L.J.S. Allen, Discrete and continuous models of populations and epidemics, J. Math. Syst. Estim. Control 1 (1991), no. 3, 335–369.
 C. Barril, A`. Calsina and J. Rippol, A practical approach to R0 in continuous time ecological models, Math. Meth. Appl. Sci. 41 (2017), 8432–8445.
 S. Busenberg, M. Iannelli and H. Thieme, Global behavior of an age-structured epidemic model, SIAM J. Math. Anal. 22 (1991), no. 4, 1065–1080.
 Y. Cha, M. Iannelli, and E. Milner, Existence and uniqueness of endemic states for the age-structured SIR epidemic model, Math. Biosci. 150 (1998), 177–190.
 O. Diekmann, J.A.P. Heesterbeek, Mathematical Epidemiology of Infectious Diseases: Model Building, Analysis and Interpretation, Wiley, Chichester, 2000.
 O. Diekmann, J.A.P. Heesterbeek and J.A.J. Metz, On the definition and the computation of the basic reproduction ratio R in models for infectious diseases in heterogeneous populations, J. Math. Biol. 28 (1990), 365–382.
 K. Dietz and D. Schenzle, Proportionate mixingmodels for age-dependent infection transmission, J. Math. Biol. 22 (1985), 117–120.
 N. Dunford and J. T. Schwartz, Linear Operators Part I: General Theory, Interscience publishers, New York, 1958.
 M. El-Doma, Analysis of an age-dependent SIS epidemic model with vertical transmission and proportionate mixing assumption, Math. Comput. Model. 29 (1999), 31–43.
 D. Greenhalgh, Analytical threshold and stability results on age-structured epidemic models with vaccination, Theor. Popul. Bio. 33 (1988), 266–290.
 D. Greenhalgh and K. Dietz, Some bounds on estimates for reproductive ratios derived from the age-specific force of infection, Math. Biosci. 124 (1994), 9–57.
 M.E. Gurtin and R.C. MacCamy, Product Solutions and Asymptotic Behavior for Age-Dependent, Dispersing Populations, 1981.
 H.J. Heijmans, The dynamical behaviour of the age-size-distribution of a cell population, Springer Berlin Heidelberg, 1986, pp. 185–202.
 M. Iannelli, Mathematical Theory of Age-Structured Population Dynamics, Giardini Editori e Stampatori in Pisa, 1995.
 H. Inaba, On a new perspective of the basic reproduction number in heterogeneous environments, J. Math.Bio. 65 (2012), 309–348.
 H. Inaba, Threshold and stability results for an age-structured epidemic model, J. Math. Bio. 28 (1990), 149–175.
 H. Inaba, A semigroup approach to the strong ergodic theorem of the multistate stable population process, Math. Popul. Stud. 1 (1988), 49–77.
 H. Inaba, Age-Structured Population Dynamics in Demography and Epidemiology, Springer, Singapore, 2017.
 W.O. Kermack and A.G. McKendrick, Contributions to the mathematical theory of epidemics I, Proc. R. Soc. 115 (1927), 700–721.
 S.G. Kilbas, A.A. Kilbas, and O.I. Marichev, Fractional Integrals and Derivatives: Theory and Applications, Gordon and Breach, Yverdon, 1993
 A.A. Kilbas, H.H. Srivastava and J.J. Trujillo, Theory and Applications of Fractional Differential Equations, . Vol. 204, Elsevier, 2006.
 M.A. Krasnoselskii, Positive Solutions of Operator Equations, Groningen, Noordhoff, 1964.
 M. Langlais, Large time behaviour in a nonlinear age-dependent population dynamics problem with spatial diffusion, J. Math. Bio. 26 (1988), no. 3, 319–346. Math., 19(3): 607-628 (1970).
 R.M. May and R.M. Anderson, Endemic infections in growing populations, Math. Biosci. 77 (1985), 141–156.
 A. Mckendrick, Applications of mathematics to medical problems, Proc. Edinburgh Math. Soc. 44 (1926), 98–130.
 K.S. Miller and B. Ross, An Introduction to the Fractional Calculus and Fractional Differential Equations, Wiley, 1993.
 H.L. Smith and H.R. Thieme, Dynamical Systems and Population Persistence, Graduate Studies in Mathematics 118, Amer. Math. Soc. Providence, Rhode Island, 2011.
 D.W. Tudor, An age-dependent epidemic model with applications to measles, Math. Biosci. 73 (1985), 131–147.
 G.B. Webb, Theory of Nonlinear Age-dependent Population Dynamics, Marcel Dekker, New York and Basel, 1985.
 H.M. Yang, Directly transmitted infections modeling considering an age-structured contact rate, Math. Comput. Model. 29 (1999), 39–48.
 H. Ye, J. Gao, and Y. Ding, A generalized Gronwall inequality and its application to a fractional differential equation J. Math. Anal. Appl. 328 (2007), no. 2, 1075–1081.
 M. Zbair, A.Qaffou, F. Cherkaoui and K. Hilal, Bayesian Inference of a Discrete Fractional SEIRD Model, Recent Advances in Fuzzy Sets Theory, Fractional Calculus, Dynamic Systems and Optimization, Cham: Springer International Publishing, 2022, pp. 138–146.
 Y. Zhou and F. Jiao, Existence of mild solutions for fractional neutral evolution equations, Comput. Math. Appl. 59 (2010), no. 3, 1063–1077.