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Abstract and Applied Analysis
Volume 2014 (2014), Article ID 546795, 5 pages
Dynamics of a Viral Infection Model with General Contact Rate between Susceptible Cells and Virus Particles
1Department of Mathematics, School of Biomedical Engineering, Third Military Medical University, Chongqing 400038, China
2Nineteen Student Battalion, School of Biomedical Engineering, Third Military Medical University, Chongqing 400038, China
Received 23 December 2013; Accepted 9 January 2014; Published 13 February 2014
Academic Editor: Weiming Wang
Copyright © 2014 Chenxi Dai et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
- H. Dahari, J. E. Layden-Almer, E. Kallwitz et al., “A mathematical model of hepatitis C virus dynamics in patients with high baseline viral loads or advanced liver disease,” Gastroenterology, vol. 136, no. 4, pp. 1402–1409, 2009.
- L. Rong and A. S. Perelson, “Modeling latently infected cell activation: viral and latent reservoir persistence, and viral blips in HIV-infected patients on potent therapy,” PLoS Computational Biology, vol. 5, no. 10, Article ID e1000533, 2009.
- K. Wang, W. Tan, Y. Tang, and G. Deng, “Numerical diagnoses of superinfection in chronic hepatitis B viral dynamics,” Intervirology, vol. 54, no. 6, pp. 349–356, 2011.
- J. Pang, J.-A. Cui, and J. Hui, “The importance of immune responses in a model of hepatitis B virus,” Nonlinear Dynamics, vol. 67, no. 1, pp. 723–734, 2012.
- Q. Li, F. Lu, and K. Wang, “Modeling of HIV-1 infection: insights to the role of monocytes/macrophages, latently infected T4 cells, and HAART regimes,” PLoS ONE, vol. 7, no. 9, Article ID e46026, 2012.
- G. Huang, A. Fan, and K. Wang, “Dynamics behavior of mutation during reproduction on HIV-1 drug resistance,” International Journal of Biomathematics, vol. 6, no. 3, Article ID 1350018, 2013.
- M. A. Nowak, S. Bonhoeffer, A. M. Hill, R. Boehme, H. C. Thomas, and H. Mcdade, “Viral dynamics in hepatitis B virus infection,” Proceedings of the National Academy of Sciences of the United States of America, vol. 93, no. 9, pp. 4398–4402, 1996.
- S. Bonhoeffer, R. M. May, G. M. Shaw, and M. A. Nowak, “Virus dynamics and drug therapy,” Proceedings of the National Academy of Sciences of the United States of America, vol. 94, no. 13, pp. 6971–6976, 1997.
- D. Ebert, C. D. Zschokke-Rohringer, and H. J. Carius, “Dose effects and density-dependent regulation of two microparasites of Daphnia magna,” Oecologia, vol. 122, no. 2, pp. 200–209, 2000.
- R. R. Regoes, D. Ebert, and S. Bonhoeffer, “Dose-dependent infection rates of parasites produce the Allee effect in epidemiology,” Proceedings of the Royal Society B, vol. 269, no. 1488, pp. 271–279, 2002.
- K. Wang and Y. Kuang, “Novel dynamics of a simple Daphnia-microparasite model with dose-dependent infection,” Discrete and Continuous Dynamical Systems S, vol. 4, no. 6, pp. 1599–1610, 2011.
- J. P. LaSalle, The Stability of Dynamical Systems, Regional Conference Series in Applied Mathematics, SIAM, Philadelphia, Pa, USA, 1976.
- H. R. Thieme, “Persistence under relaxed point-dissipativity (with application to an endemic model),” SIAM Journal on Mathematical Analysis, vol. 24, no. 2, pp. 407–435, 1993.
- O. Diekmann, J. A. P. Heesterbeek, and J. A. J. Metz, “On the definition and the computation of the basic reproduction ratio in models for infectious diseases in heterogeneous populations,” Journal of Mathematical Biology, vol. 28, no. 4, pp. 365–382, 1990.
- P. van den Driessche and J. Watmough, “Reproduction numbers and sub-threshold endemic equilibria for compartmental models of disease transmission,” Mathematical Biosciences, vol. 180, no. 1-2, pp. 29–48, 2002.
- P. de Leenheer and H. L. Smith, “Virus dynamics: a global analysis,” SIAM Journal on Applied Mathematics, vol. 63, no. 4, pp. 1313–1327, 2003.
- A. Korobeinikov, “Global properties of basic virus dynamics models,” Bulletin of Mathematical Biology, vol. 66, no. 4, pp. 879–883, 2004.
- A. Murase, T. Sasaki, and T. Kajiwara, “Stability analysis of pathogen-immune interaction dynamics,” Journal of Mathematical Biology, vol. 51, no. 3, pp. 247–267, 2005.