-
1
-
-
0021984692
-
Stability of the endemic equilibrium in epidemic models with subpopulations
-
Hethcote H.W., and Thieme H.R. Stability of the endemic equilibrium in epidemic models with subpopulations. Math. Biosci. 75 2 (1985) 205
-
(1985)
Math. Biosci.
, vol.75
, Issue.2
, pp. 205
-
-
Hethcote, H.W.1
Thieme, H.R.2
-
2
-
-
0034486891
-
The mathematics of infectious diseases
-
Hethcote H.W. The mathematics of infectious diseases. SIAM Rev. 42 4 (2000) 599
-
(2000)
SIAM Rev.
, vol.42
, Issue.4
, pp. 599
-
-
Hethcote, H.W.1
-
3
-
-
0017226769
-
A deterministic model for gonorrhea in a nonhomogeneous population
-
Lajmanovich A., and Yorke J.A. A deterministic model for gonorrhea in a nonhomogeneous population. Math. Biosci. 28 (1976) 221
-
(1976)
Math. Biosci.
, vol.28
, pp. 221
-
-
Lajmanovich, A.1
Yorke, J.A.2
-
4
-
-
0028989477
-
A structured epidemic model incorporating geographic mobility among regions
-
Sattenspiel L., and Dietz K. A structured epidemic model incorporating geographic mobility among regions. Math. Biosci. 128 1-2 (1995) 71
-
(1995)
Math. Biosci.
, vol.128
, Issue.1-2
, pp. 71
-
-
Sattenspiel, L.1
Dietz, K.2
-
5
-
-
0032409489
-
A two-patch model of Gambian sleeping sickness: application to vector control strategies in a village and plantations
-
Chalvet-Monfray K., Artzrouni M., Gouteux J.P., Auger P., and Sabatier P. A two-patch model of Gambian sleeping sickness: application to vector control strategies in a village and plantations. Acta Biotheor. 46 (1998) 207
-
(1998)
Acta Biotheor.
, vol.46
, pp. 207
-
-
Chalvet-Monfray, K.1
Artzrouni, M.2
Gouteux, J.P.3
Auger, P.4
Sabatier, P.5
-
6
-
-
0036482783
-
The metapopulation dynamics of an infectious disease: tuberculosis in possums
-
Fulford G.R., Roberts M.G., and Heesterbeek J.A.P. The metapopulation dynamics of an infectious disease: tuberculosis in possums. Theor. Popul. Biol. 61 (2002) 15
-
(2002)
Theor. Popul. Biol.
, vol.61
, pp. 15
-
-
Fulford, G.R.1
Roberts, M.G.2
Heesterbeek, J.A.P.3
-
7
-
-
0141850338
-
Threshold of disease transmission in a patchy environment
-
Wang W., and Mulone G. Threshold of disease transmission in a patchy environment. J. Math. Anal. Appl. 285 (2002) 321
-
(2002)
J. Math. Anal. Appl.
, vol.285
, pp. 321
-
-
Wang, W.1
Mulone, G.2
-
9
-
-
27844451285
-
The basic reproduction number in a multi-city compartmental model
-
Arino J., and van den Driessche P. The basic reproduction number in a multi-city compartmental model. Lect. Notes Contrib. Inf. Sci. 294 (2003) 135
-
(2003)
Lect. Notes Contrib. Inf. Sci.
, vol.294
, pp. 135
-
-
Arino, J.1
van den Driessche, P.2
-
11
-
-
0038042431
-
Disease propagation in connected host population with density-dependant dynamics: the case of the feline leukemia virus
-
Fromont E., Pontier D., and Langlais M. Disease propagation in connected host population with density-dependant dynamics: the case of the feline leukemia virus. J. Theoret. Biol. 223 (2003) 465
-
(2003)
J. Theoret. Biol.
, vol.223
, pp. 465
-
-
Fromont, E.1
Pontier, D.2
Langlais, M.3
-
12
-
-
0034277972
-
Local stability analysis of spatially homogeneous solutions of multi-patch systems
-
Jansen V., and Lloyd A.L. Local stability analysis of spatially homogeneous solutions of multi-patch systems. J. Math. Biol. 41 (2004) 232
-
(2004)
J. Math. Biol.
, vol.41
, pp. 232
-
-
Jansen, V.1
Lloyd, A.L.2
-
13
-
-
0842324733
-
Spatiotemporal dynamics of epidemics: synchrony in metapopulation models
-
Lloyd A.L., and Jansen V. Spatiotemporal dynamics of epidemics: synchrony in metapopulation models. Math. Biosci. 188 (2004) 1
-
(2004)
Math. Biosci.
, vol.188
, pp. 1
-
-
Lloyd, A.L.1
Jansen, V.2
-
14
-
-
2542463400
-
An epidemic model in a patchy environment
-
Wang W., and Zhao X.-Q. An epidemic model in a patchy environment. Math. Biosci. 190 (2004) 97
-
(2004)
Math. Biosci.
, vol.190
, pp. 97
-
-
Wang, W.1
Zhao, X.-Q.2
-
15
-
-
19044385162
-
The effect of population dispersal on the spread of a disease
-
Jin Y., and Wang W. The effect of population dispersal on the spread of a disease. J. Math. Anal. Appl. 308 (2005) 343
-
(2005)
J. Math. Anal. Appl.
, vol.308
, pp. 343
-
-
Jin, Y.1
Wang, W.2
-
16
-
-
33747161363
-
The effect of global travel on the spread of sars
-
Ruan S., Wang W., and Levin S.A. The effect of global travel on the spread of sars. Math. Biosci. Eng. 3 1 (2006) 205
-
(2006)
Math. Biosci. Eng.
, vol.3
, Issue.1
, pp. 205
-
-
Ruan, S.1
Wang, W.2
Levin, S.A.3
-
17
-
-
33847316873
-
Quarantine in a multi-species epidemics model with spatial dynamics
-
Arino J., Jordan R., and van den Driessche P. Quarantine in a multi-species epidemics model with spatial dynamics. Math. Biosci. 206 (2006) 46
-
(2006)
Math. Biosci.
, vol.206
, pp. 46
-
-
Arino, J.1
Jordan, R.2
van den Driessche, P.3
-
18
-
-
25144517817
-
A multi-species epidemic model with spatial dynamics
-
Arino J., Davis J.R., Hartley D., Jordan R., Miller J., and van den Driessche P. A multi-species epidemic model with spatial dynamics. Math. Med. Biol. 22 (2005) 129
-
(2005)
Math. Med. Biol.
, vol.22
, pp. 129
-
-
Arino, J.1
Davis, J.R.2
Hartley, D.3
Jordan, R.4
Miller, J.5
van den Driessche, P.6
-
19
-
-
56049107341
-
-
J. Arino, P. van den Driessche, Disease spread in metapopulations, in: X.-O Zhao, X. Zou (Eds.), Nonlinear Dynamics and Evolution Equations, vol. 48, Fields Inst. Commun. AMS, Providence, RI, 2006, pp. 1.
-
J. Arino, P. van den Driessche, Disease spread in metapopulations, in: X.-O Zhao, X. Zou (Eds.), Nonlinear Dynamics and Evolution Equations, vol. 48, Fields Inst. Commun. AMS, Providence, RI, 2006, pp. 1.
-
-
-
-
20
-
-
35348983980
-
Asymptotic profiles of the steady states for an SIS epidemic patch model
-
Allen L.J.S., Bolker B.M., Lou Y., and Nevai A.L. Asymptotic profiles of the steady states for an SIS epidemic patch model. SIAM J. Appl. Math. 67 5 (2007) 283
-
(2007)
SIAM J. Appl. Math.
, vol.67
, Issue.5
, pp. 283
-
-
Allen, L.J.S.1
Bolker, B.M.2
Lou, Y.3
Nevai, A.L.4
-
23
-
-
34250449242
-
Deterministic models of epidemics for a territory with a transport network
-
Baroyan O.V., and Rvachev L.A. Deterministic models of epidemics for a territory with a transport network. Cybern. Syst. Anal. 3 3 (1967) 67
-
(1967)
Cybern. Syst. Anal.
, vol.3
, Issue.3
, pp. 67
-
-
Baroyan, O.V.1
Rvachev, L.A.2
-
25
-
-
0027555111
-
Qualitative theory of compartmental systems
-
Jacquez J.A., and Simon C.P. Qualitative theory of compartmental systems. SIAM Rev. 35 1 (1993) 43
-
(1993)
SIAM Rev.
, vol.35
, Issue.1
, pp. 43
-
-
Jacquez, J.A.1
Simon, C.P.2
-
26
-
-
0003270351
-
Nonnegative matrices in the mathematical sciences
-
Society for Industrial and Applied Mathematics (SIAM), Philadelphia, PA
-
Berman A., and Plemmons R.J. Nonnegative matrices in the mathematical sciences. Classics in Applied Mathematics vol. 9 (1994), Society for Industrial and Applied Mathematics (SIAM), Philadelphia, PA 340
-
(1994)
Classics in Applied Mathematics
, vol.9
, pp. 340
-
-
Berman, A.1
Plemmons, R.J.2
-
27
-
-
0019049056
-
Decomposition techniques for large-scale systems with nonadditive interactions: Stability and stabilizability
-
Vidyasagar M. Decomposition techniques for large-scale systems with nonadditive interactions: Stability and stabilizability. IEEE Trans. Autom. Control 25 (1980) 773
-
(1980)
IEEE Trans. Autom. Control
, vol.25
, pp. 773
-
-
Vidyasagar, M.1
-
28
-
-
56049107103
-
-
H.L. Smith, Monotone Dynamical Systems, An Introduction to the Theory of Competitive and Cooperative Systems, AMS, Providence, RI, 1995.
-
H.L. Smith, Monotone Dynamical Systems, An Introduction to the Theory of Competitive and Cooperative Systems, AMS, Providence, RI, 1995.
-
-
-
-
29
-
-
0000885375
-
Systems of differential equations that are competitive or cooperative i: limit sets
-
Hirsch M.W. Systems of differential equations that are competitive or cooperative i: limit sets. SIAM J. Math. Anal. 13 2 (1982) 167
-
(1982)
SIAM J. Math. Anal.
, vol.13
, Issue.2
, pp. 167
-
-
Hirsch, M.W.1
-
30
-
-
84968480336
-
The dynamical system approach to differential equations
-
Hirsch M.W. The dynamical system approach to differential equations. Bull. AMS 11 1 (1984) 1
-
(1984)
Bull. AMS
, vol.11
, Issue.1
, pp. 1
-
-
Hirsch, M.W.1
-
31
-
-
0001176145
-
Systems of differential equations that are competitive or cooperative ii: convergence almost everywhere
-
Hirsch M.W. Systems of differential equations that are competitive or cooperative ii: convergence almost everywhere. SIAM J. Math. Anal. 16 3 (1985) 423
-
(1985)
SIAM J. Math. Anal.
, vol.16
, Issue.3
, pp. 423
-
-
Hirsch, M.W.1
-
32
-
-
84956106116
-
Systems of differential equations that are competitive or cooperative iii: Competing species
-
Hirsch M.W. Systems of differential equations that are competitive or cooperative iii: Competing species. Nonlinearity 1 (1988) 51
-
(1988)
Nonlinearity
, vol.1
, pp. 51
-
-
Hirsch, M.W.1
-
33
-
-
56049086905
-
Systems of differential equations that are competitive or cooperative. iv: structural stability in three-dimensional systems
-
Hirsch M.W. Systems of differential equations that are competitive or cooperative. iv: structural stability in three-dimensional systems. SIAM J. Appl. Math. 21 (1990) 1125
-
(1990)
SIAM J. Appl. Math.
, vol.21
, pp. 1125
-
-
Hirsch, M.W.1
-
35
-
-
0036845274
-
reproduction numbers and sub-threshold endemic equilibria for compartmental models of disease transmission
-
van den Driessche P., and Watmough J. reproduction numbers and sub-threshold endemic equilibria for compartmental models of disease transmission. Math. Biosci. 180 (2002) 29
-
(2002)
Math. Biosci.
, vol.180
, pp. 29
-
-
van den Driessche, P.1
Watmough, J.2
-
36
-
-
0002340103
-
Factorization and normalized iterative methods
-
Langer R.E. (Ed), University of Wisconsin
-
Varga R.S. Factorization and normalized iterative methods. In: Langer R.E. (Ed). Boundary Problems in Differential Equations (1960), University of Wisconsin 121
-
(1960)
Boundary Problems in Differential Equations
, pp. 121
-
-
Varga, R.S.1
-
38
-
-
56049087572
-
-
J.P. LaSalle, The stability of dynamical systems, in: Society for Industrial and Applied Mathematics, Philadelphia, PA, 1976, With an appendix: "Limiting equations and stability of nonautonomous ordinary differential equations" by Z. Artstein, Regional Conference Series in Applied Mathematics.
-
J.P. LaSalle, The stability of dynamical systems, in: Society for Industrial and Applied Mathematics, Philadelphia, PA, 1976, With an appendix: "Limiting equations and stability of nonautonomous ordinary differential equations" by Z. Artstein, Regional Conference Series in Applied Mathematics.
-
-
-
-
39
-
-
56049088808
-
-
O. Diekmann, J.A.P. Heesterbeek, Mathematical epidemiology of infectious diseases, in: Wiley Series in Mathematical and Computational Biology, John Wiley & Sons Ltd., Chichester, 2000, Model Building, Analysis and Interpretation.
-
O. Diekmann, J.A.P. Heesterbeek, Mathematical epidemiology of infectious diseases, in: Wiley Series in Mathematical and Computational Biology, John Wiley & Sons Ltd., Chichester, 2000, Model Building, Analysis and Interpretation.
-
-
-
-
40
-
-
0032482432
-
Collective dynamics of 'small world' networks
-
Watts D.J., and Strogatz S.H. Collective dynamics of 'small world' networks. Nature 393 (1998) 440
-
(1998)
Nature
, vol.393
, pp. 440
-
-
Watts, D.J.1
Strogatz, S.H.2
-
41
-
-
0038718854
-
The structure and function of complex networks
-
J Newman M.E. The structure and function of complex networks. SIAM Rev. 45 (2003) 167
-
(2003)
SIAM Rev.
, vol.45
, pp. 167
-
-
J Newman, M.E.1
-
42
-
-
0029055539
-
A core group model for disease transmission
-
Hadeler K.P., and Castillo-Chavez C. A core group model for disease transmission. Math. Biosci. 128 (1995) 41
-
(1995)
Math. Biosci.
, vol.128
, pp. 41
-
-
Hadeler, K.P.1
Castillo-Chavez, C.2
-
44
-
-
0026846319
-
Reproduction numbers and the stability of equilibria of SI models for heterogeneous populations
-
Simon C.P., and Jacquez J.A. Reproduction numbers and the stability of equilibria of SI models for heterogeneous populations. SIAM J. Appl. Math. 52 2 (1992) 541
-
(1992)
SIAM J. Appl. Math.
, vol.52
, Issue.2
, pp. 541
-
-
Simon, C.P.1
Jacquez, J.A.2
-
45
-
-
0023705860
-
The spread and persistence of infectious diseases in structured populations
-
Nonlinearity in Biology and Medicine (Los Alamos, NM, 1987)
-
Sattenspiel L., and Simon C.P. The spread and persistence of infectious diseases in structured populations. Math. Biosci. 90 1-2 (1988) 341 Nonlinearity in Biology and Medicine (Los Alamos, NM, 1987)
-
(1988)
Math. Biosci.
, vol.90
, Issue.1-2
, pp. 341
-
-
Sattenspiel, L.1
Simon, C.P.2
-
47
-
-
0011719231
-
Computer modelling of influenza epidemics for the whole country (ussr)
-
Baroyan O.V., Rvachev L.A., Basilevsky U.V., Ermakov V.V., Frank K.D., Rvachev M.A., and Shaskov V.A. Computer modelling of influenza epidemics for the whole country (ussr). Adv. Appl. Prob. 3 (1971) 224
-
(1971)
Adv. Appl. Prob.
, vol.3
, pp. 224
-
-
Baroyan, O.V.1
Rvachev, L.A.2
Basilevsky, U.V.3
Ermakov, V.V.4
Frank, K.D.5
Rvachev, M.A.6
Shaskov, V.A.7
-
49
-
-
0020735310
-
Endemic disease in environments with spatially heterogeneous host populations
-
Post W.M., DeAngelis D.L., and Travis C.C. Endemic disease in environments with spatially heterogeneous host populations. Math. Biosci. 63 2 (1983) 289
-
(1983)
Math. Biosci.
, vol.63
, Issue.2
, pp. 289
-
-
Post, W.M.1
DeAngelis, D.L.2
Travis, C.C.3
-
50
-
-
0029980587
-
Spatial heterogeneity in epidemic models
-
Lloyd A.L., and May R.M. Spatial heterogeneity in epidemic models. J. Theor. Biol. 179 (1996) 1
-
(1996)
J. Theor. Biol.
, vol.179
, pp. 1
-
-
Lloyd, A.L.1
May, R.M.2
-
51
-
-
0034974493
-
Models of infectious diseases in spatially heterogeneous environments
-
Rodríguez D., and Torres-Sorando L. Models of infectious diseases in spatially heterogeneous environments. Bull. Math. Biol. 63 (2001) 547-571
-
(2001)
Bull. Math. Biol.
, vol.63
, pp. 547-571
-
-
Rodríguez, D.1
Torres-Sorando, L.2
|