Directly transmitted infections modeling considering an age-structured contact rate

Mathematical and Computer Modelling

Volumn 29, Issue 8, 1999, Pages 39-48

  Yang, H M ^a  

^a UNIVERSITY OF CAMPINAS   (Brazil)

Author keywords

Age structured model; Contact rate; Force of infection; Probability

Indexed keywords

EID: 0033120227     PISSN: 08957177     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0895-7177(99)00069-2     Document Type: Article

References (23)

1. P.E.M. Fine and J.A. Clarkson, Measles in England and Wales. I. An analysis of factors underlying seasonal patterns, Int. J. Epidemiol. 11, 5-14, (1982).
2. P.E.M. Fine and J.A. Clarkson, Measles in England and Wales. II. The impact of the measles vaccination program on the distribution of immunity in the population, Int. J. Epidemiol. 11, 15-25, (1982).
3. W.P. London and J.A. York, Recurrent outbreaks of measles, chickenpox and mumps I: Seasonal variation in contact rates, Am. J. Epidemiol. 98, 453-468, (1973).
4. R.M. Anderson and R.M. May, Age-related changes in the rate of disease transmission: Implications for the design of vaccination programmes, J. Hyg. Camb. 94, 365-436, (1985).
5. D. Schenzle, An age-structured model of pre- and post-vaccination measles transmission, IMA J. Math. App. Med. Biol. 1, 169-191, (1984).
6. R.S. Azevedo Neto, A.S.B. Silveira, D.J. Nokes, H.M. Yang, S.D. Passos, M.R.A. Cardoso and E. Massad, Rubella seroepidemiology in a nonimmunized population of São Paulo State Brazil, Epidemiol. Infect. 113 (1), 161-173, (1994).
7. B.T. Grenfell and R.M. Anderson, The estimation of age-related rates of infection from case notifications and serological data, J. Hyg. 95, 419-436, (1985).
8. R.M. Anderson, and R.M. May, Infectious Diseases of Humans: Dynamics and Control, Oxford University Press, Oxford, (1991).
9. K. Dietz, Transmission and control of arbovirus diseases, in Proceedings of a SIMS Conference on Epidemiology, pp. 104-121, Alta, Utah, (July 8-12, 1974).
10. D.W. Tudor, An age-dependent epidemic model with applications to measles, Math. Biosc. 73, 131-147, (1985).
11. H.M. Yang, Directly transmitted infections modeling considering an age-structured contact rate-Epidemiological analysis, Math. Comput. Modelling (to appear).
12. C.P. Farrington, Modelling forces of infection for measles, mumps and rubella, Stat. Med. 9, 953-967, (1990).
13. E. Trucco, Mathematical model for cellular system. The von Foerster equations. Part I, Math. Bioph. 27, 285-303, (1965).
14. H.M. Yang and A.S.B. Silveira, The loss of immunity in directly transmitted infections modeling: Effects on the epidemiological parameters, B. Math. Biol. 60 (2), 355-372, (1998).
15. D.H. Griffel, Applied Functional Analysis, John Wiley & Sons, New York, (1981).
16. A. Stuart and K. Ord, Kendall's Advanced Theory of Statistics: Distribution Theory, Vol. 1, 5th Edition, Oxford University Press, New York, (1987).
17. M. Abramowitz, and I.A. Stegun, Handbook of Mathematical Functions with Formulas, Graphs and Mathematical Tables, Dover Publications, New York, (1972).
18. S.D. Passos, Personal communication, (1985).
19. P.S.P. Silveira, H.M. Yang, R.S. Azevedo Neto and E. Massad, Mathematical and computer models for infective contact rates, Math. Model. Scient. Comput. 6, 793-798, (1996).
20. R.M. Anderson, Population Dynamics of Infectious Diseases, (Edited by R.M. Anderson), Chapman & Hall, London, (1982).
21. D. Greenhalgh, Vaccination campaigns for common childhood diseases, Math. Biosc. 100, 201-240, (1990).
22. H. Inaba, Threshold and stability results for an age-structured epidemic model, J. Math. Biol. 28, 411-434, (1990).
23. F.A.B. Coutinho, E. Massad, M.N. Burattini, H.M. Yang and R.S. Azevedo Neto, Effects of vaccination programmes on transmission rates of infections and related threshold conditions for control, IMA J. Math. App. Med. Biol. 10, 187-206, (1993).