Qualitative Behavior of Numerical Solutions to an S-I-S Epidemic Model

Numerical Methods for Partial Differential Equations

Volumn 14, Issue 3, 1998, Pages 317-337

  Kim, Mi Young ^a  

^a Yonsei University   (South Korea)

Author keywords

Asymptotic behavior; Finite difference; Method of characteristics; Periodic solution; s i s epidemic model

Indexed keywords

EID: 0345787252     PISSN: 0749159X     EISSN: None     Source Type: Journal    
DOI: 10.1002/(sici)1098-2426(199805)14:3<317::aid-num3>3.0.co;2-p     Document Type: Article

References (16)

1. S. Busenberg, K. Cooke, and M. Iannelli, "Endemic thresholds and stability in a class of age-structured epidemics," SIAM J. Appl. Math. 48, 1379-1395 (1988).
2. S. Busenberg, M. Iannelli, and H. Thieme, "Global behavior of an age-structured epidemic model," SIAM J. Math. Anal. 22, 1065-1080 (1991).
3. S. Busenberg, M. Iannelli, and H. Thieme, "Dynamics of an age-structured epidemic model, dynamical systems," vol. 4, Nankai Series in Pure, Applied Mathematics and Theoretical Physics, Vol. 4, S.-T. Liao, T.-R. Ding, Y.-Q. Ye, Eds., World Scientific, 1993.
4. M. Langlais, "A mathematical analysis of the SIS intracohort model with age-structure," in Mathematical Population Dynamics: Analysis of Heterogeneity, Theory of Epidemics, O. Arino, D. Axelrod, M. Kimmel, and M. Langlais, Eds., vol. I, 1995, pp. 103-117.
5. M. Langlais, "Global behavior in age structured SIS models with seasonal periodicities and vertical transmission," preprint.
6. M. Iannelli, F. Milner, and A. Pugliese, "Analytical and numerical results for the age structured SIS epidemic model with mixed inter-intracohort transmission," SIAM J. Math. Anal. 23, 662-688 (1992).
7. T. Lafaye and M. Langlais, "Threshold methods for threshold models in age dependent population dynamics and epidemiology," Calcolo 29, 49-79 (1992).
8. M. Iannelli, M.-Y. Kim, and E.-J. Park, "Splitting methods for the numerical approximation of some models of age-structured population dynamics and epidemiology," Appl. Math. Comput. 87, 69-93 (1997).
9. M.-Y. Kim and E.-J. Park, "An upwind scheme for a nonlinear model in age structured population dynamics," Comput. Math. Appl. 30, 5-17 (1995).
10. M. Iannelli, M.-Y. Kim, and E.-J. Park, "Asymptotic behavior for an SIS epidemic model and its approximation," Nonlinear Anal., to appear.
11. M. Gurtin and R. C. MacCamy, "Non-linear age-dependent population dynamics," Archs Ration. Mech. Analysis 54, 281-300 (1974).
12. G. F. Webb, Theory of Nonlinear Age-Dependent Population Dynamics, Marcel Dekker, New York, 1985.
13. F. Hoppensteadt, "Mathematical theories of populations: demographics, genetics, and epidemics," SIAM Ref. Conference in Applied Math., Philadelphia, 1975.
14. S. Busenberg and K. Cooke, "Vertically transmitted diseases, models and dynamics," Biomathematics, Vol. 23, Springer-Verlag, Berlin-Heidelberg-New York, 1993.
15. M. Iannelli, M.-Y. Kim, E.-J. Park, and A. Pugliese, "Global boundedness of the discrete solution to the Gurtin-MacCamy system," preprint.
16. M.-Y. Kim and E.-J. Park, "Long-time behavior of numerical solutions to Gurtin-MacCamy equations by method of characteristics," preprint.