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Bacteriophage-resistant and bacteriophage-sensitive bacteria in a chemostat
Global analysis of a simple parasite-host model with homoclinic orbits
1. | Faculty of Science, Air Force Engineering University, Xi'an 710051, China, China |
2. | Department of Applied Mathematics, Xi'an Jiaotong University, Xi'an 710049, China |
References:
[1] |
D. Ebert, M. Lipsitch and K. L. Mangin, The effect of parasites on host population density and extinction: Experimental epidemiology with Daphnia and six microparasites, American Naturalist, 156 (2000), 459-477.
doi: 10.1086/303404. |
[2] |
T.-W. Hwang and Y. Kuang, Deterministic extinction effect of parasites on host populations, J. Math. Biol., 46 (2003), 17-30.
doi: 10.1007/s00285-002-0165-7. |
[3] |
Kaifa Wang and Y. Kuang, Fluctuation and extinction dynamics in host-microparasite systems, Comm. Pure Appl. Anal., 10 (2011), 1537-1548.
doi: 10.3934/cpaa.2011.10.1537. |
[4] |
S. Hews, S. Eikenberry, J. D. Nagy and Y. Kuang, Rich dynamics of a hepatitis B viral infection model with logistic hepatocyte growth, J. Math. Biol., 60 (2010), 573-590.
doi: 10.1007/s00285-009-0278-3. |
[5] |
S. Eikenberry, S. Hews, J. D. Nagy and Y. Kuang, The dynamics of a delay model of HBV infection with logistic hepatocyte growth, Math. Biosc. Eng., 6 (2009), 283-299. |
[6] |
F. Berezovsky, G. Karev, B. Song and C. Castillo-Chavez, A simple epidemic model with surprising dynamics, Math. Biosci. Eng., 2 (2005), 133-152. |
[7] |
Z. Zhang, T. Ding, et al., "Qualitative Theory of Differential Equations," Translations of Mathematical Monographs, Vol. 101, Amer. Math. Soc., Providence, Rhode Island, 1992. |
[8] |
Zhien Ma and Jia Li, "Dynamical Modeling and Analysis of Epidemics," Singapore, 2009. |
show all references
References:
[1] |
D. Ebert, M. Lipsitch and K. L. Mangin, The effect of parasites on host population density and extinction: Experimental epidemiology with Daphnia and six microparasites, American Naturalist, 156 (2000), 459-477.
doi: 10.1086/303404. |
[2] |
T.-W. Hwang and Y. Kuang, Deterministic extinction effect of parasites on host populations, J. Math. Biol., 46 (2003), 17-30.
doi: 10.1007/s00285-002-0165-7. |
[3] |
Kaifa Wang and Y. Kuang, Fluctuation and extinction dynamics in host-microparasite systems, Comm. Pure Appl. Anal., 10 (2011), 1537-1548.
doi: 10.3934/cpaa.2011.10.1537. |
[4] |
S. Hews, S. Eikenberry, J. D. Nagy and Y. Kuang, Rich dynamics of a hepatitis B viral infection model with logistic hepatocyte growth, J. Math. Biol., 60 (2010), 573-590.
doi: 10.1007/s00285-009-0278-3. |
[5] |
S. Eikenberry, S. Hews, J. D. Nagy and Y. Kuang, The dynamics of a delay model of HBV infection with logistic hepatocyte growth, Math. Biosc. Eng., 6 (2009), 283-299. |
[6] |
F. Berezovsky, G. Karev, B. Song and C. Castillo-Chavez, A simple epidemic model with surprising dynamics, Math. Biosci. Eng., 2 (2005), 133-152. |
[7] |
Z. Zhang, T. Ding, et al., "Qualitative Theory of Differential Equations," Translations of Mathematical Monographs, Vol. 101, Amer. Math. Soc., Providence, Rhode Island, 1992. |
[8] |
Zhien Ma and Jia Li, "Dynamical Modeling and Analysis of Epidemics," Singapore, 2009. |
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