G. Aronsson and I. Mellander, A deterministic model in biomathematics. asymptotic behavior and threshold conditions, Mathematical Biosciences, vol.49, issue.3-4, pp.207-222, 1980.
DOI : 10.1016/0025-5564(80)90079-6

N. Bacaër, A. Dads, and N. , On the biological interpretation of a definition for the parameter R 0 in periodic population models, Journal of Mathematical Biology, vol.7, issue.6, pp.601-621, 2012.
DOI : 10.3934/mbe.2010.7.195

N. Bacaër, On the stochastic SIS epidemic model in a periodic environment, Journal of Mathematical Biology, vol.24, issue.8, pp.491-511, 2015.
DOI : 10.1137/0324032

F. Campillo, N. Champagnat, and C. Fritsch, On the variations of the principal eigenvalue with respect to a parameter in growth-fragmentation models Communications in Mathematical Sciences, pp.1801-1819, 2017.

J. Clairambault, S. Gaubert, and B. Perthame, An inequality for the Perron and Floquet eigenvalues of monotone differential systems and age structured equations Comptes Rendus Mathematique, Number, vol.345, issue.10, pp.549-554, 2007.

S. Gaubert and T. Lepoutre, Discrete limit and monotonicity properties of the Floquet eigenvalue in an age structured cell division cycle model, Journal of Mathematical Biology, vol.146, issue.3, pp.1663-1703, 2015.
DOI : 10.1007/s10955-011-0357-x

URL : https://hal.archives-ouvertes.fr/hal-00773211

M. W. Hirsch, The dynamical systems approach to differential equations, Bulletin of the American Mathematical Society, vol.11, issue.1, pp.1-64, 1984.
DOI : 10.1090/S0273-0979-1984-15236-4

URL : http://www.ams.org/bull/1984-11-01/S0273-0979-1984-15236-4/S0273-0979-1984-15236-4.pdf

J. F. Kingman, A CONVEXITY PROPERTY OF POSITIVE MATRICES, The Quarterly Journal of Mathematics, vol.12, issue.1, pp.283-284, 1961.
DOI : 10.1093/qmath/12.1.283

H. L. Smith, Cooperative systems of differential equations with concave nonlinearities Nonlinear Analysis Theory Methods and Application, pp.1037-1052, 1986.

J. Jiang, The algebraic criteria for the asymptotic behavior of cooperative systems with concave nonlinearities, System Science and Mathematical Sciences, vol.6, issue.3, pp.193-208, 1993.

S. Mirrahimi, B. Perthame, and P. Souganidis, Time fluctuations in a population model of adaptive dynamics Annales de l'Institut Henri Poincar (C) Non Linear Analysis, pp.41-58, 2015.

D. Xiao, Dynamics and bifurcations on a class of population model with seasonal constant-yield harvesting Discrete and Continuous Dynamical Systems Series B, pp.699-719, 2016.