbolic and algebraic computation, ISSAC '08, 2008.
DOI : 10.1145/1390768.1390805
URL : http://gregensburger.com/papers/issac08.pdf

L. F. Shampine and S. Thompson, Solving DDEs in Matlab, Applied Numerical Mathematics, vol.37, issue.4, pp.441-458, 2001.
DOI : 10.1016/S0168-9274(00)00055-6

N. Verdì-ere, L. Denis-vidal, and G. Joly-blanchard, A new method for estimating derivatives based on a distribution approach, Numerical Algorithms, vol.15, issue.4, pp.163-186, 2012.
DOI : 10.1007/s11075-008-9236-1

N. Verdì-ere, L. Denis-vidal, G. Joly-blanchard, and D. Domurado, Identifiability and Estimation of Pharmacokinetic Parameters for the Ligands of the Macrophage Mannose Receptor, Int. J. Appl. Math. Comput. Sci, vol.15, issue.4, pp.517-526, 2005.

. Wikipedia, Delay Differential Equations. https://en.wikipedia.org

S. Zhu, Modeling, identifiability analysis and parameter estimation of a spatialtransmission model of chikungunya in a spatially continuous domain, 2017.