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Long time behavior of some epidemic models
1. | Department of Mathematics, Purdue University, 150 N. University St., West Lafayette, IN 47907, United States |
References:
[1] |
S. Busenberg and C. Castillo-Chavez, Interaction, pair formation and force of infection terms in sexually transmitted diseases, Mathematical and Statistical Approaches to AIDS Epidemiology, 289-300, Lecture Notes in Biomath., 83, Springer, Berlin, 1989. |
[2] |
C. Castillo-Chavez and H. R. Thieme, On the role of variable infectivity in the dynamics of the human immunodeficiency virus epidemic, Mathematical and Statistical Approaches to AIDS Epidemiology, 157-176, Lecture Notes in Biomath., 83, Springer, Berlin, 1989. |
[3] |
P. C. Fife, Asymptotic States for Equations of Reaction and Diffusion, Bull. AMS, 84 (1978), 693-726.
doi: 10.1090/S0002-9904-1978-14502-9. |
[4] |
M. E. Gurtin and R. C. MacCamy, On the diffusion of biological populations, Math. Biosci., 33 (1977), 35-49.
doi: 10.1016/0025-5564(77)90062-1. |
[5] |
W. S. C. Gurney and R. M. Nisbet, The Regulation of Inhomogeneous Populations, J. Theor. Biol., 52 (1975), 441-457.
doi: 10.1016/0022-5193(75)90011-9. |
[6] |
M. Iannelli, R. Loro, F. A. Milner, A. Pugliese and G. Rabbiolo, An AIDS model with distributed incubation and variable infectiousness: applications to i.v. drug users in Latium, Italy, Eur. J. Epidemiol., 8 (1992), 585-593.
doi: 10.1007/BF00146381. |
[7] |
W. O. Kermack and A. G. McKendrick, A Contribution to the Mathematical Theory of Epidemics, Proc. Roy. Soc. Lond. A, 115 (1927), 700-721
doi: 10.1098/rspa.1927.0118. |
[8] |
T. G. Kurtz and J. Xiong, Particle representation for a class of nonlinear SPDEs, Stoch. Proc. and Their Appl., 83 (1999), 103-126.
doi: 10.1016/S0304-4149(99)00024-1. |
[9] |
F. A. Milner and R. Zhao, S-I-R Model with Directed Spatial Diffusion, Mathematical Population Studies, 15 (2008), 160-181.
doi: 10.1080/08898480802221889. |
[10] |
M. Mimura and M. Yamaguti, Pattern formation in interacting and diffusing systems in population biology, Adv. Biophys., 15 (1982), 19-65.
doi: 10.1016/0065-227X(82)90004-1. |
[11] |
B. K. Oksendal, "Stochastic Differential Equations: An Introduction with Applications," 6th edition, Springer-Verlag, Berlin, 2003. |
[12] |
G. F. Webb, A reaction-diffusion model for a deterministic diffusive epidemic, J. Math. Anal. Appl., 84 (1981), 150-161.
doi: 10.1016/0022-247X(81)90156-6. |
show all references
References:
[1] |
S. Busenberg and C. Castillo-Chavez, Interaction, pair formation and force of infection terms in sexually transmitted diseases, Mathematical and Statistical Approaches to AIDS Epidemiology, 289-300, Lecture Notes in Biomath., 83, Springer, Berlin, 1989. |
[2] |
C. Castillo-Chavez and H. R. Thieme, On the role of variable infectivity in the dynamics of the human immunodeficiency virus epidemic, Mathematical and Statistical Approaches to AIDS Epidemiology, 157-176, Lecture Notes in Biomath., 83, Springer, Berlin, 1989. |
[3] |
P. C. Fife, Asymptotic States for Equations of Reaction and Diffusion, Bull. AMS, 84 (1978), 693-726.
doi: 10.1090/S0002-9904-1978-14502-9. |
[4] |
M. E. Gurtin and R. C. MacCamy, On the diffusion of biological populations, Math. Biosci., 33 (1977), 35-49.
doi: 10.1016/0025-5564(77)90062-1. |
[5] |
W. S. C. Gurney and R. M. Nisbet, The Regulation of Inhomogeneous Populations, J. Theor. Biol., 52 (1975), 441-457.
doi: 10.1016/0022-5193(75)90011-9. |
[6] |
M. Iannelli, R. Loro, F. A. Milner, A. Pugliese and G. Rabbiolo, An AIDS model with distributed incubation and variable infectiousness: applications to i.v. drug users in Latium, Italy, Eur. J. Epidemiol., 8 (1992), 585-593.
doi: 10.1007/BF00146381. |
[7] |
W. O. Kermack and A. G. McKendrick, A Contribution to the Mathematical Theory of Epidemics, Proc. Roy. Soc. Lond. A, 115 (1927), 700-721
doi: 10.1098/rspa.1927.0118. |
[8] |
T. G. Kurtz and J. Xiong, Particle representation for a class of nonlinear SPDEs, Stoch. Proc. and Their Appl., 83 (1999), 103-126.
doi: 10.1016/S0304-4149(99)00024-1. |
[9] |
F. A. Milner and R. Zhao, S-I-R Model with Directed Spatial Diffusion, Mathematical Population Studies, 15 (2008), 160-181.
doi: 10.1080/08898480802221889. |
[10] |
M. Mimura and M. Yamaguti, Pattern formation in interacting and diffusing systems in population biology, Adv. Biophys., 15 (1982), 19-65.
doi: 10.1016/0065-227X(82)90004-1. |
[11] |
B. K. Oksendal, "Stochastic Differential Equations: An Introduction with Applications," 6th edition, Springer-Verlag, Berlin, 2003. |
[12] |
G. F. Webb, A reaction-diffusion model for a deterministic diffusive epidemic, J. Math. Anal. Appl., 84 (1981), 150-161.
doi: 10.1016/0022-247X(81)90156-6. |
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