Seasonally varying epidemics with and without latent period: A comparative simulation study

Mathematical Medicine and Biology

Volumn 24, Issue 1, 2007, Pages 1-15

  Moneim, I A ^a  

^a KING SAUD UNIVERSITY   (Saudi Arabia)

Author keywords

Bifurcation; Epidemics; Filter; Periodicity; Poincar ; Section; SEIR; Simulation; SIR

Indexed keywords

BANDPASS FILTERS;

COMPARATIVE SIMULATION; FILTER; PERIODIC SOLUTION; PERIODICITY; POINCARÉ; SECTION; SEIR; SIMULATION; SIMULATION STUDIES; SIR;

EPIDEMIOLOGY;

ARTICLE; CHICKENPOX; CONTROLLED STUDY; ENDEMIC DISEASE; EPIDEMIC; HUMAN; INTERMETHOD COMPARISON; MATHEMATICAL MODEL; MEASLES; MUMPS; PREDICTION; RUBELLA; SEASONAL VARIATION; SIMULATION; VIRUS INFECTION; VIRUS TRANSMISSION;

EID: 33847608267     PISSN: 14778599     EISSN: 14778602     Source Type: Journal    
DOI: 10.1093/imammb/dql023     Document Type: Article

References (20)

1. Anderson, R. M. & May, R. M. (1991) Infectious Diseases of Humans: Dynamics and Control. Oxford: Oxford University Press.
2. Aron, J. L. & Schwartz, I. (1984) Seasonality and period-doubling bifurcations in an epidemic model. J. Theor. Biol., 110, 665-679.
3. Bolker, B. M. (1993) Chaos and biological complexity in measles dynamics: A comparative numerical study. IMA J. Math. Appl. Med. Biol., 10, 83-95.
4. Dietz, K. (1976) The incidence of infectious diseases under the influence of seasonal fluctuations. Proceedings of a Workshop on Mathematical Modelling in Medicine, Mainz. (J. Berger, W. Bühler, R. Repges, and P. Tautu eds). Lecture Notes in Biomathematics, vol. 11. Berlin, Germany: Springer, pp. 1-15.
5. Dowell, F. (2001) Seasonal variations in host susceptibility and cycles of certain infectious diseases. Emerg. Infect. Dis., 7, 369-374.
6. Duncan, C. J., Duncan, S. R. & Scott, R. (1997) The dynamics of measles epidemics. Theor. Popul. Biol., 52, 155-163.
7. Engbert, R. & Drepper, F. (1994) Chance and chaos in population biology-models of recurrent epidemics and food chain dynamics. Chaos Solitons Fractals, 4, 1147-1169.
8. Greenhalgh, D. (1990) Deterministic models for common childhood diseases. Int. J. Syst. Sci., 21, 1-20.
9. Greenhalgh, D. & Moneim, I. A. (2003) SIRS epidemic model and simulations using different types of seasonal contact rate. Syst. Anal. Model. Simul., 43, 573-600.
10. Grossman, Z., Gumowski, I. & Dietz, K. (1977) The incidence of infectious diseases under the influence of seasonal fluctuations in analytical approach. Nonlinear Systems and Applications to Life Sciences, An International Conference (V. Lakshmikantham ed.). New York: Academic Press, pp. 525-546.
11. Hethcote, H. W. (1989) Three basic epidemiological models. Applied Mathematical Ecology (L. Gross, T. G. Hallam, and S. A. Levin eds). New York: Springer, pp. 119-144.
12. Kuznetsov, Y. A. & Piccardi, C. (1994) Bifurcation analysis of periodic SEIR and SIR epidemic models. J. Math. Biol., 32, 109-121.
13. Ma, J. & Ma, Z. (2006) Epidemics threshold conditions for seasonally forced SEIR models. Math. Biosci. Eng., 3, 161-172.
14. Moneim, I. A. & Greenhalgh, D. (2005a) Threshold and stability results for an SIRS epidemic model with a general periodic vaccination strategy. J. Biol. Syst., 13, 131-150.
15. Moneim, I. A. & Greenhalgh, D. (2005b) Use of a periodic vaccination strategy to control the spread of epidemics with seasonally varying contact rate. Math. Biosci. Eng., 13, 591-611.
16. Schenzle, D. (1984) An age-structured model of pre-and post-vaccination measles transmission. IMA J. Math. Appl. Med. Biol., 1, 169-191.
17. Schwartz, I. B. (1985) Multiple recurrent outbreaks and predictability in seasonally forced nonlinear epidemic models. J. Math. Biol., 21, 347-361.
18. Schwartz, I. B. (1992) Small amplitude, long period outbreaks in seasonally driven epidemics. J. Math. Biol., 30, 473-491.
19. Schwartz, I. B. & Smith, H. L. (1983) Infinite subharmonic bifurcations in an SEIR model. J. Math. Biol., 18, 233-253.
20. Thieme, H. R. (1993) Persistence under relaxed point-dissapitivity (with application to an endemic model). SIAM J. Math. Anal., 24, 407-435.