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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 48109-0620, 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) : 445-458. 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) : 313-346. 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 and Continuous Dynamical Systems - B, 2014, 19 (4) : 999-1025. doi: 10.3934/dcdsb.2014.19.999 |
[4] |
Toshikazu Kuniya, Mimmo Iannelli. $R_0$ and the global behavior of an age-structured SIS epidemic model with periodicity and vertical transmission. Mathematical Biosciences & Engineering, 2014, 11 (4) : 929-945. 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) : 549-561. doi: 10.3934/proc.2015.0549 |
[6] |
Karen R. Ríos-Soto, Baojun Song, Carlos Castillo-Chavez. Epidemic spread of influenza viruses: The impact of transient populations on disease dynamics. Mathematical Biosciences & Engineering, 2011, 8 (1) : 199-222. doi: 10.3934/mbe.2011.8.199 |
[7] |
Xi Huo. Modeling of contact tracing in epidemic populations structured by disease age. Discrete and Continuous Dynamical Systems - B, 2015, 20 (6) : 1685-1713. doi: 10.3934/dcdsb.2015.20.1685 |
[8] |
M. Guru Prem Prasad, Tarakanta Nayak. Dynamics of { $\lambda tanh(e^z): \lambda \in R$\ ${ 0 }$ }. Discrete and Continuous Dynamical Systems, 2007, 19 (1) : 121-138. doi: 10.3934/dcds.2007.19.121 |
[9] |
Christine K. Yang, Fred Brauer. Calculation of $R_0$ for age-of-infection models. Mathematical Biosciences & Engineering, 2008, 5 (3) : 585-599. doi: 10.3934/mbe.2008.5.585 |
[10] |
Soohyun Bae. On the elliptic equation Δu+K up = 0 in $\mathbb{R}$n. Discrete and Continuous Dynamical Systems, 2013, 33 (2) : 555-577. 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) : 239-259. doi: 10.3934/mbe.2009.6.239 |
[12] |
Bing Zeng, Pei Yu. A hierarchical parametric analysis on Hopf bifurcation of an epidemic model. Discrete and Continuous Dynamical Systems - S, 2022 doi: 10.3934/dcdss.2022069 |
[13] |
Sumei Li, Yicang Zhou. Backward bifurcation of an HTLV-I model with immune response. Discrete and Continuous Dynamical Systems - B, 2016, 21 (3) : 863-881. doi: 10.3934/dcdsb.2016.21.863 |
[14] |
Muntaser Safan, Klaus Dietz. On the eradicability of infections with partially protective vaccination in models with backward bifurcation. Mathematical Biosciences & Engineering, 2009, 6 (2) : 395-407. doi: 10.3934/mbe.2009.6.395 |
[15] |
Lili Liu, Xianning Liu, Jinliang Wang. Threshold dynamics of a delayed multi-group heroin epidemic model in heterogeneous populations. Discrete and Continuous Dynamical Systems - B, 2016, 21 (8) : 2615-2630. doi: 10.3934/dcdsb.2016064 |
[16] |
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) : 595-607. doi: 10.3934/mbe.2007.4.595 |
[17] |
Cameron J. Browne, Sergei S. Pilyugin. Minimizing $\mathcal R_0$ for in-host virus model with periodic combination antiviral therapy. Discrete and Continuous Dynamical Systems - B, 2016, 21 (10) : 3315-3330. doi: 10.3934/dcdsb.2016099 |
[18] |
Jianfeng Huang, Yulin Zhao. Bifurcation of isolated closed orbits from degenerated singularity in $\mathbb{R}^{3}$. Discrete and Continuous Dynamical Systems, 2013, 33 (7) : 2861-2883. doi: 10.3934/dcds.2013.33.2861 |
[19] |
Hongying Shu, Lin Wang. Global stability and backward bifurcation of a general viral infection model with virus-driven proliferation of target cells. Discrete and Continuous Dynamical Systems - B, 2014, 19 (6) : 1749-1768. doi: 10.3934/dcdsb.2014.19.1749 |
[20] |
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) : 1455-1474. doi: 10.3934/mbe.2013.10.1455 |
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