The net reproduction rate and the type reproduction number in multiregional demography

Vienna Yearbook of Population Research

Volumn , Issue 1, 2009, Pages 197-215

  Inaba, Hisashi ^a  

^a UNIVERSITY OF TOKYO   (Japan)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 77956628403     PISSN: 17284414     EISSN: 17285305     Source Type: Journal    
DOI: 10.1553/populationyearbook2009s197     Document Type: Review

References (34)

1. Billari, F. C., P. Manfredi, and A. Valentini. 2000. "Macro-demographic effects of the transition to adulthood: Multistate stable population theory and an application to Italy." Mathematical Population Studies 9(1): 33-63.
2. Coleman, D. 2006. "Immigration and ethnic change in low-fertility countries: A third demographic transition." Population and Development Review 32(3): 401-446.
3. 0 in models for infectious diseases in heterogeneous populations." Journal of Mathematical Biology 28: 365-382.
4. Diekmann, O. and J. A. P. Heesterbeek. 2000. Mathematical Epidemiology of Infectious Diseases: Model Building, Analysis and Interpretation. Chichester, John Wiley and Sons.
5. Dietz, K. 1993. "The estimation of the basic reproduction number for infectious diseases." Statistical Methods in Medical Research 2: 23-41.
6. Dublin, L. I. and A. J. Lotka. 1925. "On the true rate of natural increase." Journal of the American Statistical Association New Series 150(20): 305-339.
7. Heesterbeek, J. A. P. 2002. "A brief history of R0 and a recipe for its calculation." Acta Biotheoretica 50: 189-204.
8. Heesterbeek, J. A. P. and M. G. Roberts. 2007. "The type-reproduction number T in models for infectious disease control." Mathematical Biosciences 206: 3-10.
9. Inaba, H. 1986. "On the discrete model of multiregional demographic growth." Journal of Population Problems 179: 1-15. [in Japanese with English summary]
10. Inaba, H. 1987. "Mathematical foundation of multidimensional stable population theory I: Classical theory." Journal of Population Problems 184: 52-77. [in Japanese with English summary]
11. Inaba, H. 1988a. "A semigroup approach to the strong ergodic theorem of the multistate stable population process." Mathematical Population Studies 1(1): 49-77.
12. Inaba, H. 1988b. "Asymptotic properties of the inhomogeneous Lotka-Von Foerster system." Mathematical Population Studies 1(3): 247-264.
13. Inaba, H. 1992. "Duration-dependent multistate population dynamics." Working Paper Series, No. 9, Institute of Population Problems, Tokyo.
14. Inaba, H. 1995. "Human population reproduction via first marriage." Mathematical Population Studies 5(2): 123-144.
15. Inaba, H. and H. Nishiura. 2008. "The state-reproduction number for a multistate class age structured epidemic system and its application to the asymptomatic transmission model." Mathematical Biosciences 216: 77-89.
16. Keyfitz, N. and H. Caswell. 2005. Applied Mathematical Demography. 3rd Edition, New York, Springer.
17. Land, K. C. and A. Rogers (eds.) 1982. Multidimensional Mathematical Demography. New York, Academic Press.
18. Le Bras, H. 1971. "Equilibre et croissance de populations soumises à des migrations." Theoretical Population Biology 2: 100-121.
19. Lotka, A. J. 1998. Analytical Theory of Biological Populations. Translated and with an introduction by D. P. Smith and H. Rossert. New York and London, Plenum Press. [translation from original edition Théorie analytique des associations biologiques. Deuxième partie: Analyse démographique avec application particulière à l'espèce humaine. (Actualités Scientifiques et Industrielles, No. 780), Paris, Hermann et Cie, 1939.]
20. Metz, J. A. J. and O. Diekmann. 1986. The Dynamics of Physiologically Structured Populations. Lecture Notes in Biomathematics 68, Berlin, Springer.
21. Minc, H. 1988. Nonnegative Matrices. New York, John Wiley and Sons.
22. Nishiura, H., K. Dietz, and M. Eichner. 2006. "The earliest notes on the reproduction number in relation to herd immunity: Theophil Lotz and smallpox vaccination." Journal of Theoretical Biology 241: 964-967.
23. Nishiura, H. and H. Inaba. 2007. "Discussion: Emergence of the concept of the basic reproduction number from mathematical demography." Journal of Theoretical Biology 244: 357-364.
24. Preston, S. H., P. Heuveline, and M. Guillot. 2001, Demography: Measuring and Modeling Population Processes. Oxford, Blackwell.
25. Roberts, M. G. and J. A. P. Heesterbeek. 2003. "A new method for estimating the effort required to control an infectious disease." Proceedings of the Royal Society of London B 270: 1359-1364.
26. Rogers, A. 1966. "The multiregional matrix growth operator and the stable interregional age structure." Demography 3: 537-544.
27. Rogers, A. 1968. Matrix Analysis of Interregional Population Growth and Distributions. Berkeley, University of California Press.
28. Rogers, A. 1975. Introduction to Multiregional Mathematical Demography. New York, John Wiley.
29. Rogers, A. and F. Willekens. 1978. "The spatial reproductive value and the regional momentum of zero population growth." Environment and Planning A 10: 503-518.
30. Rogers, A. and F. J. Willekens (eds.) 1986. Migration and Settlement: A Multiregional Comparative Study. Dordrecht, D. Reidel.
31. Rogers, A. 1995. Multiregional Demography: Principles, Methods and Extensions. New York, John Wiley.
32. Schoen, R. 1988. Modeling Multigroup Populations. New York and London, Plenum Press.
33. Wallinga, J. and M. Lipsitch. 2007. "How generation intervals shape the relationship between growth rates and reproductive numbers." Proceedings of the Royal Society B 274: 599-604.
34. Willekens, F. 1977. "The spatial reproductive value: theory and applications." RM-77-9, Laxenburg, IIASA.