R. M. Anderson and R. M. May, Infectious Diseases of Humans: Dynamics and control, 1991.

W. Arendt, Resolvent Positive Operators, Proceedings of the London Mathematical Society, vol.3, issue.2, pp.321-349, 1987.
DOI : 10.1112/plms/s3-54.2.321

O. Arino, Some Spectral Properties for the Asymptotic Behavior of Semigroups Connected to Population Dynamics, SIAM Review, vol.34, issue.3, pp.445-476, 1992.
DOI : 10.1137/1034086

O. Arino, A survey of structured cell population dynamics, Acta Biotheoretica, vol.18, issue.1-2, pp.3-25, 1995.
DOI : 10.1007/BF00709430

N. T. Bailey, The mathematical Theory of Epidemics, 1957.

G. Butler and P. Waltman, Persistence in dynamical systems, Journal of Differential Equations, vol.63, issue.2, pp.255-263, 1986.
DOI : 10.1016/0022-0396(86)90049-5

J. Burton, L. Billings, A. T. Derek, and I. B. Schwartz, Disease persistence in epidemiological models: The interplay between vaccination and migration, Mathematical Biosciences, vol.239, issue.1, pp.91-96, 2012.
DOI : 10.1016/j.mbs.2012.05.003

V. Capasso, Mathematical Structures of Epidemic Systems, Lecture Notes in Biomathematics, vol.97, 1993.
DOI : 10.1007/978-3-540-70514-7

T. Cazenave and A. Haraux, An Introduction to Semilinear Evolution Equations, 2006.

J. M. Cushing, An Introduction to Structured Population Dynamics, 1998.
DOI : 10.1137/1.9781611970005

T. Dhirasakdanon, H. R. Thieme, and P. Van-den-driessche, A sharp threshold for disease persistence in host metapopulations, Journal of Biological Dynamics, vol.202, issue.4, pp.363-378, 2007.
DOI : 10.1007/BF00168799

K. J. Engel and R. Nagel, One-parameter semigroups for linear evolution equations, Semigroup Forum, vol.63, issue.2, 2000.
DOI : 10.1007/s002330010042

K. J. Engel and R. Nagel, A short course on operator semigroups, 2006.

H. I. Freedman and P. Moson, Persistence definitions and their connections, Proc. Amer. Soc, pp.1025-1033, 1990.
DOI : 10.1090/S0002-9939-1990-1012928-6

T. J. Hagenaars, C. A. Donnelly, N. M. Ferguson, and R. M. Anderson, The transmission dynamics of the aetiological agent of scrapie in a sheep flock, Mathematical Biosciences, vol.168, issue.2, pp.117-135, 2000.
DOI : 10.1016/S0025-5564(00)00048-1

T. J. Hagenaars, C. A. Donnelly, and N. M. Ferguson, Spatial heterogeneity and the persistence of infectious diseases, Journal of Theoretical Biology, vol.229, issue.3, pp.349-359, 2004.
DOI : 10.1016/j.jtbi.2004.04.002

W. Hirsch, H. Hanisch, and J. P. Gabriel, Differential equation models of some parasitic infections: Methods for the study of asymptotic behavior, Communications on Pure and Applied Mathematics, vol.26, issue.6, pp.733-753, 1985.
DOI : 10.1002/cpa.3160380607

J. M. Ireland, B. D. Mestel, and R. A. Norman, The effect of seasonal host birth rates on disease persistence, Mathematical Biosciences, vol.206, issue.1, pp.31-45, 2007.
DOI : 10.1016/j.mbs.2006.08.028

W. O. Kermack and A. G. Mckendrick, A Contribution to the Mathematical Theory of Epidemics, Proc. R. Soc. Lond. Ser. A, pp.115-700, 1927.

W. O. Kermack and A. G. Mckendrick, Contributions to the Mathematical Theory of Epidemics. II. The Problem of Endemicity, Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, vol.138, issue.834, pp.55-83, 1932.
DOI : 10.1098/rspa.1932.0171

W. O. Kermack and A. G. Mckendrick, Contributions to the Mathematical Theory of Epidemics: III, Proc. R. Soc. Lond. Ser. B, pp.141-94, 1933.

R. J. Leveque, Finite volume methods for hyperbolic problems, Cambridge Texts in Applied Mathematics, 2002.

X. Liu and P. Stechlinski, Infectious disease models with time-varying parameters and general nonlinear incidence rate, Applied Mathematical Modelling, vol.36, issue.5, pp.1974-1994, 2012.
DOI : 10.1016/j.apm.2011.08.019

P. Magal, C. C. Mccluskey, and G. F. Webb, Lyapunov functional and global asymptotic stability for an infection-age model, Applicable Analysis, vol.3, issue.7, pp.1109-1140, 2010.
DOI : 10.1016/j.jmaa.2007.09.074

P. Magal and C. C. Mccluskey, Two-Group Infection Age Model Including an Application to Nosocomial Infection, SIAM Journal on Applied Mathematics, vol.73, issue.2, pp.1058-1095, 2013.
DOI : 10.1137/120882056

J. D. Murray, Mathematical Biology I : An Introduction, Interdisciplinary Applied Mathematics, vol.17, 2004.

A. Pazy, Semigroups of linear operators and applications to partial differential equations, Applied Mathematical Sciences, vol.44, 1983.
DOI : 10.1007/978-1-4612-5561-1

A. Perasso and B. Laroche, Well-posedness of an epidemiological problem described by an evolution PDE, ESAIM: Proceedings, vol.25, pp.29-43, 2008.
DOI : 10.1051/proc:082503

A. Perasso, B. Laroche, Y. Chitour, and S. Touzeau, Identifiability analysis of an epidemiological model in a structured population, Journal of Mathematical Analysis and Applications, vol.374, issue.1, pp.154-165, 2011.
DOI : 10.1016/j.jmaa.2010.08.072
URL : https://hal.archives-ouvertes.fr/hal-00655939

A. Perasso and U. Razafison, Infection Load Structured SI Model With Exponential Velocity And External Source of Contamination, Proceedings of the International Conference of Applied and Engineering Mathematics, pp.2013-263, 2013.
URL : https://hal.archives-ouvertes.fr/hal-00606368

J. Prüß, Equilibrium solutions of Age-Specific Populations Dynaics of several Species, J. Math. Biol, vol.84, pp.65-84, 1981.

R. Rosà, A. Pugliese, R. Norman, and P. J. Hudson, Thresholds for disease persistence in models for tick-borne infections including non-viraemic transmission, extended feeding and tick aggregation, Journal of Theoretical Biology, vol.224, issue.3, pp.359-376, 2003.
DOI : 10.1016/S0022-5193(03)00173-5

I. Segal, Non-Linear Semi-Groups, The Annals of Mathematics, vol.78, issue.2, pp.339-364, 1963.
DOI : 10.2307/1970347

C. Shu, Essentially non-oscillatory and weighted essentially non-oscillatory schemes for hyperbolic conservation laws, Lecture Notes in Mathematics, vol.89, pp.325-432, 1998.
DOI : 10.1016/0021-9991(90)90120-P

H. L. Smith and H. R. Thieme, Dynamical systems and population persistence, Graduate Studies in Mathematics, vol.118, 2011.
DOI : 10.1090/gsm/118

H. L. Smith and H. R. Thieme, Persistence of bacteria and phages in a chemostat, Journal of Mathematical Biology, vol.102, issue.suppl, pp.951-979, 2012.
DOI : 10.1007/s00285-011-0434-4

S. M. Stringer, N. Hunter, and M. E. Woolhouse, A mathematical model of the dynamics of scrapie in a sheep flock, Mathematical Biosciences, vol.153, issue.2, pp.79-98, 1998.
DOI : 10.1016/S0025-5564(98)10036-6

H. R. Thieme and C. Castillo-chavez, How May Infection-Age-Dependent Infectivity Affect the Dynamics of HIV/AIDS?, SIAM Journal on Applied Mathematics, vol.53, issue.5, pp.1447-1479, 1993.
DOI : 10.1137/0153068

H. R. Thieme, A. Tridane, and Y. Kuang, An epidemic model with post-contact prophylaxis of distributed length I. Thresholds for disease persistence and extinction, Journal of Biological Dynamics, vol.21, issue.2, pp.221-239, 2008.
DOI : 10.1007/BF00275827

S. Touzeau, M. E. Chase-topping, L. Matthews, D. Lajous, F. Eychenne et al., Modelling the spread of scrapie in a sheep flock: evidence for increased transmission during lambing seasons, Archives of Virology, vol.354, issue.6, pp.151-735, 2006.
DOI : 10.1007/s00705-005-0666-y

G. F. Webb, Theory of Nonlinear Age-Dependent Population Dynamics, 1985.

G. F. Webb, Dynamics of populations structured by internal variables, Mathematische Zeitschrift, vol.9, issue.n. 2, pp.319-335, 1985.
DOI : 10.1007/BF01164156

G. F. Webb, Population Models Structured by Age, Size, and Spatial Position, Lecture Notes in Mathematics, vol.1936, pp.1-49, 2008.
DOI : 10.1007/978-3-540-78273-5_1

K. Yosida, Functional Analysis, Classics in Mathematics, 1995.