Global dynamics of SIS models with transport-related infection

Journal of Mathematical Analysis and Applications

Volumn 329, Issue 2, 2007, Pages 1460-1471

  Takeuchi, Yasuhiro ^a   Liu, Xianning ^b   Cui, Jingan ^c  

^a SHIZUOKA UNIVERSITY   (Japan)

^b SOUTHWEST UNIVERSITY   (China)

^c NANJING NORMAL UNIVERSITY   (China)

Author keywords

Basic reproduction number; Permanence; Stability; Transport related infection

Indexed keywords

EID: 33846578358     PISSN: 0022247X     EISSN: 10960813     Source Type: Journal    
DOI: 10.1016/j.jmaa.2006.07.057     Document Type: Article

References (17)

1. Arino J., and van den Driessche P. A multi-city epidemic model. Math. Popul. Stud. 10 (2003) 175-193
2. Castillo-Chavez C., and Thieme H.R. Asymptotically autonomous epidemic models. In: Arino O., et al. (Ed). Mathematical Population Dynamics: Analysis of Heterogeneity, I. Theory of Epidemics (1995), Wuerz, Canada 33-50
3. Cliff A., Haggett P., and Smallman-Raynor M. Measles: An Historical Geography of a Major Human Viral Disease (1993), Blackwell Reference, Oxford
4. Cui J., Takeuchi Y., and Saito Y. Spreading disease with transport-related infection. J. Theoret. Biol. 239 (2006) 376-390
5. Fulford G.R., Roberts M.G., and Heesterbeek J.A.P. The metapopulation dynamics of an infectious disease: Tuberculosis in possums. Theor. Popul. Biol. 61 (2002) 15-29
6. Leenheer P.D., and Smith H.L. Virus dynamics: A global analysis. SIAM J. Appl. Math. 63 (2003) 1313-1327
7. Liu X., and Takeuchi Y. Spread of disease with transport-related infection and entry screening. J. Theoret. Biol. 242 (2006) 517-528
8. Longini I. A mathematical model for predicting the geographic spread of new infectious agents. Math. Biosci. 90 (1988) 367-383
9. Rvachev L., and Longini I. A mathematical model for the global spread of influenza. Math. Biosci. 75 (1985) 3-22
10. Sattenspiel L., and Dietz K. A structured epidemic model incorporating geographic mobility among regions. Math. Biosci. 128 (1995) 71-91
11. Sattenspiel L., and Herring D.A. Structured epidemic models and the spread of influenza in the central Canada subarctic. Human Biol. 70 (1998) 91-115
12. Sattenspiel L., and Herring D.A. Simulating the effect of quarantine on the spread of the 1918-19 flu in central Canada. Bull. Math. Biol. 65 (2003) 1-26
13. Smith H.L., and Waltman P. The Theory of the Chemostat (1995), Cambridge Univ. Press, Cambridge
14. Thieme H.R. Persistence under relaxed point-dissipativity (with application to an endemic model). SIAM J. Math. Anal. 24 (1993) 407-435
15. Wang W., and Mulone G. Threshold of disease transmission in a patch environment. J. Math. Anal. Appl. 285 (2003) 321-335
16. Wang W., and Zhao X.-Q. An epidemic model in a patchy environment. Math. Biosci. 190 (2004) 97-112
17. Wang W., and Zhao X.-Q. An age-structured epidemic model in a patchy environment. SIAM J. Appl. Math. 65 (2005) 1597-1614