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Chemostats and epidemics: Competition for nutrients/hosts
Different types of backward bifurcations due to density-dependent treatments
1. | Department of Mathematical Sciences, Montclair State University, Upper Montclair, NJ 07043 |
2. | Department of Mathematics, Shanghai University, 99 Shangda Road, Shanghai 200444, China |
References:
[1] |
F. Brauer and C. Castillo-Chavez, "Mathematical Models in Population Biology and Epidemiology,", Second edition, 40 (2012).
doi: 10.1007/978-1-4614-1686-9. |
[2] |
H. Cao, Y. Zhou and B. Song, Complex dynamics of discrete SEIS models with simple demography,, Discrete Dynamics in Nature and Society, 2011 (6539).
doi: 10.1155/2011/653937. |
[3] |
C. Castillo-Chavez and B. Song, Dynamical models of tuberculosis and their applications,, Math. Biosc. Eng., 1 (2004), 361.
doi: 10.3934/mbe.2004.1.361. |
[4] |
X. S. Chen, X. D. Gong, G. J. Liang and G. C. Zhang, Epidemiologic trends of sexually transmitted diseases in China,, Sex Transm. Dis., 27 (2000), 138.
doi: 10.1097/00007435-200003000-00003. |
[5] |
J. Cui, X. Mu and H. Wan, Saturation recovery leads to multiple endemic equilibria and backward bifurcation,, J. Theor. Biol., 254 (2008), 275.
doi: 10.1016/j.jtbi.2008.05.015. |
[6] |
H. W. Hethcote and J. A. Yorke, "Gonorrhea Transmission Dynamics and Control,", Lecture Notes in Biomathematics, (1984).
|
[7] |
Z. Hu, S. Liu and H. Wang, Backward bifurcation of an epidemic model with standard incidence rate and treatment rate,, Nonlinear Analysis, 9 (2008), 2302.
doi: 10.1016/j.nonrwa.2007.08.009. |
[8] |
X. Li, W. Li and Mini Ghosh, Stability and bifurcation of an epidemic model with nonlinear incidence and treatment,, Applied Mathematics and Computation, 210 (2009), 141.
doi: 10.1016/j.amc.2008.12.085. |
[9] |
B. R. Morin, L. Medina-Rios, E. T. Camacho and C. Castillo-Chavez, Static behavioral effects on gonorrhea transmission dynamics in a MSM population,, J. Theor. Biol., 267 (2012), 35.
doi: 10.1016/j.jtbi.2010.07.027. |
[10] |
P. van den Driessche and J. Watmough, Reproduction numbers and sub-threshold endemic equilibria for compartmental models of disease transmission,, Math. Biosci., 180 (2002), 29.
doi: 10.1016/S0025-5564(02)00108-6. |
[11] |
W. Wang, Backward bifurcation of an epidemic model with treatment,, Math. Biosci., 201 (2006), 58.
doi: 10.1016/j.mbs.2005.12.022. |
[12] |
X. Zhang and X. Liu, Bifurcation of an epidemic model with saturated treatment function,, J. Math. Anal. Appl., 348 (2008), 433.
doi: 10.1016/j.jmaa.2008.07.042. |
[13] |
Centers for Disease Control and Prevention, Gonorrhea-CDC fact sheet,, June 2012. Available from: \url{http://www.cdc.gov/std/gonorrhea/STDFact-gonorrhea-detailed.htm}., (2012). Google Scholar |
[14] |
, China Yearbook., Available from: \url{http://www.yearbook.cn/}., (). Google Scholar |
[15] |
, Ministry of Health of the People's Republic of China., Available from: \url{http://www.moh.gov.cn/publicfiles/business/htmlfiles/mohjbyfkzj/s2907/index.htm}., (). Google Scholar |
show all references
References:
[1] |
F. Brauer and C. Castillo-Chavez, "Mathematical Models in Population Biology and Epidemiology,", Second edition, 40 (2012).
doi: 10.1007/978-1-4614-1686-9. |
[2] |
H. Cao, Y. Zhou and B. Song, Complex dynamics of discrete SEIS models with simple demography,, Discrete Dynamics in Nature and Society, 2011 (6539).
doi: 10.1155/2011/653937. |
[3] |
C. Castillo-Chavez and B. Song, Dynamical models of tuberculosis and their applications,, Math. Biosc. Eng., 1 (2004), 361.
doi: 10.3934/mbe.2004.1.361. |
[4] |
X. S. Chen, X. D. Gong, G. J. Liang and G. C. Zhang, Epidemiologic trends of sexually transmitted diseases in China,, Sex Transm. Dis., 27 (2000), 138.
doi: 10.1097/00007435-200003000-00003. |
[5] |
J. Cui, X. Mu and H. Wan, Saturation recovery leads to multiple endemic equilibria and backward bifurcation,, J. Theor. Biol., 254 (2008), 275.
doi: 10.1016/j.jtbi.2008.05.015. |
[6] |
H. W. Hethcote and J. A. Yorke, "Gonorrhea Transmission Dynamics and Control,", Lecture Notes in Biomathematics, (1984).
|
[7] |
Z. Hu, S. Liu and H. Wang, Backward bifurcation of an epidemic model with standard incidence rate and treatment rate,, Nonlinear Analysis, 9 (2008), 2302.
doi: 10.1016/j.nonrwa.2007.08.009. |
[8] |
X. Li, W. Li and Mini Ghosh, Stability and bifurcation of an epidemic model with nonlinear incidence and treatment,, Applied Mathematics and Computation, 210 (2009), 141.
doi: 10.1016/j.amc.2008.12.085. |
[9] |
B. R. Morin, L. Medina-Rios, E. T. Camacho and C. Castillo-Chavez, Static behavioral effects on gonorrhea transmission dynamics in a MSM population,, J. Theor. Biol., 267 (2012), 35.
doi: 10.1016/j.jtbi.2010.07.027. |
[10] |
P. van den Driessche and J. Watmough, Reproduction numbers and sub-threshold endemic equilibria for compartmental models of disease transmission,, Math. Biosci., 180 (2002), 29.
doi: 10.1016/S0025-5564(02)00108-6. |
[11] |
W. Wang, Backward bifurcation of an epidemic model with treatment,, Math. Biosci., 201 (2006), 58.
doi: 10.1016/j.mbs.2005.12.022. |
[12] |
X. Zhang and X. Liu, Bifurcation of an epidemic model with saturated treatment function,, J. Math. Anal. Appl., 348 (2008), 433.
doi: 10.1016/j.jmaa.2008.07.042. |
[13] |
Centers for Disease Control and Prevention, Gonorrhea-CDC fact sheet,, June 2012. Available from: \url{http://www.cdc.gov/std/gonorrhea/STDFact-gonorrhea-detailed.htm}., (2012). Google Scholar |
[14] |
, China Yearbook., Available from: \url{http://www.yearbook.cn/}., (). Google Scholar |
[15] |
, Ministry of Health of the People's Republic of China., Available from: \url{http://www.moh.gov.cn/publicfiles/business/htmlfiles/mohjbyfkzj/s2907/index.htm}., (). Google Scholar |
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