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A final size relation for epidemic models
Comparison between stochastic and deterministic selectionmutation models
1.  Department of Mathematics, University of Louisiana at Lafayette, Lafayette, Louisiana 705041010, United States 
2.  Center for Research in Scientific Computation, North Carolina State University, Raleigh, North Carolina 276958205, United States 
[1] 
PierreEmmanuel Jabin. Small populations corrections for selectionmutation models. Networks & Heterogeneous Media, 2012, 7 (4) : 805836. doi: 10.3934/nhm.2012.7.805 
[2] 
Azmy S. Ackleh, Youssef M. Dib, S. R.J. Jang. Competitive exclusion and coexistence in a nonlinear refugemediated selection model. Discrete & Continuous Dynamical Systems  B, 2007, 7 (4) : 683698. doi: 10.3934/dcdsb.2007.7.683 
[3] 
Hao Wang, Katherine Dunning, James J. Elser, Yang Kuang. Daphnia species invasion, competitive exclusion, and chaotic coexistence. Discrete & Continuous Dynamical Systems  B, 2009, 12 (2) : 481493. doi: 10.3934/dcdsb.2009.12.481 
[4] 
M. R. S. Kulenović, Orlando Merino. Competitiveexclusion versus competitivecoexistence for systems in the plane. Discrete & Continuous Dynamical Systems  B, 2006, 6 (5) : 11411156. doi: 10.3934/dcdsb.2006.6.1141 
[5] 
Yixiang Wu, Necibe Tuncer, Maia Martcheva. Coexistence and competitive exclusion in an SIS model with standard incidence and diffusion. Discrete & Continuous Dynamical Systems  B, 2017, 22 (3) : 11671187. doi: 10.3934/dcdsb.2017057 
[6] 
Azmy S. Ackleh, Keng Deng, Yixiang Wu. Competitive exclusion and coexistence in a twostrain pathogen model with diffusion. Mathematical Biosciences & Engineering, 2016, 13 (1) : 118. doi: 10.3934/mbe.2016.13.1 
[7] 
Azmy S. Ackleh, Linda J. S. Allen. Competitive exclusion in SIS and SIR epidemic models with total cross immunity and densitydependent host mortality. Discrete & Continuous Dynamical Systems  B, 2005, 5 (2) : 175188. doi: 10.3934/dcdsb.2005.5.175 
[8] 
Maia Martcheva, Mimmo Iannelli, XueZhi Li. Subthreshold coexistence of strains: the impact of vaccination and mutation. Mathematical Biosciences & Engineering, 2007, 4 (2) : 287317. doi: 10.3934/mbe.2007.4.287 
[9] 
Yu Wu, Xiaopeng Zhao, Mingjun Zhang. Dynamics of stochastic mutation to immunodominance. Mathematical Biosciences & Engineering, 2012, 9 (4) : 937952. doi: 10.3934/mbe.2012.9.937 
[10] 
P. Magal, G. F. Webb. Mutation, selection, and recombination in a model of phenotype evolution. Discrete & Continuous Dynamical Systems  A, 2000, 6 (1) : 221236. doi: 10.3934/dcds.2000.6.221 
[11] 
Alain Rapaport, Mario Veruete. A new proof of the competitive exclusion principle in the chemostat. Discrete & Continuous Dynamical Systems  B, 2019, 24 (8) : 37553764. doi: 10.3934/dcdsb.2018314 
[12] 
Francesca Verrilli, Hamed Kebriaei, Luigi Glielmo, Martin Corless, Carmen Del Vecchio. Effects of selection and mutation on epidemiology of Xlinked genetic diseases. Mathematical Biosciences & Engineering, 2017, 14 (3) : 755775. doi: 10.3934/mbe.2017042 
[13] 
Nhu N. Nguyen, George Yin. Stochastic partial differential equation models for spatially dependent predatorprey equations. Discrete & Continuous Dynamical Systems  B, 2017, 22 (11) : 119. doi: 10.3934/dcdsb.2019175 
[14] 
H. L. Smith, X. Q. Zhao. Competitive exclusion in a discretetime, sizestructured chemostat model. Discrete & Continuous Dynamical Systems  B, 2001, 1 (2) : 183191. doi: 10.3934/dcdsb.2001.1.183 
[15] 
Ludwig Arnold, Igor Chueshov. Cooperative random and stochastic differential equations. Discrete & Continuous Dynamical Systems  A, 2001, 7 (1) : 133. doi: 10.3934/dcds.2001.7.1 
[16] 
Yanxia Dang, Zhipeng Qiu, Xuezhi Li. Competitive exclusion in an infectionage structured vectorhost epidemic model. Mathematical Biosciences & Engineering, 2017, 14 (4) : 901931. doi: 10.3934/mbe.2017048 
[17] 
Can Huang, Zhimin Zhang. The spectral collocation method for stochastic differential equations. Discrete & Continuous Dynamical Systems  B, 2013, 18 (3) : 667679. doi: 10.3934/dcdsb.2013.18.667 
[18] 
Jasmina Djordjević, Svetlana Janković. Reflected backward stochastic differential equations with perturbations. Discrete & Continuous Dynamical Systems  A, 2018, 38 (4) : 18331848. doi: 10.3934/dcds.2018075 
[19] 
Arnulf Jentzen. Taylor expansions of solutions of stochastic partial differential equations. Discrete & Continuous Dynamical Systems  B, 2010, 14 (2) : 515557. doi: 10.3934/dcdsb.2010.14.515 
[20] 
Jan A. Van Casteren. On backward stochastic differential equations in infinite dimensions. Discrete & Continuous Dynamical Systems  S, 2013, 6 (3) : 803824. doi: 10.3934/dcdss.2013.6.803 
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