A delayed SIR epidemic model with saturation incidence and a constant infectious period

Journal of Applied Mathematics and Computing

Volumn 35, Issue 1-2, 2011, Pages 229-250

  Xu, Rui ^a   Du, Yanke ^a  

^a INSTITUTE OF APPLIED MATHEMATICS   (China)

Author keywords

Infectious period; Permanence; Saturation incidence; SIR epidemic model; Stability; Time delay

Indexed keywords

BASIC REPRODUCTION NUMBER; CHARACTERISTIC EQUATION; DISEASE-FREE EQUILIBRIUM; ENDEMIC EQUILIBRIUM; EXPLICIT FORMULA; GLOBAL ATTRACTIVENESS; GLOBALLY ASYMPTOTICALLY STABLE; INFECTIOUS PERIOD; ITERATION TECHNIQUES; LOCAL STABILITY; LOWER BOUNDS; NUMERICAL SIMULATION; PERMANENCE; SATURATION INCIDENCE; SIR EPIDEMIC MODEL; SUFFICIENT CONDITIONS;

POPULATION STATISTICS; TIME DELAY;

DISEASE CONTROL;

EID: 78651371641     PISSN: 15985865     EISSN: None     Source Type: Journal    
DOI: 10.1007/s12190-009-0353-3     Document Type: Article

References (18)

1. E. Beretta T. Hara W. Ma Y. Takeuchi 2001 Global asymptotic stability of an SIR epidemic model with distributed time delay Nonlinear Anal. 47 4107 4115 1042.34585 10.1016/S0362-546X(01)00528-4 1972351
2. E. Beretta Y. Kuang 2002 Geometric stability switch criteria in delay differential systems with delay dependent parameters SIAM J. Math. Anal. 33 1144 1165 1013.92034 10.1137/S0036141000376086 1897706
3. E. Beretta Y. Takeuchi 1995 Global stability of an SIR epidemic model with time delays J. Math. Biol. 33 250 260 0811.92019 10.1007/BF00169563 1331508
4. E. Beretta Y. Takeuchi 1997 Convergence results in SIR epidemic model with varying population sizes Nonlinear Anal. 28 1909 1921 0879.34054 10.1016/S0362-546X(96)00035-1 1436361
5. V. Capasso G. Serio 1978 A generalization of the Kermack-Mckendrick deterministic epidemic model Math. Biosci. 42 41 61 10.1016/0025-5564(78)90006-8 529097
6. S. Gakkhar K. Negi 2008 Pulse vaccination in SIRS epidemic model with non-monotonic incidence rate Chaos Solitons Fractals 35 626 638 1131.92052 10.1016/j.chaos.2006.05.054 2359846
7. S. Gao Z. Teng D. Xie 2009 Analysis of a delayed SIR epidemic model with pulse vaccination Chaos Solitons Fractals 40 1004 1011 1197.34123 10.1016/j.chaos.2007.08.056 2527842
8. S. Gao D. Xie L. Chen 2007 Pulse vaccination strategy in a delayed SIR epidemic model with vertical transmission Discrete Contin. Dyn. Syst. Ser. B 7 77 86 1191.34062 2257452
9. Hale, J.: Theory of Functional Differential Equations. Springer, Heidelberg (1977)
10. J. Hui L. Chen 2004 Impulsive vaccination of SIR epidemic models with nonlinear incidence rates Discrete Contin. Dyn. Syst. Ser. B 4 595 605 1100.92040 10.3934/dcdsb.2004.4.595 2073963
11. Y. Jin W. Wang S. Xiao 2007 An SIRS model with a nonlinear incidence rate Chaos Solitons Fractals 34 1482 1497 1152.34339 10.1016/j.chaos.2006.04.022 2335398
12. J. Liu Y. Zhou 2009 Global stability of an SIRS epidemic model with transport-related infection Chaos Solitons Fractals 40 145 158 1197.34098 10.1016/j.chaos.2007.07.047 2517923
13. W. Ma M. Song Y. Takeuchi 2004 Global stability of an SIR epidemic model with time delay Appl. Math. Lett. 17 1141 1145 1071.34082 10.1016/j.aml.2003.11. 005 2091848
14. W. Ma Y. Takeuchi T. Hara E. Beretta 2002 Permanence of an SIR epidemic model with distributed time delays Tohoku Math. J. 54 581 591 1014.92033 10.2748/tmj/1113247650 1936269
15. G. Pang L. Chen 2007 A delayed SIRS epidemic model with pulse vaccination Chaos Solitons Fractals 34 1629 1635 1152.34379 10.1016/j.chaos.2006.04.061 2335410
16. B. Shulgin L. Stone Z. Agur 1998 Pulse vaccination strategy in the SIR epidemic model Bull. Math. Biol. 60 1123 1148 0941.92026 10.1016/S0092-8240(98) 90005-2
17. L. Stone B. Shulgin Z. Agur 2000 Theoretical examination of the pulse vaccination policy in the SIR epidemic model Math. Comput. Modell. 31 207 215 1043.92527 10.1016/S0895-7177(00)00040-6 1756756
18. Y. Takeuchi W. Ma E. Beretta 2000 Global asymptotic properties of a SIR epidemic model with nite incubation time Nonlinear Anal. 42 931 947 0967.34070 10.1016/S0362-546X(99)00138-8 1780445