-
1
-
-
33947541669
-
0 for vector-borne diseases with a periodic vector population
-
0 for vector-borne diseases with a periodic vector population. Bull Math Biol 69: 1067-1091.
-
(2007)
Bull Math Biol
, vol.69
, pp. 1067-1091
-
-
Bacaër, N.1
-
2
-
-
74049108998
-
Periodic matrix population models: growth rate, basic reproduction number, and entropy
-
Bacaër N (2009) Periodic matrix population models: growth rate, basic reproduction number, and entropy. Bull Math Biol 71: 1781-1792.
-
(2009)
Bull Math Biol
, vol.71
, pp. 1781-1792
-
-
Bacaër, N.1
-
3
-
-
49549125423
-
Resonance of the epidemic threshold in a periodic environment
-
Bacaër N, Abdurahman X (2008) Resonance of the epidemic threshold in a periodic environment. J Math Biol 57: 649-673.
-
(2008)
J Math Biol
, vol.57
, pp. 649-673
-
-
Bacaër, N.1
Abdurahman, X.2
-
4
-
-
79953038195
-
Genealogy with seasonality, the basic reproduction number, and the influenza pandemic
-
Bacaër N, Ait Dads EH (2011a) Genealogy with seasonality, the basic reproduction number, and the influenza pandemic. J Math Biol 62: 741-762.
-
(2011)
J Math Biol
, vol.62
, pp. 741-762
-
-
Bacaër, N.1
Ait Dads, E.H.2
-
6
-
-
33748152440
-
The epidemic threshold of vector-borne diseases with seasonality
-
Bacaër N, Guernaoui S (2006) The epidemic threshold of vector-borne diseases with seasonality. J Math Biol 53: 421-436.
-
(2006)
J Math Biol
, vol.53
, pp. 421-436
-
-
Bacaër, N.1
Guernaoui, S.2
-
7
-
-
36148974693
-
Growth rate and basic reproduction number for population models with a simple periodic factor
-
Bacaër N, Ouifki R (2007) Growth rate and basic reproduction number for population models with a simple periodic factor. Math Biosci 210: 647-658.
-
(2007)
Math Biosci
, vol.210
, pp. 647-658
-
-
Bacaër, N.1
Ouifki, R.2
-
11
-
-
0000201875
-
On the formulation and analysis of general deterministic structured population models I. Linear theory
-
Diekmann O, Gyllenberg M, Metz JAJ, Thieme HR (1998) On the formulation and analysis of general deterministic structured population models I. Linear theory. J Math Biol 36: 349-388.
-
(1998)
J Math Biol
, vol.36
, pp. 349-388
-
-
Diekmann, O.1
Gyllenberg, M.2
Metz, J.A.J.3
Thieme, H.R.4
-
12
-
-
77953160649
-
The construction of next-generation matrices for compartmental epidemic models
-
Diekmann O, Heesterbeek JAP, Roberts MG (2010) The construction of next-generation matrices for compartmental epidemic models. J R Soc Interface 6 7(47): 873-885.
-
(2010)
J R Soc Interface 6
, vol.7
, Issue.47
, pp. 873-885
-
-
Diekmann, O.1
Heesterbeek, J.A.P.2
Roberts, M.G.3
-
15
-
-
0036025407
-
0 and a recipe for its calculation
-
0 and a recipe for its calculation. Acta Biotheor 50: 189-204.
-
(2002)
Acta Biotheor
, vol.50
, pp. 189-204
-
-
Heesterbeek, J.A.1
-
16
-
-
0029184066
-
Threshold quantities for helminth infections
-
Heesterbeek JAP, Roberts MG (1995a) Threshold quantities for helminth infections. J Math Biol 33: 415-434.
-
(1995)
J Math Biol
, vol.33
, pp. 415-434
-
-
Heesterbeek, J.A.P.1
Roberts, M.G.2
-
17
-
-
0343506610
-
Threshold quantities for infectious diseases in periodic environments
-
Heesterbeek JAP, Roberts MG (1995b) Threshold quantities for infectious diseases in periodic environments. J Biol Syst 3(3): 779-787.
-
(1995)
J Biol Syst
, vol.3
, Issue.3
, pp. 779-787
-
-
Heesterbeek, J.A.P.1
Roberts, M.G.2
-
18
-
-
0004407733
-
The dynamical behaviour of the age-size-distribution of a cell population
-
In: Metz JAJ, Diekmann O (eds), Springer, Berlin
-
Heijmans HJAM (1986) The dynamical behaviour of the age-size-distribution of a cell population. In: Metz JAJ, Diekmann O (eds) The dynamics of physiologically structured populations. Lect Notes Biomath, vol 68. Springer, Berlin, pp 185-202.
-
(1986)
The dynamics of physiologically structured populations. Lect Notes Biomath
, vol.68
, pp. 185-202
-
-
Heijmans, H.J.A.M.1
-
19
-
-
0024467542
-
Weak ergodicity of population evolution processes
-
Inaba H (1989) Weak ergodicity of population evolution processes. Math Biosci 96: 195-219.
-
(1989)
Math Biosci
, vol.96
, pp. 195-219
-
-
Inaba, H.1
-
20
-
-
0025118998
-
Threshold and stability results for an age-structured epidemic model
-
Inaba H (1990) Threshold and stability results for an age-structured epidemic model. J Math Biol 28: 411-434.
-
(1990)
J Math Biol
, vol.28
, pp. 411-434
-
-
Inaba, H.1
-
21
-
-
38249011393
-
Strong ergodicity for perturbed dual semigroups and application to age-dependent population dynamics
-
Inaba H (1992) Strong ergodicity for perturbed dual semigroups and application to age-dependent population dynamics. J Math Anal Appl 165(1): 102-132.
-
(1992)
J Math Anal Appl
, vol.165
, Issue.1
, pp. 102-132
-
-
Inaba, H.1
-
22
-
-
70450164770
-
The basic reproduction number of an infectious disease in a stable population: the impact of population growth rate on the eradication threshold
-
Inaba H, Nishiura H (2008a) The basic reproduction number of an infectious disease in a stable population: the impact of population growth rate on the eradication threshold. Math Model Nat Phenom 3(7): 194-228.
-
(2008)
Math Model Nat Phenom
, vol.3
, Issue.7
, pp. 194-228
-
-
Inaba, H.1
Nishiura, H.2
-
23
-
-
54349112795
-
The state-reproduction number for a multistate class age structured epidemic system and its application to the asymptomatic transmission model
-
Inaba H, Nishiura H (2008b) The state-reproduction number for a multistate class age structured epidemic system and its application to the asymptomatic transmission model. Math Biosci 216: 77-89.
-
(2008)
Math Biosci
, vol.216
, pp. 77-89
-
-
Inaba, H.1
Nishiura, H.2
-
24
-
-
0040825727
-
Branching processes in periodically varying environment
-
Jagers P, Nerman O (1985) Branching processes in periodically varying environment. Ann Probab 13: 254-268.
-
(1985)
Ann Probab
, vol.13
, pp. 254-268
-
-
Jagers, P.1
Nerman, O.2
-
26
-
-
0005130113
-
The progeny of a population element
-
Lotka AJ (1928) The progeny of a population element. Am J Hygiene 8: 875-901.
-
(1928)
Am J Hygiene
, vol.8
, pp. 875-901
-
-
Lotka, A.J.1
-
27
-
-
84864350669
-
The spread of generations
-
Lotka AJ (1929) The spread of generations. Hum Biol 1(3): 305-320.
-
(1929)
Hum Biol
, vol.1
, Issue.3
, pp. 305-320
-
-
Lotka, A.J.1
-
28
-
-
47949108698
-
Analytical theory of biological populations
-
Plenum Press, New York. English translation from the French original edition Théorie Analytique des Associations Biologiques. Deuxième Partie: Analyse De0́mographique avec Application Particulière è l'Espèce Humaine. Actualités Scientifiques et Industrielles, No. 780. Hermann et Cie, Paris (1939)
-
Lotka AJ (1998) Analytical theory of biological populations. The Plenum Series on Demographic Methods and Population Analysis. Plenum Press, New York. English translation from the French original edition Théorie Analytique des Associations Biologiques. Deuxième Partie: Analyse Démographique avec Application Particulière è l'Espèce Humaine. Actualités Scientifiques et Industrielles, No. 780. Hermann et Cie, Paris (1939).
-
(1998)
The Plenum Series on Demographic Methods and Population Analysis
-
-
Lotka, A.J.1
-
29
-
-
84864343711
-
Iterations of linear bounded operators in non self-adjoint eigenvalue problems and Kellogg's iteration process
-
Marek I (1962) Iterations of linear bounded operators in non self-adjoint eigenvalue problems and Kellogg's iteration process. Czech Math J 12: 536-554.
-
(1962)
Czech Math J
, vol.12
, pp. 536-554
-
-
Marek, I.1
-
30
-
-
0000855503
-
Frobenius theory of positive operators: comparison theorems and applications
-
Marek I (1970) Frobenius theory of positive operators: comparison theorems and applications. SIAM J Appl Math 19: 607-628.
-
(1970)
SIAM J Appl Math
, vol.19
, pp. 607-628
-
-
Marek, I.1
-
31
-
-
24044522878
-
General relative entropy inequality: an illustration on growth models
-
Michel P, Mischler S, Perthame B (2005) General relative entropy inequality: an illustration on growth models. J Math Pures Appl 84: 1235-1260.
-
(2005)
J Math Pures Appl
, vol.84
, pp. 1235-1260
-
-
Michel, P.1
Mischler, S.2
Perthame, B.3
-
32
-
-
33751309622
-
Discussion: emergence of the concept of the basic reproduction number from mathematical demography
-
Nishiura H, Inaba H (2007) Discussion: emergence of the concept of the basic reproduction number from mathematical demography. J Theor Biol 244: 357-364.
-
(2007)
J Theor Biol
, vol.244
, pp. 357-364
-
-
Nishiura, H.1
Inaba, H.2
-
33
-
-
33746067846
-
The earliest notes on the reproduction number in relation to herd immunity: Theophil Lotz and smallpox vaccination
-
Nishiura H, Dietz K, Eichner M (2006) The earliest notes on the reproduction number in relation to herd immunity: Theophil Lotz and smallpox vaccination. J Theor Biol 241: 964-967.
-
(2006)
J Theor Biol
, vol.241
, pp. 964-967
-
-
Nishiura, H.1
Dietz, K.2
Eichner, M.3
-
34
-
-
0004446478
-
On spectral properties of some positive operators
-
Sawashima I (1964) On spectral properties of some positive operators. Nat Sci Report Ochanomizu Univ 15: 53-64.
-
(1964)
Nat Sci Report Ochanomizu Univ
, vol.15
, pp. 53-64
-
-
Sawashima, I.1
-
36
-
-
0021523081
-
Renewal theorems for linear periodic Volterra integral equations
-
Thieme HR (1984) Renewal theorems for linear periodic Volterra integral equations. J Integr Equ 7: 253-277.
-
(1984)
J Integr Equ
, vol.7
, pp. 253-277
-
-
Thieme, H.R.1
-
37
-
-
67649378819
-
Spectral bound and reproduction number for infinite-dimensional population structure and time heterogeneity
-
Thieme HR (2009) Spectral bound and reproduction number for infinite-dimensional population structure and time heterogeneity. SIAM J Appl Math 70(1): 188-211.
-
(2009)
SIAM J Appl Math
, vol.70
, Issue.1
, pp. 188-211
-
-
Thieme, H.R.1
-
38
-
-
47149095789
-
Threshold dynamics for compartmental epidemic models in periodic environments
-
Wang W, Zhao XQ (2008) Threshold dynamics for compartmental epidemic models in periodic environments. J Dyn Differ Equ 20: 699-717.
-
(2008)
J Dyn Differ Equ
, vol.20
, pp. 699-717
-
-
Wang, W.1
Zhao, X.Q.2
-
39
-
-
0004201980
-
-
Princeton: Princeton University Press
-
Widder DV (1946) The Laplace transform. Princeton University Press, Princeton.
-
(1946)
The Laplace Transform
-
-
Widder, D.V.1
|