Reproduction numbers and the expanding fronts for a diffusion–advection SIS model in heterogeneous time-periodic environment

Nonlinear Analysis: Real World Applications

Volumn 33, Issue , 2017, Pages 100-120

  Ge, Jing ^a,c   Lei, Chengxia ^b   Lin, Zhigui ^c  

^a HUAIYIN NORMAL UNIVERSITY   (China)

^b UNIVERSITY OF SCIENCE AND TECHNOLOGY OF CHINA   (China)

^c YANGZHOU UNIVERSITY   (China)

Author keywords

Advection; Basic reproduction number; Environmental heterogeneity; Reaction diffusion systems; Time periodic

Indexed keywords

DIFFUSION;

BASIC REPRODUCTION NUMBER; DIFFUSION SYSTEMS; ENVIRONMENTAL HETEROGENEITY; HETEROGENEOUS ENVIRONMENTS; PERIODIC ENVIRONMENT; REPRODUCTION NUMBERS; SPATIAL HETEROGENEITY; TIME-PERIODIC;

ADVECTION;

EID: 84978062912     PISSN: 14681218     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.nonrwa.2016.06.005     Document Type: Article

References (30)

1. [1] Allen, L.J.S., Bolker, B.M., Lou, Y., Nevai, A.L., Asymptotic profiles of the steady states for an SIS epidemic reaction–diffusion model. Discrete Contin. Dyn. Syst. Ser. A 21 (2008), 1–20.
2. [2] Peng, R., Asymptotic profile of the positive steady state for an SIS epidemic reaction–diffusion model, I. J. Differential Equations 247 (2009), 1096–1119.
3. [3] Peng, R., Yi, F.Q., Asymptotic profile of the positive steady state for an SIS epidemic reaction–diffusion model: effects of epidemic risk and population movement. Physica D 259 (2013), 8–25.
4. [4] Peng, R., Zhao, X.Q., A reaction–diffusion SIS epidemic model in a time-periodic environment. Nonlinearity 25 (2012), 1451–1471.
5. [5] Du, Y.H., Lin, Z.G., Spreading–vanishing dichotomy in the diffusive logistic model with a free boundary. SIAM J. Math. Anal. 42 (2010), 377–405 SIAM J. Math. Anal. 45 (2013), 1995–1996 Erratum.
6. [6] Du, Y.H., Lou, B.D., Spreading and vanishing in nonlinear diffusion problems with free boundaries. J. Eur. Math. Soc. 17 (2015), 2673–2724.
7. [7] Du, Y.H., Guo, Z.M., Spreading–vanishing dichotomy in a diffusive logistic model with a free boundary, II. J. Differential Equations 250 (2011), 4336–4366.
8. [8] Gu, H., Lin, Z.G., Lou, B.D., Long time behavior of solutions of a diffusion–advection logistic model with free boundaries. Appl. Math. Lett. 37 (2014), 49–53.
9. [9] Wu, C.H., The minimal habitat size for spreading in a weak competition system with two free boundaries. J. Differential Equations 259 (2015), 873–897.
10. [10] Du, Y.H., Guo, Z.M., Peng, R., A diffusive logistic model with a free boundary in time-periodic environment. J. Funct. Anal. 265 (2013), 2089–2142.
11. [11] Lei, C.X., Lin, Z.G., Zhang, Q.Y., The spreading front of invasive species in favorable habitat or unfavorable habitat. J. Differential Equations 257 (2014), 145–166.
12. [12] Peng, R., Zhao, X.Q., The diffusive logistic model with a free boundary and seasonal succession. Discrete Contin. Dyn. Syst. 33 (2013), 2007–2031.
13. [13] Wang, M.X., The diffusive logistic equation with a free boundary and sign-changing coefficient. J. Differential Equations 258 (2015), 1252–1266.
14. [14] Wang, M.X., A diffusive logistic equation with a free boundary and sign-changing coefficient in time-periodic environment. J. Funct. Anal. 270 (2016), 483–508.
15. [15] Zhou, P., Xiao, D.M., The diffusive logistic model with a free boundary in heterogeneous environment. J. Differential Equations 256 (2014), 1927–1954.
16. [16] Ahn, I., Baek, S., Lin, Z.G., The spreading fronts of an infective environment in a man-environment-man epidemic model. Appl. Math. Model. 40 (2016), 7082–7101.
17. [17] Ge, J., Kim, K.I., Lin, Z.G., Zhu, H.P., A SIS reaction–diffusion–advection model in a low-risk and high-risk domain. J. Differential Equations 259 (2015), 5486–5509.
18. [18] Gu, H., Lou, B.D., Zhou, M.L., Long time behavior of solutions of Fisher–KPP equation with advection and free boundaries. J. Funct. Anal. 269 (2015), 1714–1768.
19. [19] Kaneko, Y., Matsuzawa, H., Spreading speed and sharp asymptotic profiles of solutions in free boundary problems for nonlinear advection-diffusion equations. J. Math. Anal. Appl. 428 (2015), 43–76.
20. [20] Li, M., Lin, Z.G., The spreading fronts in a mutualistic model with advection. Discrete Contin. Dyn. Syst. B 20 (2015), 2089–2105.
21. [21] Y.G. Zhao, M.X. Wang, A reaction–diffusion–advection equation with mixed and free boundary conditions, arXiv:1504.00998.
22. [22] Lin, Z.G., A free boundary problem for a predator–prey model. Nonlinearity 20 (2007), 1883–1892.
23. [23] Mimura, M., Yamada, Y., Yotsutani, S., A free boundary problem in ecology. Japan J. Appl. Math. 2 (1985), 151–186.
24. [24] Mimura, M., Yamada, Y., Yotsutani, S., Free boundary problems for some reaction–diffusion equations. Hiroshima Math. J. 17 (1987), 241–280.
25. [25] Chen, Q.L., Li, F.Q., Wang, F., The diffusive competition problem with a free boundary in heterogeneous time-periodic environment. J. Math. Anal. Appl. 433 (2016), 1594–1613.
26. [26] Hess, P., Periodic–parabolic boundary value problems and positivity. Pitman Research Notes in Mathematics, Vol. 247, 1991, Longman Sci. Tech, Harlow.
27. N. Discrete Contin. Dyn. Syst. 32 (2012), 619–641.
28. [28] Razvan, S., Gabriel, D., Numerical approximation of a free boundary problem for a predator–prey model. Numerical Analysis and its Applications, 2008, Springer Berlin, Heidelberg, 548–555.
29. [29] Iwami, S., Takeuchi, Y., Liu, X., Avian-human influenza epidemic model. Math. Biosci. 207 (2007), 1–25.
30. [30] Shan, C.H., Zhu, H.P., Bifurcations and complex dynamics of an SIR model with the impact of the number of hospital beds. J. Differential Equations 257 (2014), 1662–1688.