Global stability of the steady states of an SIS epidemic reaction-diffusion model

Nonlinear Analysis, Theory, Methods and Applications

Volumn 71, Issue 1-2, 2009, Pages 239-247

  Peng, Rui ^a,b   Liu, Shengqiang ^c  

^a CHINA THREE GORGES UNIVERSITY   (China)

^b UNIVERSITY OF NEW ENGLAND   (Australia)

^c HARBIN INSTITUTE OF TECHNOLOGY   (China)

Author keywords

Disease free equilibrium; Endemic equilibrium; Global stability; Lyapunov functional; SIS epidemic reaction diffusion model; Spatial heterogeneity; Steady state

Indexed keywords

DISEASE-FREE EQUILIBRIUM; ENDEMIC EQUILIBRIUM; GLOBAL STABILITY; LYAPUNOV FUNCTIONAL; SIS EPIDEMIC REACTION-DIFFUSION MODEL; SPATIAL HETEROGENEITY; STEADY STATE;

DIFFUSION IN LIQUIDS; STABILITY; SWITCHING CIRCUITS; TELECOMMUNICATION NETWORKS;

SURVEYING INSTRUMENTS;

EID: 64849104334     PISSN: 0362546X     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.na.2008.10.043     Document Type: Article

References (13)

1. Allen L.J.S., Bolker B.M., Lou Y., and Nevai A.L. Asymptotic profiles of the steady states for an SIS epidemic disease patch model. SIAM, J. Appl. Math. 67 5 (2007) 1283-1309
2. Allen L.J.S., Bolker B.M., Lou Y., and Nevai A.L. Asymptotic profiles of the steady states for an SIS epidemic reaction-diffusion model. Discrete Contin. Dyn. Syst. A 21 1 (2008) 1-20
3. Cantrell R.S., and Cosner C. Spatial Ecology via Reaction-diffusion Equations. Ser. Math. Comput. Biology (2003), Wiley, Chichester, UK
4. Henry D. Geometric Theory of Semilinear Parabolic Equations. 3rd ed. Lecture Notes in Mathematics vol. 840 (1993), Springer-Verlag, Berlin-New York
5. Hess P. Periodic-parabolic Boundary Value Problems and Positivity. Pitman Res., Notes in Mathematics vol. 247 (1991), Longman Sci. Tech, Harlow
6. Huston V., López-Goméz J., Mischaikow K., and Vikers G. Limit behavior for a competing species problem with diffusion. Dynamical Systems and Applications. World Sci. Appl. Anal. vol. 4 (1995), World Scientific, River Edge, NJ 501-533
7. Lieberman G.M. Second order parabolic differential equations (1996), World Scientific Publ. Co., Inc, River Edge, NJ
8. Lou Y., Martinez S., and Poláčik P. Loops and branches of coexistence states in a Lotka-Volterra competition model. J. Differential Equations 230 2 (2006) 720-742
9. Ni W.M., and Tang M.X. Turing patterns in the Lengyel-Epstein system for the CIMA reactions. Trans. Amer. Math. Soc. 357 10 (2005) 3953-3969
10. R. Peng, Asymptotic Profile of the Positive Steady State for an SIS Epidemic Reaction-diffusion Model, Part I (submitted for publication)
11. R. Peng, Asymptotic Profile of the Positive Steady State for an SIS Epidemic Reaction-diffusion Model, Part II (in preparation)
12. Protter M.H., and Weinberger H.F. Maximum Principles in Differential Equations. 2nd ed. (1984), Springer, Berlin
13. Wang M.X. Non-constant positive steady-states of the Sel'kov model. J. Differential Equations 190 2 (2003) 600-620