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Competition of motile and immotile bacterial strains in a petri dish
Mathematical modelling and control of echinococcus in Qinghai province, China
1. | Department of Mathematics, Shanghai University, 99 Shangda Road, Shanghai 200444, China, China, China |
2. | Department of Mathematical Sciences, Montclair State University, 1 Normal Avenue, Montclair, NJ 07043 |
References:
[1] |
CDC., Parasites and health: Echinococcosis, DPDx, July (2009), Web. February 2010, http://www.dpd.cdc.gov/DPDx/html/Echinococcosis.htm. |
[2] |
S. H. Yu, H. Wang, X. H. Wu, X. Ma, Y. F. Liu, Y. M. Zhao, Y. Morishima and M. Kawanaka, Cystic and alveolar echinococcosis: An epidemiological survey in a Tibetan population in Southeast Qinghai, China, Jpn.J.Infect.Dis., 61 (2008), 242-246. |
[3] |
Y. R. Yang, M. C. Rosenzvit, L. H. Zhang, J. Z. Zhang and D. P. Mcmanus, Molecular study of echinococcus in west-central China, Parasitology, 131 (2005), 547-555. |
[4] |
H. Wang, L. Li and B. Zhang etc, Status of human hydatid disease report, in "National Survey of Important Human Parasitic Diseases" People's Health Publishing House, Beijing, (2008), 73-79. |
[5] |
CDC., Web. April (2010). http://www.chinacdc.cn/jkzt/tfggwssj/zzfb/crbjcykz/201004/t20100420_24967.htm. |
[6] |
X. Zhe, Medlive, Web. April (2011). http://disease.medlive.cn/wiki/entry/10001076_301_0. |
[7] |
R. M. Anderson and R. M. May, "Infectious Diseases of Humans," Oxford Univ. Press, New York, 1991. |
[8] |
Y. Yang, Z. Feng, D. Xu, G. Sandland and D. J. Minchella, Evolution of host resistance to parasite infection in the snail-schistosome-human system, Journal of Mathematical Biology, 65 (2012), 201-236.
doi: 10.1007/s00285-011-0457-x. |
[9] |
C. Castillo-Chavez, Z. Feng and D. Xu, A schistosomiasis model with mating structure and time delay, Mathematical Biosciences, 211 (2008), 333-341.
doi: 10.1016/j.mbs.2007.11.001. |
[10] |
Z. Feng, A. Eppert, F. Milner and D. Minchella, Estimation of parameters governing the transmission dynamics of schistosomes, Applied Mathematics Letters, 17 (2004), 1105-1112,
doi: 10.1016/j.aml.2004.02.002. |
[11] |
S. G. Ruan, D. M. Xiao and J. C. Beier, On the delayed Ross-Macdonald model for malaria transmission, Bulletin of Mathematical Biology, 70 (2008), 1098-1114.
doi: 10.1007/s11538-007-9292-z. |
[12] |
Z. M. Chen and L. Zou et.al, Mathematical modelling and control of schistosomiasis in Hubei province, China, Acta Tropica, 115 (2010), 119-125. |
[13] |
P. R. Torgersona, D. H. Williamsb and M. N. Abo-Shehada, Modelling the prevalence of Echinococcus and Taenia species in small ruminants of different ages in northern Jordan, Veterinary Parasitology, 79 (1998), 35-51. |
[14] |
R. M. Mukbel, P. R. Torgerson and M. N. Abo-Shehada, Prevalence of hydatidosis among donkeys in northern Jordan, Veterinary Parasitology, 88 (2000), 35-42. |
[15] |
O. Diekmann and J. A. P. Heesterbeek, Mathematical epidemiology of infectious diseases, Model building analyis and interpretation, Wiley Series in Mathematical and Computational Biology, (2000). |
[16] |
P. van den Driessche and J. Watmough, Reproductive numbers and sub-threshold endemic equilibria for compartmentmodels of disease transmission, Math. Biosci., 180 (2002), 183-201.
doi: 10.1016/S0025-5564(02)00108-6. |
[17] |
H. B. Guo and M. Y. Li., Global stability in a mathematical model of tuberculosis, Canadian applied mathematics quarterly, 14 (2006), Number 2. |
[18] |
J. P. LaSalle, "The Stability of Dynamical Systems," Regional Conference Series in Applied Mathematics, SIAM, Philadelphia, 1976. |
[19] |
J. Dushoff, W. Huang and C. Castillo-Chavez, Backward bifurcations and batas- trophe in simple models of fatal diseases, Journal of Mathematical Biology, 36 (1998), 227-248.
doi: 10.1007/s002850050099. |
[20] |
C. Castillo-Chavez and B. Song, Dynamical models of tuberculosis and their applications, Math. Biosci. Eng., 1 (2004), 361-404.
doi: 10.3934/mbe.2004.1.361. |
[21] |
, China Yearbook. http://tongji.cnki.net/kns55/brief/result.aspx?stab=shuzhi. |
[22] |
S. Marino, I. B. Hogue, C. J. Ray and D. E. Kirschner, A methodology for performing global uncertainty and sensitivity analysis in systems biology, Journal of Theoretical Biology, 254 (2008), 178-196. |
[23] |
H. Wang and D. L. A, Analysis of pulmonary echinococcosis cyst excision in 136 cases, Chinese Journal of Misdiagnostics, 11 (2011). |
[24] |
P. S. Craig, P. Giraudoux, D. Shi and B. Bartholomot, An epidemiological and ecological study of human alveolar echinococcosis transmission in south Gansu, China, Acta Tropica, 77 (2000), 167-177. |
show all references
References:
[1] |
CDC., Parasites and health: Echinococcosis, DPDx, July (2009), Web. February 2010, http://www.dpd.cdc.gov/DPDx/html/Echinococcosis.htm. |
[2] |
S. H. Yu, H. Wang, X. H. Wu, X. Ma, Y. F. Liu, Y. M. Zhao, Y. Morishima and M. Kawanaka, Cystic and alveolar echinococcosis: An epidemiological survey in a Tibetan population in Southeast Qinghai, China, Jpn.J.Infect.Dis., 61 (2008), 242-246. |
[3] |
Y. R. Yang, M. C. Rosenzvit, L. H. Zhang, J. Z. Zhang and D. P. Mcmanus, Molecular study of echinococcus in west-central China, Parasitology, 131 (2005), 547-555. |
[4] |
H. Wang, L. Li and B. Zhang etc, Status of human hydatid disease report, in "National Survey of Important Human Parasitic Diseases" People's Health Publishing House, Beijing, (2008), 73-79. |
[5] |
CDC., Web. April (2010). http://www.chinacdc.cn/jkzt/tfggwssj/zzfb/crbjcykz/201004/t20100420_24967.htm. |
[6] |
X. Zhe, Medlive, Web. April (2011). http://disease.medlive.cn/wiki/entry/10001076_301_0. |
[7] |
R. M. Anderson and R. M. May, "Infectious Diseases of Humans," Oxford Univ. Press, New York, 1991. |
[8] |
Y. Yang, Z. Feng, D. Xu, G. Sandland and D. J. Minchella, Evolution of host resistance to parasite infection in the snail-schistosome-human system, Journal of Mathematical Biology, 65 (2012), 201-236.
doi: 10.1007/s00285-011-0457-x. |
[9] |
C. Castillo-Chavez, Z. Feng and D. Xu, A schistosomiasis model with mating structure and time delay, Mathematical Biosciences, 211 (2008), 333-341.
doi: 10.1016/j.mbs.2007.11.001. |
[10] |
Z. Feng, A. Eppert, F. Milner and D. Minchella, Estimation of parameters governing the transmission dynamics of schistosomes, Applied Mathematics Letters, 17 (2004), 1105-1112,
doi: 10.1016/j.aml.2004.02.002. |
[11] |
S. G. Ruan, D. M. Xiao and J. C. Beier, On the delayed Ross-Macdonald model for malaria transmission, Bulletin of Mathematical Biology, 70 (2008), 1098-1114.
doi: 10.1007/s11538-007-9292-z. |
[12] |
Z. M. Chen and L. Zou et.al, Mathematical modelling and control of schistosomiasis in Hubei province, China, Acta Tropica, 115 (2010), 119-125. |
[13] |
P. R. Torgersona, D. H. Williamsb and M. N. Abo-Shehada, Modelling the prevalence of Echinococcus and Taenia species in small ruminants of different ages in northern Jordan, Veterinary Parasitology, 79 (1998), 35-51. |
[14] |
R. M. Mukbel, P. R. Torgerson and M. N. Abo-Shehada, Prevalence of hydatidosis among donkeys in northern Jordan, Veterinary Parasitology, 88 (2000), 35-42. |
[15] |
O. Diekmann and J. A. P. Heesterbeek, Mathematical epidemiology of infectious diseases, Model building analyis and interpretation, Wiley Series in Mathematical and Computational Biology, (2000). |
[16] |
P. van den Driessche and J. Watmough, Reproductive numbers and sub-threshold endemic equilibria for compartmentmodels of disease transmission, Math. Biosci., 180 (2002), 183-201.
doi: 10.1016/S0025-5564(02)00108-6. |
[17] |
H. B. Guo and M. Y. Li., Global stability in a mathematical model of tuberculosis, Canadian applied mathematics quarterly, 14 (2006), Number 2. |
[18] |
J. P. LaSalle, "The Stability of Dynamical Systems," Regional Conference Series in Applied Mathematics, SIAM, Philadelphia, 1976. |
[19] |
J. Dushoff, W. Huang and C. Castillo-Chavez, Backward bifurcations and batas- trophe in simple models of fatal diseases, Journal of Mathematical Biology, 36 (1998), 227-248.
doi: 10.1007/s002850050099. |
[20] |
C. Castillo-Chavez and B. Song, Dynamical models of tuberculosis and their applications, Math. Biosci. Eng., 1 (2004), 361-404.
doi: 10.3934/mbe.2004.1.361. |
[21] |
, China Yearbook. http://tongji.cnki.net/kns55/brief/result.aspx?stab=shuzhi. |
[22] |
S. Marino, I. B. Hogue, C. J. Ray and D. E. Kirschner, A methodology for performing global uncertainty and sensitivity analysis in systems biology, Journal of Theoretical Biology, 254 (2008), 178-196. |
[23] |
H. Wang and D. L. A, Analysis of pulmonary echinococcosis cyst excision in 136 cases, Chinese Journal of Misdiagnostics, 11 (2011). |
[24] |
P. S. Craig, P. Giraudoux, D. Shi and B. Bartholomot, An epidemiological and ecological study of human alveolar echinococcosis transmission in south Gansu, China, Acta Tropica, 77 (2000), 167-177. |
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