
Previous Article
Controlling a model for bone marrow dynamics in cancer chemotherapy
 MBE Home
 This Issue

Next Article
On deriving lumped models for blood flow and pressure in the systemic arteries
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 
2018 Impact Factor: 1.313
Tools
Metrics
Other articles
by authors
[Back to Top]