Primary: 92D30, 91D25; Secondary: 35K57, 37N25, 35B40.

Export file:

Format

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

Content

• Citation Only
• Citation and Abstract

Competitive exclusion and coexistence in a two-strain pathogen model with diffusion

1. Department of Mathematics, University of Louisiana at Lafayette, Lafayette, Louisiana 70504-1010
2. Department of Mathematics, University of Louisiana at Lafayette, Lafayette, Louisiana 70504

## Abstract    Related pages

We consider a two-strain pathogen model described by a system of reaction-diffusion equations. We define a basic reproduction number $R_0$ and show that when the model parameters are constant (spatially homogeneous), if $R_0 >1$ then one strain will outcompete the other strain and drive it to extinction, but if $R_0 \le 1$ then the disease-free equilibrium is globally attractive. When we assume that the diffusion rates are equal while the transmission and recovery rates are heterogeneous, then there are two possible outcomes under the condition $R_0 >1$: 1) Competitive exclusion where one strain dies out. 2) Coexistence between the two strains. Thus, spatial heterogeneity promotes coexistence.
Figure/Table
Supplementary
Article Metrics

Citation: Azmy S. Ackleh, Keng Deng, Yixiang Wu. Competitive exclusion and coexistence in a two-strain pathogen model with diffusion. Mathematical Biosciences and Engineering, 2016, 13(1): 1-18. doi: 10.3934/mbe.2016.13.1

References

• 1. Journal of Mathematical Biology, 47 (2003), 153-168.
• 2. Discrete and Continuous Dynamical Systems Series B, 5 (2005), 175-188.
• 3. Journal of Mathematical Biology, 68 (2014), 453-475.
• 4. Journal of Differential Equations, 33 (1979), 201-225.
• 5. Mathematical Biosciences, 186 (2003), 191-217.
• 6. SIAM Journal on Applied Mathematics, 67 (2007), 1283-1309.
• 7. Discrete and Continuous Dynamical Systems, 21 (2008), 1-20.
• 8. Journal Mathematical Biology, 35 (1997), 825-842.
• 9. Journal of Theoretical Biology, 177 (1995), 159-165.
• 10. Science, 287 (2000), 650-654.
• 11. Journal of Mathematical Biology, 27 (1989), 179-190.
• 12. Rocky Mountain Journal of Mathematics, 26 (1996), 1-35.
• 13. Wiley, Chichester, West Sussex, UK, 2003.
• 14. SIAM Journal on Applied Mathematics, 56 (1996), 494-508.
• 15. Journal of Mathematical Biology, 35 (1997), 503-522.
• 16. submitted.
• 17. Bulletin of the Australian Mathematical Society, 44 (1991), 79-94.
• 18. American Mathematical Society, Providence, 1988.
• 19. Springer-Verlag, New York, 1981.
• 20. Transactions of the American Mathematical Society, 348 (1996), 4083-4094.
• 21. Mathematical Biosciences and Engineering, 7 (2010), 51-66.
• 22. SIAM Journal on Mathematical Analysis, 35 (2003), 453-491.
• 23. Journal of Differential Equations, 211 (2005), 135-161.
• 24. Funkcialaj Ekvacioj, 32 (1989), 191-213.
• 25. Journal of Differential Equations, 223 (2006), 400-426.
• 26. Journal of Differential Equations, 230 (2006), 720-742.
• 27. Journal of Biological Dynamics, 3 (2009), 235-251.
• 28. Plenum Press, New York, 1992.
• 29. Nonlinear Analysis, 71 (2009), 239-247.
• 30. Journal of Differential Equations, 247 (2009), 1096-1119.
• 31. Nonlinearity, 25 (2012), 1451-1471.
• 32. Physica D, 259 (2013), 8-25.
• 33. Journal of Biological Dynamics, 6 (2012), 406-439.

• 1. Maia Martcheva, Necibe Tuncer, Yixiang Wu, Coexistence and competitive exclusion in an SIS model with standard incidence and diffusion, Discrete and Continuous Dynamical Systems - Series B, 2016, 22, 3, 1167, 10.3934/dcdsb.2017057
• 2. Yixiang Wu, Xingfu Zou, Asymptotic profiles of steady states for a diffusive SIS epidemic model with mass action infection mechanism, Journal of Differential Equations, 2016, 261, 8, 4424, 10.1016/j.jde.2016.06.028
• 3. Lai Zhang, Ling Lin, Jing Ge, A diffusive SIS epidemic model incorporating the media coverage impact in the heterogeneous environment, Discrete and Continuous Dynamical Systems - Series B, 2017, 22, 7, 2763, 10.3934/dcdsb.2017134
• 4. Junping Shi, Yixiang Wu, Xingfu Zou, Coexistence of Competing Species for Intermediate Dispersal Rates in a Reaction–Diffusion Chemostat Model, Journal of Dynamics and Differential Equations, 2019, 10.1007/s10884-019-09763-0
• 5. Lin Zhao, Zhi-Cheng Wang, Shigui Ruan, Dynamics of a time-periodic two-strain SIS epidemic model with diffusion and latent period, Nonlinear Analysis: Real World Applications, 2020, 51, 102966, 10.1016/j.nonrwa.2019.102966