The mathematical theory of infectious diseases and its applications, 1975. ,
The Mathematics of Infectious Diseases, SIAM Rev, vol.42, pp.599-653, 2000. ,
Age-related changes in the rate of disease transmission: implications for the design of vaccination programmes, Epidemiol. Infect, vol.94, pp.365-436, 1985. ,
An Age-Structured Model of Pre-and Post-Vaccination Measles Transmission, Math. Med. Biol. J. IMA, vol.1, pp.169-191, 1984. ,
The basic reproduction number in some discrete-time epidemic models, J. Differ. Equations Appl, vol.14, pp.1127-1147, 2008. ,
Time series modelling of childhood diseases: a dynamical systems approach, Appl. Statist, vol.49, pp.187-205, 2000. ,
Population biology of infectious diseases: Part I, Nature, vol.280, pp.361-367, 1979. ,
, Mathematical models in population biology and epidemiology, 2012.
A contribuition to the mathematical theory of epidemics, Proc. R. Soc. Lond. A, vol.115, pp.700-721, 1927. ,
, An Introduction to Mathematical Epidemiology, 2015.
An Introduction to Structured Population Dynamics, 1998. ,
On the definition and the computation of the basic reproduction ratio R 0 in models for infectious diseases in heterogeneous populations, J. Math. Biol, vol.28, pp.365-382, 1990. ,
How may infection-age-dependent infectivity affect the dynamics of HIV/AIDS ?, SIAM J. Appl. Math, vol.53, pp.1447-1479, 1993. ,
, Mathematics in Population Biology, 2003.
Global stability of an SIR epidemic model with time delays, J. Math. Biol, vol.33, pp.250-260, 1995. ,
A generalization of the Kermack-McKendrick deterministic epidemic model, Math. Biosci, vol.42, pp.43-61, 1978. ,
Analysis of an SEIRS epidemic model with two delays, J. Math. Biol, vol.35, pp.240-260, 1996. ,
On the delayed Ross-Macdonald model for malaria transmission, Bull. Math. Biol, vol.70, pp.1098-1114, 2008. ,
An Introduction to Stochastic Epidemic Models, pp.81-130, 2008. ,
Stationary distribution of a stochastic SIS epidemic model with vaccination, Phys. A (Amsterdam, Neth.), vol.394, pp.187-197, 2014. ,
The threshold of a stochastic SIS epidemic model with vaccination, Appl. Math. Comput, vol.243, pp.718-727, 2014. ,
Spatial, temporal, and genetic heterogeneity in host populations and the design of immunization programs, IMA J. Math. Appl. Med. Biol, vol.1, pp.233-266, 1994. ,
Mathematical models of vaccination, Br. Med. Bull, vol.62, pp.187-199, 2002. ,
Simulations of rubella vaccination strategies in China, Math. Biosci, vol.202, pp.371-385, 2006. ,
Optimal ages of vaccination for measles, Math. Biosci, vol.89, pp.29-52, 1988. ,
Immune Responses After 2 Versus 3 Doses of HPV Vaccination up to 4 1/2 Years After Vaccination: An Observational Study Among Dutch Routinely Vaccinated Girls, J. Infect. Dis, vol.215, pp.359-367, 2017. ,
HPV-immune response to infection and vaccination, Infect. Agents Cancer, vol.5, pp.19-25, 2010. ,
Epidemiology and transmission dynamics of genital HPV infection, Vaccine, pp.52-61, 2006. ,
Economical Value of Vaccines for the Developing Countries-The Case of Instituto Butantan, a Public Institution in Brazil, PLoS Negl Trop Dis, vol.5, p.1300, 2011. ,
Is There a Resurgence of Vaccine Preventable Diseases in the US?, Journal of Pediatric Nursing, vol.44, pp.115-118, 2019. ,
, Measles in 2019 going backward, vol.380, pp.2185-2187, 2019.
Global Stability Results in a SVIR Epidemic Model with Immunity Loss Rat Depending on the Vaccine-Age, Abstract and Applied Analysis, pp.1-8, 2015. ,
Modelling the effects of temporary immune protection and vaccination against infectious diseases, Appl. Math. Comput, vol.189, pp.1723-1736, 2007. ,
Essai d'une nouvelle analyse de la mortalité causée par la petite vérole et des avantages de l'inoculation pour la prévenir, Histoire de l'Acad, Roy. Sci.(Paris) avec Mem, pp.1-45, 1760. ,
Global stability of an SVIR model with age of vaccination, Appl. Math. Comput, vol.226, pp.528-540, 2014. ,
Strain replacement in an epidemic model with super-infection and perfect vaccination, Math. Biosci, vol.195, pp.23-46, 2005. ,
Stability and bifurcation of an SIVS epidemic model with treatment and age of vaccination, Appl. Math. Modell, vol.34, pp.437-450, 2010. ,
Analysis of a delayed vaccinated SIR epidemic model with temporary immunity and lévy jumps, Nonlinear Anal. Hybrid Syst, vol.27, pp.29-43, 2018. ,
Global stability of a multi-group model with generalized nonlinear incidence and vaccination age, Discrete Contin. Dyn. Sys. B, vol.21, pp.977-996, 2016. ,
, Theory of Nonlinear Age-Dependent Population Dynamics, 1985.
Existence, uniqueness and continuous dependence for hereditary systems, Ann. Mat. Pura Appl, vol.85, pp.63-81, 1970. ,
, Introduction to Functional Differential Equations, 1993.
, An Introduction to Delay Differential Equations with Applications to the Life Sciences, 2011.
Age-structured and delay differential-difference model of hematopoietic stem cell dynamics, Discrete Contin. Dyn. Syst. Ser. B, vol.20, pp.2765-2791, 2015. ,
URL : https://hal.archives-ouvertes.fr/hal-01249892
Stability of functional differential equations of neutral type, J. Differ. Equations, vol.7, pp.334-355, 1970. ,
An introduction to the basic reproduction number in mathematical epidemiology, ESAIM Proc. Surv, vol.62, pp.123-138, 2018. ,
Persistence definitions and their connections, Proc. Am. Math. Soc, vol.109, pp.1025-1033, 1990. ,
Lyapunov-Krasovskii functional for uniform stability of coupled differential-functional equations, Automatica, vol.45, pp.798-804, 2009. ,
New versions of Barbalat's lemma with applications, J. Control Theory Appl, vol.8, pp.545-547, 2010. ,