JOURNAL BROWSE
Search
Advanced SearchSearch Tips
A GENERAL UNIQUENESS RESULT OF AN ENDEMIC STATE FOR AN EPIDEMIC MODEL WITH EXTERNAL FORCE OF INFECTION
facebook(new window)  Pirnt(new window) E-mail(new window) Excel Download
 Title & Authors
A GENERAL UNIQUENESS RESULT OF AN ENDEMIC STATE FOR AN EPIDEMIC MODEL WITH EXTERNAL FORCE OF INFECTION
Cha, Young-Joon;
  PDF(new window)
 Abstract
We present a general uniqueness result of an endemic state for an S-I-R model with external force of infection. We reduce the problem of finding non-trivial steady state solutions to that of finding zeros of a real function of one variable so that we can easily prove the uniqueness of an endemic state. We introduce an assumption which was usually used to show stability of a non-trivial steady state. It turns out that such an assumption adopted from a stability analysis is crucial for proving the uniqueness as well, and the assumption holds for almost all cases in our model.
 Keywords
endemic;S-I-R;uniqueness;inter-cohort;external force;
 Language
English
 Cited by
 References
1.
V. Andreassen, Instability in an SIR-model with age-dependent susceptibility, Mathematical Population Dynamics: Analysis of Heterogeneity, vol. 1, Theory of Epidemics, Proc. 3rd International Conference on Mathematical Population Dynamics, Pau, France, 1992, Wuerz Publishing Ltd., Winnipeg, Canada, 1995, 3-14

2.
S. Busenberg, K. Cooke, and M. Iannelli, Endemic thresholds and stability in a class of age-structured epidemics, SIAM J. Appl. Math. 48 (1988), 1379-1395 crossref(new window)

3.
S. Busenberg, M. Iannelli, and H. Thieme, Dynamics of an age-structured epidemic model, Dynamical Systems, S.-T. Liao, T.-R. Ding, and Y.-Q. Ye (Eds.), Nankai Series in Pure, Applied Mathematics, and Theoretical Physics, vol. 4, World Scientific, 1993

4.
Y. Cha, Existence and uniqueness of endemic states for an epidemic model with external force of infection, Commun. Korean Math. Soc. 17 (2002), no. 1, 175-187 crossref(new window)

5.
Y. Cha, Local stability of endemic states for an epidemic model with external force of infection, Commun. Korean Math. Soc. 18 (2003), no. 1, 133-149 crossref(new window)

6.
Y. Cha and F. A. Milner, A uniqueness result of an endemic state for an S-I-R epidemic model, submitted to a journal

7.
Y. Cha, M. Iannelli, and F. A. Milner, Existence and uniqueness of endemic states for the age structured S-I-R model, Math. Biosc. 150 (1998), 177-190 crossref(new window)

8.
Y. Cha, Stability change of an epidemic model, Dynamic Systems and Applications 9 (2000), 361-376

9.
K. Dietz and D. Schenzle, Proportionate mixing models for age-dependent infection transmission, J. Math. BioI. 22 (1985), 117-120 crossref(new window)

10.
El Doma, Analysis of nonlinear integro-differential equations arising in age dependent epidemic models, Nonl. Anal. T. M. A. 11 (1987), 913-937 crossref(new window)

11.
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 crossref(new window)

12.
H. Inaba, Threshold and stability results for an age-structured epidemic model, J. Math. BioI. 28 (1990), 411-434 crossref(new window)

13.
A. G. McKendrick, Applications of mathematics to medical problems, Proc. Edinburgh Math. Soc. 44 (1926), 98-130 crossref(new window)

14.
H. Thieme, Stability change for the endemic equilibrium in age-structured models for the spread of S-I-R type infectious diseases, Differential Equations Models in Biology, Epidemiology and Ecology, Lectures Notes in Biomathematics, vol. 92, Springer Verlag, 1991, 139-158

15.
H. von Foerster, The Kinetics of Cellular Proliferation, Grune and Stratton, New York, 1959