Monotonicity of the number of passages in linear chains and of the basic reproduction number in epidemic models

Zeitschrift für Analysis und ihre Anwendungen

Volumn 19, Issue 1, 2000, Pages 61-75

  Muller J ^a   Hadeler, K P ^a  

^a UNIVERSITY OF TÜBINGEN   (Germany)

Author keywords

Basic reproduction number; Epidemiology; Linear chain; Markov chain

Indexed keywords

EID: 22844457218     PISSN: 02322064     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (28)

1. Bailey, N.: The Mathematical Theory of Infectious Diseases and its Applications. London: Charles Griffin & Co. Ltd 1975.
2. Blythe, S., Castillo-Chavez, C., Palmer, J. and M. Cheng: Toward a unified theory of sexual mixing and pair formation. Math. Biosc. 107 (1991), 376 - 405.
3. Busenberg, S. N. and K. P. Hadeler: Demography and epidemics. Math. Biosc. 101 (1990), 63 - 74.
4. Diekmann, O., De Jong, M., De Koeijer, A. and P. Reijnders: The force of infection in populations of varying size: a modelling problem. J. Biol. Syst. 3 (1995), 519 - 529.
5. Diekmann, O., Dietz, K. and J. Heesterbeek: The basic reproduction ratio for sexually transmitted diseases. Part I: Theoretical considerations. Math. Biosc. 107 (1991), 325 - 339.
6. 0 in models for infectious diseases in heterogeneous populations. J. Math. Biol. 28 (1990), 365 - 382.
7. Dietz, K.: Transmission and control of arbovirus diseases. In: Epidemiology (ed.: K. Cooke). Philadelphia: SIAM 1975, pp. 104 - 121.
8. Dietz, K. and K. P. Hadeler: Epidemiological models for sexually transmitted diseases. J. Math. Biol. 26 (1988), 1 - 25.
9. Dietz, K., Heesterbeek, J. and D. Tudor: The basic reproducion ratio for sexually transmitted diseases. Part 2: Effects of variable HIV infectivity. Math. Biosc. 117 (1993), 35 - 47.
10. Dietz, K. and D. Schenzle: Proportionate mixing models for age-dependent infection transmission. J. Math. Biol. 22 (1985), 117 - 120.
11. Greenhalgh G.: Vaccination campaigns for common childhood diseases. Math. Biosc. 100 (1990), 201 - 240.
12. Hadeler, K. P.: Periodic solutions of homogeneous equations. J. Diff. Equ. 95 (1992), 183 - 202.
13. Hadeler; K. P.: Structured population models for HIV infection. Pair formation and non-constant infectivity. In: AIDS Epidemiology: Methodological Issues (eds.: N. P. Jewell et al.). Boston: Birkhäuser 1992, pp. 156 - 173.
14. Hadeler, K. P. and C. Castillo-Chavez: A core group model for disease transmission. Math. Biosc. 128 (1995), 41 - 55.
15. Hadeler, K. P. and K. Ngoma: Homogeneous models for sexually transmitted diseases. Rocky Mountain J. Math. 20 (1990), 967 - 985.
16. Hadeler, K. P. and P. van den Driessche: Backward bifurcation in epidemic control. Math. Biosc. 146 (1997), 15 - 35.
17. Hadeler, K. P., Waldstätter, R. and A. Wörz-Busekros: Models for pair formation in bisexual populations. J. Math. Biol. 26 (1988), 635 - 649.
18. Hethcote, H. W.: Qualitative analysis of communicable disease models. Math. Biosc. 28 (1976), 335 - 356.
19. Kendall, D.: Stochastic processes and population growth. Royal Stat. Soc. (Ser. B2) 11 (1949), 230 - 264.
20. Kermack, W. and A. McKendrick: A contribution to the mathematical theory of epidemics. Proc. Roy. Soc. (Ser. A) 115 (1927), 700 - 721;
21. reprinted in: Applicable Mathematics of Nonphysical Phenomena (eds.: G. Oliveira-Pinto and B. W. Conolly). Chichester: Ellis Horwood 1982, pp. 222 - 247.
22. Kretzschmar, M. and K. Dietz: The effect of pair formation and variable infectivity on the spread of an infection without recovery. Math. Biosc. 148 (1998), 83 - 113.
23. Müller, J. and K. P. Hadeler: Variable infectivity in sexually transmitted diseases. Dynamik, Analysis, effiziente Simulation und Ergodentheorie (DANSE), Preprint 2/97, Tübingen 1997.
24. Novak, M., Anderson, R., McLean, A., Wolfs, T., Goudsmit, J. and R. May: Antigenic diversity threshold and the development of AIDS. Science 254 (1991), 963 - 969.
25. Novak, M. and R. May: Mathematical biology of HIV-infection: Antigenic variation and diversity threshold. Math. Biosc. 106 (1991), 1 - 21.
26. Pantaleo, G., Graziosi, C. and A. Fauci: The immunopathogenesis of human immunodeficiency virus infection. N. Engl. J. Med. 328 (1993), 327 - 335.
27. Stilianakis, N., Dietz, K. and D. Schenzle: On the antigenic diversity threshold models for AIDS. Math. Biosc. 121 (1994), 235 - 247.
28. Stilianakis, N., Schenzle, D. and K. Dietz: Analysis of a model for the pathogenesis of AIDS. Math. Biosc. 145 (1997), 27 - 46.