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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, Volume 22, Issue 3, May 2017      doi:10.3934/dcdsb.2017057

 
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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)

Abstract: This paper investigates a two strain SIS model with diffusion, spatially heterogeneous coefficients of the reaction part and distinct diffusion rates of the separate epidemiological classes. First, it is shown that the model has bounded classical solutions. Next, it is established that the model with spatially homogeneous coefficients leads to competitive exclusion and no coexistence is possible in this case. Furthermore, it is proved that if the invasion number of strain $j$ is larger than one, then the equilibrium of strain $i$ is unstable; if, on the other hand, the invasion number of strain $j$ is smaller than one, then the equilibrium of strain $i$ is neutrally stable. In the case when all diffusion rates are equal, global results on competitive exclusion and coexistence of the strains are established. Finally, evolution of dispersal scenario is considered and it is shown that the equilibrium of the strain with the larger diffusion rate is unstable. Simulations suggest that in this case the equilibrium of the strain with the smaller diffusion rate is stable.

Keywords:  Evolution of dispersal, competitive exclusion, reproduction numbers, invasion numbers, epidemic model with diffusion.
Mathematics Subject Classification:  Primary: 35K57, 35B35; Secondary: 92D25.

Received: August 2015;      Revised: November 2015;      Available Online: December 2016.

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