Analysis of the permanence of an SIR epidemic model with logistic process and distributed time delay

Communications in Nonlinear Science and Numerical Simulation

Volumn 17, Issue 9, 2012, Pages 3696-3707

  Li, Chun Hsien ^a   Tsai, Chiung Chiou ^b   Yang, Suh Yuh ^c  

^a NATIONAL KAOHSIUNG NORMAL UNIVERSITY   (Taiwan)

^b TAOYUAN INNOVATION INSTITUTE OF TECHNOLOGY   (Taiwan)

^c NATIONAL CENTRAL UNIVERSITY   (Taiwan)

Author keywords

Asymptotic stability; Permanence; SIR epidemic model; Time delay

Indexed keywords

ASYMPTOTIC STABILITY; DELAY CONTROL SYSTEMS; EPIDEMIOLOGY; TIMING CIRCUITS;

ATTRACTIVITY; CONDITION; DISEASE-FREE EQUILIBRIUM; DISTRIBUTED TIME DELAYS; ENDEMIC EQUILIBRIUM; LOGISTICS PROCESS; PERMANENCE; PROCESS TIME; SIR EPIDEMIC MODEL; TIME-DELAYS;

TIME DELAY;

EID: 84862783309     PISSN: 10075704     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.cnsns.2012.01.018     Document Type: Article

References (22)

1. Beretta E., Hara T., Ma W., Takeuchi Y. Global asymptotic stability of an SIR epidemic model with distributed time delay. Nonlinear Anal Theory Methods Appl 2001, 47:4107-4115.
2. Beretta E., Takeuchi Y. Global stability of an SIR epidemic model with time delays. J Math Biol 1995, 33:250-260.
3. Beretta E., Takeuchi Y. Convergence results in SIR epidemic models with varying population sizes. Nonlinear Anal Theory Methods Appl 1997, 28:1909-1921.
4. Buonomo B., d'Onofrio A., Lacitignola D. Global stability of an SIR epidemic model with information dependent vaccination. Math Biosci 2008, 216:9-16.
5. Hale J.K., Lunel S.M. Introduction to Functional Differential Equations 1993, Springer-Verlag, New York.
6. Huo H.-F., Ma Z.-P. Dynamics of a delayed epidemic model with non-monotonic incidence rate. Commun Nonlinear Sci Numer Simul 2010, 15:459-468.
7. Jin Z., Ma Z. The stability of an SIR epidemic model with time delays. Math Biosci Eng 2006, 3:101-109.
8. Kuang Y. Delay Differential Equations with Applications in Population Dynamics 1993, Academic Press, San Diego.
9. Li C.-H., Tsai C.-C., Yang S.-Y. Permanence of an SIR epidemic model with density dependent birth rate and distributed time delay. Appl Math Comput 2011, 218:1682-1693.
10. Li M.Y., Graef J.R., Wang L., Karsai J. Global dynamics of an SEIR model with varying total population size. Math Biosci 1999, 160:191-213.
11. Li M.Y., Smith H.L., Wang L. Global dynamics of an SEIR epidemic model with vertical transmission. SIAM J Appl Math 2001, 62:58-69.
12. Liu J., Zhou Y. Global stability of an SIRS epidemic model with transport-related infection. Chaos Solitons Fract 2009, 40:145-158.
13. McCluskey C.C. Complete global stability for an SIR epidemic model with delay - distributed or discrete. Nonlinear Anal RWA 2010, 11:55-59.
14. Ma W., Song M., Takeuchi Y. Global stability of an SIR epidemic model with time delay. Appl Math Lett 2004, 17:1141-1145.
15. Ma W., Takeuchi Y., Hara T., Beretta E. Permanence of an SIR epidemic model with distributed time delays. Tohoku Math J 2002, 54:581-591.
16. Song M., Ma W. Asymptotic properties of a revised SIR epidemic model with density dependent birth rate and time delay, Dynamics of Continuous. Discrete Impulsive Syst 2006, 13A:199-208.
17. Song M., Ma W., Takeuchi Y. Permanence of a delayed SIR epidemic model with density dependent birth rate. J Comp Appl Math 2007, 201:389-394.
18. Takeuchi Y., Ma W., Beretta E. Global asymptotic properties of a delay SIR epidemic model with finite incubation times. Nonlinear Anal Theory Methods Appl 2000, 42:931-947.
19. Wen L., Yang X. Global stability of a delayed SIRS model with temporary immunity. Chaos Solitons Fract 2008, 38:221-226.
20. Xu R., Ma Z. Stability of a delayed SIRS epidemic model with a nonlinear incidence rate. Chaos Soliton Fract 2009, 41:2319-2325.
21. N. Yoshida and T. Hara, Permanence of a delayed SIR epidemic model with logistic process, Kyoto Univ. RIMS Kokyuroku 1372 (2004) 17-23.
22. Yoshida N., Hara T. Global stability of a delayed SIR epidemic model with density dependent birth and death rates. J Comp Appl Math 2007, 201:339-347.