참고문헌
- R. Levins, T. Awerbuch, U. Brinkman, I. Eckardt, P. Epstein, N. Makhoul, C.A. de Possas, C. Puccia, A. Spielman, and M.E. Wilson, The emergence of new diseases, American Scientist, Vol. 82(1994), 52–60.
- R. Preston, The Hot Zone, Random House, New York, 1994.
- M.B.A. Oldstone, Viruses, Plagues, and History, Oxford University Press, New York, 1998.
- L. Garrett, The Coming Plague, Penguin, New York, 1995.
- H.W. Hethcote, Three basic epidemiological models, in Applied Mathematical Ecology, L. Gross, T. G. Hallam, and S. A. Levin, eds., Springer-Verlag, Berlin, 1989.
- V. Capasso and G. Serio, A generalization of the Kermack-Mckendrick deterministic epi- demic model, Math. Biosci. Vol. 42(1978), 43-61. https://doi.org/10.1016/0025-5564(78)90006-8
- R.M. Anderson and R.M. May, Population Dynamics of Infectious Diseases, Springer-Verlag, Berlin, Heidelberg, New York, 1982.
- S.N. Busenberg and K.L. Cooke,Vertically Transmitted Diseases, Biomathematics 23, Springer-Verlag, Berlin, 1993.
- S.N. Busenberg, K.L. Cooke and M. Iannelli, Endemic thresholds and stability in a class of age-structured epidemics, SIAM J. Appl. Math. Vol. 48(1988), 1379–1395. https://doi.org/10.1137/0148085
- C. Castillo-Chavez, H. W. Hethcote, V. Andreasen, S. A. Levin and W. M. Liu, Epidemi-ological models with age structure, proportionate mixing, and cross-immunity, J. Math.Biol. Vol. 27(1989), 233–258. https://doi.org/10.1007/BF00275810
- L. Esteva and C. Vargas, A model for dengue disease with variable human population, J. Math. Biol. Vol. 38(1999), 220–240. https://doi.org/10.1007/s002850050147
- Z. Feng and J.X. Velasco-Hernandez, Competitive exclusion in a vector-host model for the dengue fever, J. Math. Biol. Vol. 35(1997), 523–544. https://doi.org/10.1007/s002850050064
- J.M. Hyman and J. Li, An intuitive formulation for the reproductive number for the spread of diseases in heterogeneous populations, Math. Biosci. Vol. 167(2000), 65–86. https://doi.org/10.1016/S0025-5564(00)00025-0
- G.Z. Zeng, L.S. Chen, L. H. Sun, Complexity of an SIR epidemic dynamics model with impulsive vaccination control, Chaos, Solitons and Fractals Vol. 26(2005), 495–505. https://doi.org/10.1016/j.chaos.2005.01.021
- J. Hui, L.S. Chen, Impulsive vaccination of SIR epidemic models with nonlinear incidence rates, Discrete and Continuous Dynamical Systems, Series B Vol. 3(2004), 595–606.
- B. Shulgin, L. Stone, Z. Agur, Pulse vaccination strategy in the sir epidemic model, Bull. Math. Biol. Vol. 60(1998), 1–26. https://doi.org/10.1006/bulm.1997.0010
- H.W. Hethcote, M.A. Lewis, P. Van Den Driessche, An epidemiological model with delay and a nonlinear incidence rate, J. Math. Biol. Vol. 27(1989), 49-64. https://doi.org/10.1007/BF00276080
- H.W. Hethcote and P. Van Den Driessche, Some epidemiological models with nonlinear incidence, J. Math. Biol. Vol. 29(1991), 271–287. https://doi.org/10.1007/BF00160539
- H.W. Hethcote, The mathematics of infectious diseases, SIAM Rev. Vol. 42(2000), No.4, 599–653. https://doi.org/10.1137/S0036144500371907
- Y.N. Xiao and Lansun Chen, An SIS epidemic model with stage structure and a delay, Acta Math. Appl. Sinica, English series Vol. 18(2002), 607–618. https://doi.org/10.1007/s102550200063
- J.M. Hyman, J. Li, E.A. Stanley, The differential infectivity and staged progression models for the transmission of HIV, Math. Biosci. Vol. 155(1999), 77–109. https://doi.org/10.1016/S0025-5564(98)10057-3
- H. Hethcote and P. van den Driessche, An SIS epidemic model with variable population size and a delay, J. Math. Biol. Vol. 34(1995), 177-194. https://doi.org/10.1007/BF00178772
- M.Y. Li, H.L. Smith, L.C.Wang, Global dynamics of an SEIR epidemic model with vertical transmission, SIAM J. Appl. Math., Vol. 62(2001), No.1, 58–69. https://doi.org/10.1137/S0036139999359860
- W.M. Liu, S. A. Levin, Y. Isawa, Influence of nonlinear incidence rates upon the behaviour of SIRS epidemiological models, J. Math. Biol. Vol. 23(1986), 187–204. https://doi.org/10.1007/BF00276956
- W.M. Liu, H. W. Hethcote and S. A. Levin, Dynamical behavior of epidemiological models with nonlinear incidence rates, J. Math. Biol. Vol. 25(1987), 359–380. https://doi.org/10.1007/BF00277162
- W.R. Derrick, P. van den Driessche, A disease transmission model in a nonconstant population, J. Math. Biol. Vol. 31(1993), 495-512.
- W.R. Derrick, P. van den Driessche, Homoclinic orbits in a disease transmission model with nonlinear incidence and nonconstant population, Discrete Contin. Dyn. Syst. Ser. B Vol. 3(2003), 299–309.
- S.G. Ruan, W.D. Wang, Dynamical behavior of an epidemic model with a nonlinear incidence rate, J. Diff. Equat. Vol. 188(2003), 135–163. https://doi.org/10.1016/S0022-0396(02)00089-X
- A.B. Gumel et al., Modelling strategies for controlling SARS outbreaks, Proc. R. Soc. Lond. B Vol. 271(2004), 2223–2232.
- G.M. Leung et al., The impact of community psychological response on outbreak control for severe acute respiratory syndrome in Hong Kong, J. Epidemiol. Community Health Vol. 57(2003), 857–863. https://doi.org/10.1136/jech.57.11.857
- D.M. Xiao, S. G Ruan, Global Analysis of an Epidemic Model with Nonmonotone Incidence Rate, Mathematical Biosciences Vol. 208(2007), 419–429 https://doi.org/10.1016/j.mbs.2006.09.025
- A. Halany, Differential Equations, Academic Press, New York, 1966.
- Z.L. Agur et al., Pulse mass measles vaccination across age cohorts, Proc. National Acad Scz, USA. Vol. 90(1993), 11698–11702.
- A.B. Sabin, Measles, killer of millions in developing countries: Strategies of elimination and continuation control, Eur. J. Epidemiol. Vol. 7(1991), 1–22.
- C.A. DeQuadros, J. K. Andrus, J. M. Olive, Eradication of the poliomyelitis, Progress, The American Pediatric Infectious Disease Journal Vol. 10(1991), No.3, 222–229.
- M. Ramsay, N. Gay, E. Miller, The epidemiology of measles in England and Wales: Rationale for 1994 nation vaccination campaign, Communicable Disease Report Vol. 4(1994), No.12, 141–146.
- S.J. Gao, L.S. Chen, J.J. Nieto, A. Torres, Analysis of a delayed epidemic model with pulse vaccination and saturation incidence, Vaccine Vol. 24(2006), 6037–6045. https://doi.org/10.1016/j.vaccine.2006.05.018
- D. Nokes, J. Swinton, The control of childhood viral infections by pulse vaccination, IMA J. Math. AppI. Biol. Med. Vol. 12(1995), 29–53. https://doi.org/10.1093/imammb/12.1.29
- XiaoDong Lin, Josephw-H.So., Global stability of the endemic equilibrium and uniform persistence in epidemic models with subpopulations, J. Austral. Math. Soc. Ser. B Vol. 34(1994), 282–295. https://doi.org/10.1017/S0334270000008900
- V. Lakshmikantham, D. D. Bainov, P. S. Simeonov, Theory of Impulsive Differential Equations, World Scientific, Singapore, 1989.
- D. D. Bainov, P. S. Simeonov, Impulsive Differential Equations: Periodic Solutions and Applications, Longman, London, 1993.
- V. Hutson, K. Schmitt, Permanence in dynamical systems, Math. Biosci. Vol. 111(1992), 1-71. https://doi.org/10.1016/0025-5564(92)90078-B
- P. Waltman, A brief survey of persistence in dynamical systems. Delay Differential Equations and Dynamical Systems (S. Busenberg and M. Martelli, eds.), 31-40. Lecture Notes in Mathematics 1475, Springer, New York, 1991.
- X.Q. Zhao, Uniform persistence and periodic coexistence states in infinite–dimensional periodic semiflows with applications, Canad. Appl. Math. Quart. Vol. 3(1995), 473–495.