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On the eradicability of infections with partially protective vaccination in models with backward bifurcation
The discounted reproductive number for epidemiology
1.  Department of Mathematics, Pennsylvania State University, State College, PA 16802, United States 
2.  Department of Epidemiology and Public Health, Yale University School of Medicine, New Haven, CT 06520, United States, United States 
[1] 
Ariel CintrónArias, Carlos CastilloChávez, Luís M. A. Bettencourt, Alun L. Lloyd, H. T. Banks. The estimation of the effective reproductive number from disease outbreak data. Mathematical Biosciences & Engineering, 2009, 6 (2) : 261282. doi: 10.3934/mbe.2009.6.261 
[2] 
Eduardo EspinosaAvila, Pablo Padilla Longoria, Francisco HernándezQuiroz. Game theory and dynamic programming in alternate games. Journal of Dynamics & Games, 2017, 4 (3) : 205216. doi: 10.3934/jdg.2017013 
[3] 
Astridh Boccabella, Roberto Natalini, Lorenzo Pareschi. On a continuous mixed strategies model for evolutionary game theory. Kinetic & Related Models, 2011, 4 (1) : 187213. doi: 10.3934/krm.2011.4.187 
[4] 
Anna Lisa Amadori, Astridh Boccabella, Roberto Natalini. A hyperbolic model of spatial evolutionary game theory. Communications on Pure & Applied Analysis, 2012, 11 (3) : 9811002. doi: 10.3934/cpaa.2012.11.981 
[5] 
Michael Hochman. Lectures on dynamics, fractal geometry, and metric number theory. Journal of Modern Dynamics, 2014, 8 (3&4) : 437497. doi: 10.3934/jmd.2014.8.437 
[6] 
E. Muñoz Garcia, R. PérezMarco. Diophantine conditions in small divisors and transcendental number theory. Discrete & Continuous Dynamical Systems  A, 2003, 9 (6) : 14011409. doi: 10.3934/dcds.2003.9.1401 
[7] 
Hilla Behar, Alexandra Agranovich, Yoram Louzoun. Diffusion rate determines balance between extinction and proliferation in birthdeath processes. Mathematical Biosciences & Engineering, 2013, 10 (3) : 523550. doi: 10.3934/mbe.2013.10.523 
[8] 
Tinggui Chen, Yanhui Jiang. Research on operating mechanism for creative products supply chain based on game theory. Discrete & Continuous Dynamical Systems  S, 2015, 8 (6) : 11031112. doi: 10.3934/dcdss.2015.8.1103 
[9] 
Serap Ergün, Bariş Bülent Kırlar, Sırma Zeynep Alparslan Gök, GerhardWilhelm Weber. An application of crypto cloud computing in social networks by cooperative game theory. Journal of Industrial & Management Optimization, 2017, 13 (5) : 115. doi: 10.3934/jimo.2019036 
[10] 
Eunha Shim, Beth Kochin, Alison Galvani. Insights from epidemiological game theory into genderspecific vaccination against rubella. Mathematical Biosciences & Engineering, 2009, 6 (4) : 839854. doi: 10.3934/mbe.2009.6.839 
[11] 
Hideo Deguchi. A reactiondiffusion system arising in game theory: existence of solutions and spatial dominance. Discrete & Continuous Dynamical Systems  B, 2017, 22 (10) : 38913901. doi: 10.3934/dcdsb.2017200 
[12] 
WaiKi Ching, SinMan Choi, Min Huang. Optimal service capacity in a multipleserver queueing system: A game theory approach. Journal of Industrial & Management Optimization, 2010, 6 (1) : 73102. doi: 10.3934/jimo.2010.6.73 
[13] 
KingYeung Lam. Diracconcentrations in an integropde model from evolutionary game theory. Discrete & Continuous Dynamical Systems  B, 2019, 24 (2) : 737754. doi: 10.3934/dcdsb.2018205 
[14] 
Vadim Yu. Kaloshin and Brian R. Hunt. A stretched exponential bound on the rate of growth of the number of periodic points for prevalent diffeomorphisms II. Electronic Research Announcements, 2001, 7: 2836. 
[15] 
Vadim Yu. Kaloshin and Brian R. Hunt. A stretched exponential bound on the rate of growth of the number of periodic points for prevalent diffeomorphisms I. Electronic Research Announcements, 2001, 7: 1727. 
[16] 
Jungho Park. Dynamic bifurcation theory of RayleighBénard convection with infinite Prandtl number. Discrete & Continuous Dynamical Systems  B, 2006, 6 (3) : 591604. doi: 10.3934/dcdsb.2006.6.591 
[17] 
Franco Flandoli, Matti Leimbach. Mean field limit with proliferation. Discrete & Continuous Dynamical Systems  B, 2016, 21 (9) : 30293052. doi: 10.3934/dcdsb.2016086 
[18] 
Fuchen Zhang, Chunlai Mu, Shouming Zhou, Pan Zheng. New results of the ultimate bound on the trajectories of the family of the Lorenz systems. Discrete & Continuous Dynamical Systems  B, 2015, 20 (4) : 12611276. doi: 10.3934/dcdsb.2015.20.1261 
[19] 
Wen Jin, Horst R. Thieme. Persistence and extinction of diffusing populations with two sexes and short reproductive season. Discrete & Continuous Dynamical Systems  B, 2014, 19 (10) : 32093218. doi: 10.3934/dcdsb.2014.19.3209 
[20] 
Georgios Konstantinidis. A game theoretic analysis of the cops and robber game. Journal of Dynamics & Games, 2014, 1 (4) : 599619. doi: 10.3934/jdg.2014.1.599 
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