Periodic solutions: A robust numerical method for an S-I-R model of epidemics

Journal of Mathematical Biology

Volumn 39, Issue 6, 1999, Pages 471-492

  Milner, F A ^a   Pugliese, A ^b  

^a PURDUE UNIVERSITY   (United States)

^b UNIVERSITY OF TRENTO   (Italy)

Author keywords

Epidemic model; Instability of equilibrium; Numerical methods; Periodic solutions

Indexed keywords

ACQUIRED IMMUNE DEFICIENCY SYNDROME; ALGORITHM; ARTICLE; BIOLOGICAL MODEL; EPIDEMIC; HUMAN; HUMAN IMMUNODEFICIENCY VIRUS INFECTION; MATHEMATICS; PERIODICITY; STATISTICS;

ACQUIRED IMMUNODEFICIENCY SYNDROME; ALGORITHMS; DISEASE OUTBREAKS; HIV INFECTIONS; HUMANS; MATHEMATICS; MODELS, BIOLOGICAL; PERIODICITY;

EID: 0033253851     PISSN: 03036812     EISSN: None     Source Type: Journal    
DOI: 10.1007/s002850050175     Document Type: Article

References (16)

1. L. M. Abia and J. C. Lopez-Marcos: Runge-Kutta methods for age-structured population models. Appl. Numer. Math. 17 (1995), 1-17.
2. R. M. Anderson: The epidemiology of HIV infection: variable incubation plus infectious periods and heterogeneity in sexual activity. J. Royal Stat. Society A 151 (1988), 66-93.
3. P. Bacchetti and A. Moss: Incubation period of AIDS in San Francisco Nature 338 (1989), 251-253.
4. S. P. Blythe and R. M. Anderson: Variable infectiousness in HIV transmission models IMA. J. Math. Appl. Med. Biol. 5 (1988), 181-200.
5. C. Castillo-Chavez, K. Cooke, W. Huang and S. A. Levin: On the role of long incubation periods in the dynamics of acquired immunodeficiency syndrome (AIDS). 1. Single population models. J. Math. Biol. 27 (1989), 373-398.
6. C. Castillo-Chavez, K. Cooke, W. Huang and S. A. Levin: Mathematical and Statistical Approaches to AIDS Epidemiology, C. Castillo-Chavez (Ed.). Lecture Notes in Biomathematics, vol. 83, Springer, 1989.
7. M. Iannelli, R. Loro, F. A. Milner, A. Pugliese, and G. Rabbiolo: An AIDS Model with Distributed Incubation and Variable Infectivity: Applications to IV-Drug Users in Latium Europ. J. Epidem. 8 (1992), 585-593.
8. M. Iannelli, F. A. Milner, and A. Pugliese: Analytical and Numerical Results for The Age- Structured S-I-S Model with Mixed Inter-Intracohort Transmission SIAM. J. Math. Anal. 23 (1992), 662-688.
9. W. O. Kermack and A. G. McKendrick: A contribution to the mathematical theory of epidemics. Proc. Roy. Soc. A 115 (1927), 700-721.
10. M. Kubo and M. Langlais: Periodic solutions for a population dynamics problem with age dependence and spatial structure. J. Math. Biol. 29 (1991), 363-378.
11. T. Lafaye and M. Langlais: Threshold methods for threshold models in age dependent population dynamics and epidemiology. Calcolo 29 (1993), 49-79.
12. I. M. Longini jr., W. S. Clark, M. Haber and R. Horsburgh jr.: Mathematical and Statistical Approaches to AIDS Epidemiology, C. Castillo-Chavez (Ed.). Lecture Notes in Biomathematics, vol. 83, Springer, 1989.
13. L. Michaelis and M. I. Menten: Die Kinetik der Invertinwirkung. Biochem. Z. 49 (1913), 333-369.
14. F. A. Milner and G. Rabbiolo: Rapidly Converging Numerical Algorithms for Models of Population Dynamics. J. Math. Biol. 30 (1992), 733-753.
15. C. Castillo-Chávez and H. Thieme: How may infection-age-dependent infectivity affect the dynamics of HIV/AIDS?, SIAM. J. Appl. Math. 53 (1993) 1447-1479.
16. H. Thieme and C. Castillo-Chavez: Mathematical and Statistical Approaches to AIDS Epidemiology C. Castillo-Chavez (Ed.). Lecture Notes in Biomathematics, vol. 83, Springer, 1989, pp. 157-176.