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Influence of backward bifurcation on interpretation of $R_0$ in a model of epidemic tuberculosis with reinfection
1.  Department of Microbiology and Immunology, The University of Michigan Medical School, Ann Arbor, MI 481090620, United States, United States 
[1] 
Linda J. S. Allen, P. van den Driessche. Stochastic epidemic models with a backward bifurcation. Mathematical Biosciences & Engineering, 2006, 3 (3) : 445458. doi: 10.3934/mbe.2006.3.445 
[2] 
Hisashi Inaba. The Malthusian parameter and $R_0$ for heterogeneous populations in periodic environments. Mathematical Biosciences & Engineering, 2012, 9 (2) : 313346. doi: 10.3934/mbe.2012.9.313 
[3] 
Xiaomei Feng, Zhidong Teng, Kai Wang, Fengqin Zhang. Backward bifurcation and global stability in an epidemic model with treatment and vaccination. Discrete & Continuous Dynamical Systems  B, 2014, 19 (4) : 9991025. doi: 10.3934/dcdsb.2014.19.999 
[4] 
Toshikazu Kuniya, Mimmo Iannelli. $R_0$ and the global behavior of an agestructured SIS epidemic model with periodicity and vertical transmission. Mathematical Biosciences & Engineering, 2014, 11 (4) : 929945. doi: 10.3934/mbe.2014.11.929 
[5] 
Ellina Grigorieva, Evgenii Khailov, Andrei Korobeinikov. Optimal control for an epidemic in populations of varying size. Conference Publications, 2015, 2015 (special) : 549561. doi: 10.3934/proc.2015.0549 
[6] 
Xi Huo. Modeling of contact tracing in epidemic populations structured by disease age. Discrete & Continuous Dynamical Systems  B, 2015, 20 (6) : 16851713. doi: 10.3934/dcdsb.2015.20.1685 
[7] 
Karen R. RíosSoto, Baojun Song, Carlos CastilloChavez. Epidemic spread of influenza viruses: The impact of transient populations on disease dynamics. Mathematical Biosciences & Engineering, 2011, 8 (1) : 199222. doi: 10.3934/mbe.2011.8.199 
[8] 
M. Guru Prem Prasad, Tarakanta Nayak. Dynamics of { $\lambda tanh(e^z): \lambda \in R$\ ${ 0 }$ }. Discrete & Continuous Dynamical Systems  A, 2007, 19 (1) : 121138. doi: 10.3934/dcds.2007.19.121 
[9] 
Christine K. Yang, Fred Brauer. Calculation of $R_0$ for ageofinfection models. Mathematical Biosciences & Engineering, 2008, 5 (3) : 585599. doi: 10.3934/mbe.2008.5.585 
[10] 
Soohyun Bae. On the elliptic equation Δu+K u^{p} = 0 in $\mathbb{R}$^{n}. Discrete & Continuous Dynamical Systems  A, 2013, 33 (2) : 555577. doi: 10.3934/dcds.2013.33.555 
[11] 
Tom Burr, Gerardo Chowell. The reproduction number $R_t$ in structured and nonstructured populations. Mathematical Biosciences & Engineering, 2009, 6 (2) : 239259. doi: 10.3934/mbe.2009.6.239 
[12] 
Sumei Li, Yicang Zhou. Backward bifurcation of an HTLVI model with immune response. Discrete & Continuous Dynamical Systems  B, 2016, 21 (3) : 863881. doi: 10.3934/dcdsb.2016.21.863 
[13] 
Muntaser Safan, Klaus Dietz. On the eradicability of infections with partially protective vaccination in models with backward bifurcation. Mathematical Biosciences & Engineering, 2009, 6 (2) : 395407. doi: 10.3934/mbe.2009.6.395 
[14] 
Lili Liu, Xianning Liu, Jinliang Wang. Threshold dynamics of a delayed multigroup heroin epidemic model in heterogeneous populations. Discrete & Continuous Dynamical Systems  B, 2016, 21 (8) : 26152630. doi: 10.3934/dcdsb.2016064 
[15] 
Nicolas Bacaër, Xamxinur Abdurahman, Jianli Ye, Pierre Auger. On the basic reproduction number $R_0$ in sexual activity models for HIV/AIDS epidemics: Example from Yunnan, China. Mathematical Biosciences & Engineering, 2007, 4 (4) : 595607. doi: 10.3934/mbe.2007.4.595 
[16] 
Cameron J. Browne, Sergei S. Pilyugin. Minimizing $\mathcal R_0$ for inhost virus model with periodic combination antiviral therapy. Discrete & Continuous Dynamical Systems  B, 2016, 21 (10) : 33153330. doi: 10.3934/dcdsb.2016099 
[17] 
Jianfeng Huang, Yulin Zhao. Bifurcation of isolated closed orbits from degenerated singularity in $\mathbb{R}^{3}$. Discrete & Continuous Dynamical Systems  A, 2013, 33 (7) : 28612883. doi: 10.3934/dcds.2013.33.2861 
[18] 
Hongying Shu, Lin Wang. Global stability and backward bifurcation of a general viral infection model with virusdriven proliferation of target cells. Discrete & Continuous Dynamical Systems  B, 2014, 19 (6) : 17491768. doi: 10.3934/dcdsb.2014.19.1749 
[19] 
Gerardo Chowell, R. Fuentes, A. Olea, X. Aguilera, H. Nesse, J. M. Hyman. The basic reproduction number $R_0$ and effectiveness of reactive interventions during dengue epidemics: The 2002 dengue outbreak in Easter Island, Chile. Mathematical Biosciences & Engineering, 2013, 10 (5&6) : 14551474. doi: 10.3934/mbe.2013.10.1455 
[20] 
Yoichi Enatsu, Yukihiko Nakata. Stability and bifurcation analysis of epidemic models with saturated incidence rates: An application to a nonmonotone incidence rate. Mathematical Biosciences & Engineering, 2014, 11 (4) : 785805. doi: 10.3934/mbe.2014.11.785 
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