Dispersal, disease and life-history evolution
Tài liệu tham khảo
Allen, 2000, Comparison of deterministic and stochastic SIS and SIR models in discrete time, Math. Biosci., 163, 1, 10.1016/S0025-5564(99)00047-4
Allen, 1994, Some discrete-time SI, SIR and SIS epidemic models, Math. Biosci., 124, 83, 10.1016/0025-5564(94)90025-6
Anderson, 1992
R. Arreola, A. Crossa, M.C. Velasco, Discrete-time S–E–I–S models with dispersal between two patches, Biometric Department, MTBI Cornell University Technical Report, 2000
Bailey, 1963, The simple stochastic epidemic: a complete solution in terms of known functions, Biometrika, 50, 235, 10.1093/biomet/50.3-4.235
Baroyan, 1969, An attempt at large-scale influenza epidemic modelling by means of a computer, Bull. Int. Epidemiol. Assoc., 18, 22
Baroyan, 1967, Deterministic epidemic models for a territory with a transport network, Kibernetika, 3, 67
Baroyan, 1978, Model of influenza epidemics spread through the territory of Bulgaria and its significance, J. Epidemiol. Microbiol. Infect. Dis., Sofia, 15, 168
V.O. Baroyan, L.A. Rvachev, Y.G. Ivannikov, Modelling and Prediction of Influenza Epidemics in USSR, Moscow, Gamelei Institute of Epidemiology and Microbiology, 1977
J.H. Barrera, A. Cintron-Arias, N. Davidenko, L.R. Denogean, S.R. Franco-Gonzalez, Dynamics of a two-dimensional discrete-time SIS model, Biometric Department, MTBI Cornell University Technical Report, 1999
J. Best, V. Pasour, N.Tisch, C. Castillo-Chavez, Delayed density dependence and the dynamic consequences of dispersal between patches (preprint, 2001)
F. Brauer, C. Castillo-Chavez, Mathematical Models in Population Biology and Epidemiology, Texts in Applied Mathematics, Springer, New York (2001)
Castillo-Chavez, 1998, El transporte público y la dinámica de la tuberculosis a nivel poblacional. A portaciones mathematicas, Ser. Commun., 22, 209
Castillo-Chavez, 1988, The role of long periods of infectiousness in the dynamics of acquired immunodeficiency syndrome (AIDS), J. Math. Biol., 27, 373, 10.1007/BF00290636
Castillo-Chavez, 1988, Cross immunity in the dynamics of homogeneous and heterogeneous populations, 303
C. Castillo-Chavez, S. Blower, P. van den Driessche, D. Kirschner, A.-A. Yakubu, in: Mathematical Approaches For Emerging and Reemerging Infectious Diseases: An Introduction to Models, Methods and Theory, Springer, New York, in press
C. Castillo-Chavez, A-A. Yakubu, Discrete-time S–I–S models with complex dynamics, in: Proc. WCNA 2000, Nonlinear Anal. TMA, in press
C. Castillo-Chavez, A-A. Yakubu, Discrete-time S–I–S models with simple and complex population dynamics, in: C. Castillo-Chavez, S. Blower, P. van den Driessche, D. Kirschner, A.-A. Yakubu (Eds.), Mathematical Approaches For Emerging and Reemerging Infectious Diseases: An Introduction to Models, Methods and Theory, Springer, Berlin, in press
C. Castillo-Chavez, A.A. Yakubu, Intraspecific competition, dispersal and disease dynamics in discrete-time patchy environments, in: C. Castillo-Chavez, S. Blower, P. van den Driessche, D. Kirschner, A-A. Yakubu (Eds.), Mathematical Approaches For Emerging and Reemerging Infectious Diseases: An Introduction to Models, Methods and Theory, Springer, Berlin, in press
D. Cohen, S.A. Levin, The interaction between dispersal and dormancy strategies in varying and heterogeneous environments, in: E. Teramoto, M. Yamaguti, Mathematical Topics in Population Biology, Morphogenesis and Neurosciences, Proc. Kyoto, Springer, Berlin, 1985, 1987, p. 110
Cooke, 1973, Some equations modelling growth processes and gonorrhea epidemics, Math. Biosci., 16, 75, 10.1016/0025-5564(73)90046-1
Cull, 1986, Local and global stability for population models, Biol. Cybern., 54, 141, 10.1007/BF00356852
Doebeli, 1995, Dispersal and dynamics, Theoret. Popul. Biol., 47, 82, 10.1006/tpbi.1995.1004
Doebeli, 1997, Evolution of dispersal rates in metapopulation models: branching and cylic dynamics in phenotype space, Evolution, 51, 1730, 10.2307/2410996
Dushoff, 1998, Backwards bifurcations and catastrophe in simple models of fatal diseases, J. Math. Biol., 36, 227, 10.1007/s002850050099
Ewald, 1994
Feng, 2000, A model for tuberculosis with exogenous reinfection, Theoret. Popul. Biol., 57, 235, 10.1006/tpbi.2000.1451
J. Flores, C. Garcia, C.W. Melgar, C. Saenz, Dynamics of Rubella virus in populations with different vaccination policies, Biometric Department (BU-1424-M), MTBI Cornell University Technical Report, 1997
P.A. Gonzalez, R. Saenz, B. Sanchez, The influence of dispersal between two patches on the dynamics of a disease. Biometric Department, MTBI Cornell University Technical Report, 2000
Hadeler, 1995, A core group model for disease transmission, Math. Biosci., 128, 41, 10.1016/0025-5564(94)00066-9
Hadeler, 1997, Backward bifurcation in epidemic control, Math. Biosci., 146, 15, 10.1016/S0025-5564(97)00027-8
M.P. Hassell, R.C. Anderson, J.E. Cohen et al., Impact of diseases on host populations (group report), in: R.M. Anderson, R.M. May (Eds.), Population Biology of Infectious diseases, Springer, New York, 1982
Hastings, 1993, Complex interactions between dispersal and dynamics: lessons from coupled logistic equations, Ecology, 74, 1362, 10.2307/1940066
J.C. Holmes, W.M. Bethel, Modification of intermediate host behaviour by parasites, in: E.V. Canning, C.A. Wright (Eds.), Behavioural aspects of parasite transmission, Zool. J. Linn. Soc. (Suppl. 1) 51 (1972) 123
Huang, 1992, Stabilitiy and bifurcation for a multiple-group model for the dynamics of HIV/AIDS transmission, SIAM J. Appl. Math., 52, 835, 10.1137/0152047
Kribs-Zaleta, 2000, A simple vaccination model with a backward bifurcation, Math. Biosci., 164, 183, 10.1016/S0025-5564(00)00003-1
S.A. Levin, Encyclopedia of Biodiversity, in: S.A. Levin (Ed.), vol. 1, Academic Press, New York, 2000
Levin, 1974, Disturbance, patch formation and community structure, Proc. Nat. Acad. Sci. (USA), 71, 2744, 10.1073/pnas.71.7.2744
May, 1977, Simple mathematical models with very complicated dynamics, Nature, 261, 459, 10.1038/261459a0
May, 1974
McClusky, 1998, Bendixson-Dulac criteria for difference equations, J. Dyn. Diff. Eq., 10, 567, 10.1023/A:1022677008393
Nåsell, 1996, The quasi-stationary distribution of the closed endemic SIS model, Adv. Appl. Prob., 28, 895, 10.2307/1428186
Rvachev, 1968, Computer modelling experiment on large-scale epidemic, Dok. USSR Acad. Sci., 180, 294
Rvachev, 1985, A mathematical model for the global spread of influenza, Math. Biosci., 75, 1, 10.1016/0025-5564(85)90063-X
Thieme, 1992, Convergence results and a Poincaré–Bendixson trichotomy for asymptotically autonomous differential equations, J. Math. Biol., 30, 755, 10.1007/BF00173267
van den Driessche, 2000, A simple SIS epidemic model with a backward bifurcation, J. Math. Biol., 40, 525, 10.1007/s002850000032
Youmans, 1985
Zhao, 1996, Asymptotic behavior for asymptotically periodic semiflows with applications, Commun. Appl. Nonlinear Anal., 3, 43