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Pełne teksty:
Warianty tytułu
Abstrakty
CONTEXTS
0. Introduction.......................................................................................................................................................................... 5
Part I
MODELS OF EPIDEMICS FOli INFECTIOUS DISEASES
1. Informal description of the phenomenon of epidemics and construction
of mathematical models........................................................................................................................................................ 5
2. General characterization of the classical models of epidemics................................................................................ 6
3. General characterization of models based on the theory of branching processes............................................... 8
4. First group of models: geographical spread of epidemics........................................................................................ 9
5. Second group of models: influence of changes of infectioussness on the course of epidemic........................ 18
6. Third group of models: preventive activity of health service........................................................................................ 22
7. Discussion........................................................................................................................................................................... 28
Part II
SPREADING OF NON-INFECTIOUS DISEASES
8. Introduction........................................................................................................................................................................... 31
9. Formal presentation of the model of reproduction and inheritance of types........................................................... 32
10. Tests for detecting time-dependent inheritance mechanisms............................................................................... 34
11. Possibility of estimating distributions appearing in the assumptions of
the model.................................................................................................................................................................................. 37
12. Probability generating function of the number of offsprings of different types...................................................... 43
13. Discussion......................................................................................................................................................................... 44
References............................................................................................................................................................................... 48
Słowa kluczowe
Tematy
Miejsce publikacji
Warszawa
Copyright
Seria
Rozprawy Matematyczne
tom/nr w serii:
61
Liczba stron
48
Liczba rozdzia³ów
Opis fizyczny
Dissertationes Mathematicae, Tom LXI
Daty
wydano
1969
Twórcy
autor
Bibliografia
- [1] Norman T. J. Bailey, The mathematical theory of epidemics, London 1957.
- [2] M. S. Bartlett, Stochastic population models in ecology and epidemiology London 1960.
- [3] R. Bartoszyński, Some limit properties of generalized branching processes, Bull. Acad, Polon. Sci., Ser. Ill, 15 (1967), pp. 157-160.
- [4] R. Bartoszyński, A limit property of a certain branching process, ibidem 15 (1967), pp. 615-618.
- [5] R. Bartoszyński, Branching processes and the theory of epidemics, Proc. Fifth Berkeley Symposium on Probability and Statistics, Berkeley 1967, pp. 259-269.
- [6] R. Bartoszyński, A model of age-dependent inheritance of cancer proneness, Proc. 36-th Congress of ISI (abstract).
- [7] R. Bartoszyński, and H. D'Abrera, On age dependant inheritance of cancer proneness, Journ. Australian Stat. Soc. (to appear).
- [8] R. Bartoszyński, and J. Łoś, M. Wycech-Łoś, Contribution to the theory of epidemics, in Bernoulli, Bayes, Laplace Anniversary Volume, Berkeley 1963, pp. 1-8.
- [9] K. Dietz, On the model of Weiss for the spread of epidemics by carriers, Journ. of Applied Probability 3 (1966), pp. 375-382.
- [10] W. Feller, An introduction to probability theory and its applications, vol. I, New York, London, Sydney 1955.
- [11] W. Feller, An introduction to probability theory and its applications, vol. II, New York, London, Sydney 1966.
- [12] J. Gani, On a partial differential equation of epidemic theory, Biometrica 52, 3-4 (1965), pp. 617-622.
- [13] T. Harris, Theory of branching processes, Springer Verl., 1963.
- [14] D. G. Kendall, Deterministic and stochastic epidemics in closed populations, Proceed. Third Berkeley Symposium on Probability and Statistics, Berkeley 1955.
- [15] J. Neyman and E. L. Scott, A stochastic model of epidemic, published in the volume: Stochastic models in medicine and biology, ed. J. Gurland, Wisconsin 1964.
- [16] V. Siskind, A solution of the general stochastic epidemic, Biometrika 52, 3-4 (1965), pp. 613-616.
- [17] C. J. Ridler-Rowe, On a stochastic model of an epidemic, Journ. of Applied Probability 4 (1967), pp. 19-33.
- [18] G. H. Weiss, On the spread of epidemics by carriers, Biometrics 21 (1965), pp. 481-490.
- [19] T. Williams, The simple stochastic epidemic curve for large populations of susceptibles, Biometrika 52, 3-4 (1965), pp. 571-579.
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