Modeling disease spread via transport-related infection by a delay differential equation

Rocky Mountain Journal of Mathematics

Volumn 38, Issue 5, 2008, Pages 1525-1540

  Liu, Junli ^a   Wu, Jianhong ^a,b   Zhou, Yicang ^a  

^a XI'AN JIAOTONG UNIVERSITY   (China)

^b YORK UNIVERSITY   (Canada)

Author keywords

Delay; Permanence; Stability; Transport related infection

Indexed keywords

EID: 58049186148     PISSN: 00357596     EISSN: None     Source Type: Journal    
DOI: 10.1216/RMJ-2008-38-5-1525     Document Type: Conference Paper

References (16)

1. J. Arino and P. Van den Driessche, A multi-city epidemic model, Math. Population Stud. 10 (2003), 175-193.
2. J. Cui, Y. Takeuchi and Y. Saito, Spreading disease with transport-related infection, J. Theoret. Biol. 239 (2006), 376-390.
3. O. Diekmann, S.A. Van Gils, S.M. Verduyn Lunel and H.O. Walther, Delay equations, Functional-, Complex-, and Nonlinear Analysis, Springer, New York, 1995.
4. J.K. Hale and P. Waltman, Persistence in infinite-dimensional systems, SIAM J. Math. Anal. 20 (1998), 388-395.
5. X. Liu and Y. Takeuchi, Spread of disease with transport-related infection and entry screening, J. Theoret. Biol. 242 (2006), 517-528.
6. I. Longini, A mathematical model for predicting the geographic spread of new infectious agents, Math. Biosci. 90 (1988), 367-383.
7. L. Rvachev and I. Longini, A mathematical model for the global spread of influenza, Math. Biosci. 75 (1985), 3-22.
8. L. Sattenspiel and K. Dietz, Structured epidemic models incorporating geographic mobility among regions, Math. Biosci. 128 (1995), 71-91.
9. L. Sattenspiel and D.A. Herring, Structured epidemic models and the spread of influenza in the central Canada subarctic, Human Biol. 70 (1998), 91-115.
10. -, Simulating the effect of quarantine on the spread of the 1918-1919 flu in central Canada, Bull. Math. Biol. 65 (2003), 1-26.
11. H.L. Smith, Monotone dynamical systems, An introduction to the theory of competitive and cooperative systems, American Mathematical Society, Providence, RI, 1995.
12. Y. Takeuchi, X. Liu and J. Cui, Global dynamics of SIS models with transportrelated infection, J. Math. Anal. Appl. 329 (2007), 1460-1471.
13. W. Wang and G. Mulone, Threshold of disease transmission in a patch environment, J. Math. Anal. Appl. 285 (2003) 321-335.
14. W. Wang and S. Ruan, Simulating the SARS outbreak in Beijing with limited data, J. Theoret. Biol. 227 (2004), 369-379.
15. W. Wang and X.-Q Zhao, An epidemic model in a patchy environment, Math. Biosci. 190 (2004), 97-112.
16. -, An age-structured epidemic model in a patchy environment, SIAM J. Appl. Math. 65 (2005), 1597-1614.