Permanence of an SIR epidemic model with density dependent birth rate and distributed time delay

Applied Mathematics and Computation

Volumn 218, Issue 5, 2011, Pages 1682-1693

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

^a NATIONAL CENTRAL UNIVERSITY   (Taiwan)

^b NANYA INSTITUTE OF TECHNOLOGY   (Taiwan)

Author keywords

Asymptotic stability; Permanence; SIR epidemic model; Time delay

Indexed keywords

ANALOG SYSTEMS; ATTRACTIVITY; BIRTH RATES; DENSITY-DEPENDENT; DISCRETE TIME DELAY; DISEASE-FREE EQUILIBRIUM; DISTRIBUTED TIME DELAYS; ENDEMIC EQUILIBRIUM; NUMERICAL EXAMPLE; PERMANENCE; SIR EPIDEMIC MODEL;

ASYMPTOTIC STABILITY; NUMERICAL ANALYSIS; POPULATION STATISTICS; TIME DELAY;

EPIDEMIOLOGY;

EID: 80052267560     PISSN: 00963003     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.amc.2011.06.047     Document Type: Article

References (16)

1. E. Beretta, T. Hara, W. Ma, and Y. Takeuchi Global asymptotic stability of an SIR epidemic model with distributed time delay Nonlinear Anal.-Theory Methods Appl. 47 2001 4107 4115 (Pubitemid 32724581)
2. E. Beretta, and Y. Takeuchi Global stability of an SIR epidemic model with time delays J. Math. Biol. 33 1995 250 260
3. E. Beretta, and Y. Takeuchi Convergence results in SIR epidemic models with varying population sizes Nonlinear Anal.-Theory Methods Appl. 28 1997 1909 1921 (Pubitemid 127417735)
4. B. Buonomo, A. d'Onofrio, and D. Lacitignola Global stability of an SIR epidemic model with information dependent vaccination Math. Biosci. 216 2008 9 16
5. J.K. Hale, and S.M. Lunel Introduction to Functional Differential Equations 1993 Springer-Verlag New York
6. Y. Kuang Delay Differential Equations with Applications in Population Dynamics 1993 Academic Press San Diego
7. M.Y. Li, H.L. Smith, and L. Wang Global dynamics of an SEIR epidemic model with vertical transmission SIAM J. Appl. Math. 62 2001 58 69 (Pubitemid 33779898)
8. W. Ma, M. Song, and Y. Takeuchi Global stability of an SIR epidemic model with time delay Appl. Math. Lett. 17 2004 1141 1145
9. W. Ma, Y. Takeuchi, T. Hara, and E. Beretta Permanence of an SIR epidemic model with distributed time delays Tohoku Math. J. 54 2002 581 591 (Pubitemid 36177504)
10. M. Song, and W. Ma Asymptotic properties of a revised SIR epidemic model with density dependent birth rate and time delay Dyn. Contin. Discret. I 13A 2006 199 208 (Pubitemid 44965433)
11. M. Song, W. Ma, and Y. Takeuchi Permanence of a delayed SIR epidemic model with density dependent birth rate J. Comput. Appl. Math. 201 2007 389 394 (Pubitemid 46176492)
12. Y. Takeuchi, W. Ma, and E. Beretta Global asymptotic properties of a delay SIR epidemic model with finite incubation times Nonlinear Anal.-Theory Methods Appl. 42 2000 931 947
13. L. Wen, and X. Yang Global stability of a delayed SIRS model with temporary immunity Chaos Solitons Fract. 38 2008 221 226 (Pubitemid 351503988)
14. R. Xu, and Z. Ma Stability of a delayed SIRS epidemic model with a nonlinear incidence rate Chaos Soliton Fract. 41 2009 2319 2325
15. N. Yoshida, and T. Hara Permanence of a delayed SIR epidemic model with logistic process Kyoto Univ. RIMS Kokyuroku 1372 2004 17 23
16. N. Yoshida, and T. Hara Global stability of a delayed SIR epidemic model with density dependent birth and death rates J. Comput. Appl. Math. 201 2007 339 347 (Pubitemid 46176486)