Export file:

Format

  • RIS(for EndNote,Reference Manager,ProCite)
  • BibTex
  • Text

Content

  • Citation Only
  • Citation and Abstract

Dynamics of a reaction-diffusion SIRI model with relapse and free boundary

1 School of Mathematics and Information Sciences, Guangzhou University, Guangzhou, 510006, China
2 Department of Mathematics, Wilfrid Laurier University, Waterloo, Ontario, N2L 3C5, Canada

Special Issues: Spatial dynamics for epidemic models with dispersal of organisms and heterogenity of environment

This paper is concerned with the free boundary problem for a reaction-diffusion SIRI model with relapse and bilinear incidence rate. After studying the (global) existence and uniqueness of solutions, we provide some sufficient conditions on the disease spreading-vanishing dichotomies for both cases with and without relapse.
  Figure/Table
  Supplementary
  Article Metrics

References

1. D. Tudor, A deterministic model for herpes infections in human and animal populations, SIAM Rev., 32 (1990), 136-139.

2. H. Moreira, Y. Wang, Global stability in a SIRI model, SIAM Rev., 39 (1997), 497-502.

3. C. Vargas-De-León, On the global stability of infectious diseases models with relapse, Abstraction Application, 9 (2013), 50-61.

4. P. van den Driessche, X. Zou, Modeling relapse in infectious diseases, Math. Biosci., 207 (2007), 89-103.

5. S. Liu, S. Wang, L. Wang, Global dynamics of delay epidemic models with nonlinear incidence rate and relapse, Nonlinear Anal. Real World Appl., 12 (2011), 119-127.

6. P. Georgescu, A Lyapunov functional for an SIRI model with nonlinear incidence of infection and relapse, Appl. Math. Comput., 219 (2013), 8496-8507.

7. Z. Lin, A free boundary problem for a predator-prey model, Nonlinearity, 20 (2007), 1883-1892.

8. L. Rubinstein, The Stefan Problem, American Mathematical Society, Providence, RI, 1971.

9. J. Crank, Free and Moving Boundary Problem, Clarendon Press, Oxford, 1984.

10. X. Chen, A. Friedman, A free boundary problem arising in a model of wound healing, SIAM J. Math. Anal., 32 (2000), 778-800.

11. L. Caffarelli, S. Salsa, A Geometric Approach to Free Boundary Problems, Grad. Stud. Math. 68, American Mathematical Society, Providence, RI, 2005.

12. K. Kim, Z. Lin, Q. Zhang, An SIR epidemic model with free boundary, Nonlinear Anal. Real World Appl., 14 (2013), 1992-2001.

13. Y. Du, Z. Lin, Spreading-vanishing dichotomy in the diffusive logistic model with a free boundary, SIAM J. Math. Anal., 42 (2010), 377-405.

14. O. A. Ladyženskaja, V. A. Solonnikov, N. N. Ural'0ceva, Linear and Quasi-linear Equations of Parabolic Type, American Mathematical Society, Providence, RI, 1968.

15. J. F. Cao, W. T. Li, J. Wang, F. Y. Yang, A free boundary problem of a diffusive SIRS model with nonlinear incidence, Z. Angew. Math. Phys., 68 (2017), 39.

16. R. S. Cantrell, C. Cosner, Spatial ecology via reaction-diffusion equations. Wiley Series in Mathematical and Computational Biology. John Wiley & Sons, Ltd., Chichester, 2003.

17. J. P. LaSalle, S. Lefschetz, Stability by Liapunov's Direct Method with Applications, Academic Press, New York, 1961.

© 2020 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution Licese (http://creativecommons.org/licenses/by/4.0)

Download full text in PDF

Export Citation

Article outline

Show full outline
Copyright © AIMS Press All Rights Reserved