Discrete and Continuous Dynamical Systems - Series B (DCDS-B)

Coexistence and competitive exclusion in an SIS model with standard incidence and diffusion
Pages: 1167 - 1187, Issue 3, May 2017

doi:10.3934/dcdsb.2017057      Abstract        References        Full text (793.3K)           Related Articles

Yixiang Wu - Department of Mathematics, University of Louisiana at Lafayette, 105 E. University Circle, Lafayette, LA 70503, United States (email)
Necibe Tuncer - Department of Mathematical Sciences, Florida Atlantic University, 777 Glades Road, Boca Raton, FL 33431, United States (email)
Maia Martcheva - Department of Mathematics, University of Florida, 1400 Stadium Rd, Gainesville, FL 32611, United States (email)

1 A. S. Ackleh, K. Deng and Y. Wu, Competitive exclusion and coexistence in a two-strain pathogen model with diffusion, Math. Biosci. Eng., 13 (2016), 1-18.       
2 L. J. S. Allen, B. M. Bolker, Y. Lou and A. L. Nevai, Asymptotic Profiles of the steady states for an SIS epidemic reaction-diffusion model, Discrete and Continuous Dynamical Systems, Series A, 21 (2008), 1-20.       
3 H. J. Bremermann and H. R. Thieme, A competitive exclusion principle for pathogen virulence, J. Math. Biol., 27 (1989), 179-190.
4 R. S. Cantrell and C. Cosner, Spatial Ecology Via Reaction-Diffusion Equations, Wiley, Chichester, West Sussex, UK, 2003.       
5 C. Cosner, Reaction-diffusion-advection models for the effects and evolution of dispersal, Discrete and Continuous Dynamical Systems, 34 (2014), 1701-1745.       
6 J. Dockery, V. Hutson, K. Mischaikow and Polácik, The evolution of slow dispersal rates: A reaction diffusion model, J. Math. Biol., 37 (1998), 61-83.       
7 L. Dung, Dissipativity and global attractors for a class of quasilinear parabolic systems, Communications in Partial Differential Equations, 22 (1997), 413-433.       
8 S. Hsu, H. Smith and Waltman, Competitive exclusion and coexistence for competitive systems on ordered Banach spaces, Transactions of the American Mathematical Society, 348 (1996), 4083-4094.       
9 V. Hutson, K. Mischaikow and Polácik, The evolution of dispersal rates in a heterogeneous time-periodic environment, J. Math. Biol., 43 (2001), 501-533.       
10 K. I. Kim, Z. Lin and L. Zhang, Avian-human influenza epidemic model with diffusion, Nonlinear Analysis: Real World Applications, 11 (2010), 313-322.       
11 K. Lam and W.-M. Ni, Uniqueness and complete dynamics in heterogeneous completion-diffusion systems, SIAM J. Appl. Math., 72 (2012), 1695-1712.       
12 J. Lopez-Gomez and R. M. Pardo, Invertibility of linear noncooperative elliptic systems, Nonlinear Analysis: Theory, Methods & Applications, 31 (1998), 687-699.
13 K. Lam, Y. Lou and F. Lutscher, Evolution of dispersal in closed advective environments, J. Biol. Dyn., 9 (2015), 188-212.       
14 Y. Lou and Zhou, Evolution of dispersal in advective homogeneous environment: The effect of boundary conditions, J. Differential Equations, 259 (2015), 141-171.       
15 Y. Lou and F. Lutscher, Evolution of dispersal in open advective environments, J. Math. Biol., 69 (2014), 1319-1342.       
16 M. Martcheva, B. M. Bolker and R. D. Holt, Vaccine-induced pathogen strain replacement: What are the mechanisms?, J. Royal Sco. Interface, 5 (2008), 3-13.
17 M. Mimura, Coexistence in competition-diffusion systems, differential equations models in biology, epidemiology and ecology, Lecture Notes in Biomathematics, 92 (1991), 235-246.       
18 Z. Qiu, Q. Kong, X. Li and M. Martcheva, The vector-host epidemic model with multiple strains in a patchy environment, J. Math. Anal. Appl., 405 (2013), 12-36.       
19 N. Tuncer and M. Martcheva, Analytical and numerical approaches to coexistence of strains in a two-strain SIS model with diffusion, Journal of Biological Dynamics, 6 (2012), 406-439.       
20 P. Waltman, Coexistence in chemostat-like models, Rocky Mountain J. Math., 20 (1990), 777-807.       

Go to top