STABILITY OF AN SIRS EPIDEMIC MODEL WITH A VARIABLE INCIDENCE RATE AND TIME DELAY |
Seo, Young Il
(NATIONAL FISHERIES RESEARCH AND DEVELOPMENT INSTITUTE)
Cho, Gi Phil (DEPARTMENT OF MATHEMATICS, PUSAN NATIONAL UNIVERSITY) Chae, Kyoung Sook (DEPARTMENT OF MATHEMATICS, PUSAN NATIONAL UNIVERSITY) Jung, Il Hyo (DEPARTMENT OF MATHEMATICS, PUSAN NATIONAL UNIVERSITY) |
1 | N. T. J. Bailey, The Mathematical Theory of Infectious Diseases, 2nd ed., Hafner, New York, 1975. |
2 | E. Beretta, T. Hara, W. Ma, and Y. Takeuchi, Convergence results in SIR epidemic models with varying population sizes, J. Appl. Nonlinear Anal. 28 (1997), 1909-1921. DOI ScienceOn |
3 | F. Brauer and C. Castillo-Charvez, Mathematical Models in Population Biology and Epidemiology, Springer- Verlag, New York, 2001. |
4 | W. H. Herbert, The mathematics of infectious diseases, SIAM Rev. 42 (2000), 599-653. DOI ScienceOn |
5 | W. O. Kermack and A. G. Mckendrick, Contribution to the mathematical theory of epidemics, Proc. Roy. Soc. London Ser. A 115, (1927), 700-721. DOI |
6 | W. Ma, M. Song, and Y. Takeuchi, Global stability of an SIR epidemic model with time delay, Appl. Math. Lett. 17 (2004), 1141-1145. DOI ScienceOn |
7 | G. Schneckenreither, N. Popper, G. Zauner, and F. Breitenecker, Modelling SIR-type epidemics by ODEs, PDEs, difference equations and cellular automata - A comparative study, Simulation Modelling Practice and Theory, 16 (2008), 1014-1023. DOI ScienceOn |
8 | Z. Teng and Z. Zhang, Global behavior and permanence of an SIRS epidemic model with time delays, J. Nonlinear Anal. 9 (2008), 1409-1424. DOI ScienceOn |
9 | S. Ruan and W. Wang, Dynamical behavior of an epidemic model with a nonlinear incidence rate, J. Differential Equations 188 (2003), 135-163. DOI ScienceOn |
10 | G. Zaman, K. H. Kang, and I. H. Jung, Stability analysis and optimal vaccination of an SIR epidemic model, BioSystem 93 (2008), 240-249. DOI ScienceOn |
11 | Y. Jin, W. Wang, and S. Xiao, An SIRS model with a nonlinear incidence rate, J. Chaos, Solitons and Fractals 34 (2007), 1482-1497. DOI ScienceOn |
12 | P. van den Driessche and J. Watmough, A simple SIS epidemic model with a backward bifurcation, J. Math. Biol. 40 (2000), 525-540. DOI |