-
1
-
-
84868312013
-
Extinction thresholds in deterministic and stochastic epidemic models
-
Allen L.J.S., Lahodny G.E. Extinction thresholds in deterministic and stochastic epidemic models. Journal of Biological Dynamics 2012, 6:590.
-
(2012)
Journal of Biological Dynamics
, vol.6
, pp. 590
-
-
Allen, L.J.S.1
Lahodny, G.E.2
-
4
-
-
0020763656
-
The threshold behaviour of epidemic models
-
Ball F. The threshold behaviour of epidemic models. Journal of Applied Probability 1983, 20:227.
-
(1983)
Journal of Applied Probability
, vol.20
, pp. 227
-
-
Ball, F.1
-
5
-
-
0026360189
-
Dynamic population epidemic models
-
Ball F. Dynamic population epidemic models. Mathematical Biosciences 1983, 107:299.
-
(1983)
Mathematical Biosciences
, vol.107
, pp. 299
-
-
Ball, F.1
-
7
-
-
0011485892
-
The relevance of stochastic models for large-scale epidemiological phenomena
-
Bartlett M.S. The relevance of stochastic models for large-scale epidemiological phenomena. Journal of the Royal Statistical Society Series C 1964, 13:2.
-
(1964)
Journal of the Royal Statistical Society Series C
, vol.13
, pp. 2
-
-
Bartlett, M.S.1
-
8
-
-
27944465693
-
A stochastic SIS infection model incorporating indirect transmission
-
Clancy D. A stochastic SIS infection model incorporating indirect transmission. Journal of Applied Probability 2005, 42:726.
-
(2005)
Journal of Applied Probability
, vol.42
, pp. 726
-
-
Clancy, D.1
-
10
-
-
0028683292
-
The net reproductive value and stability in matrix population models
-
Cushing J.M., Zhou Y. The net reproductive value and stability in matrix population models. Natural Resource Modeling 1994, 8:297.
-
(1994)
Natural Resource Modeling
, vol.8
, pp. 297
-
-
Cushing, J.M.1
Zhou, Y.2
-
13
-
-
34250697942
-
Epidemiological models with non-exponentially distributed disease stages and applications to disease control
-
Feng Z., Xu D., Zhao H. Epidemiological models with non-exponentially distributed disease stages and applications to disease control. Bulletin of Mathematical Biology 2007, 69:1511.
-
(2007)
Bulletin of Mathematical Biology
, vol.69
, pp. 1511
-
-
Feng, Z.1
Xu, D.2
Zhao, H.3
-
14
-
-
0040972073
-
A bivariate birth-death process which approximates to the spread of a disease involving a vector
-
Griffiths D.A. A bivariate birth-death process which approximates to the spread of a disease involving a vector. Journal of Applied Probability 1972, 9:65.
-
(1972)
Journal of Applied Probability
, vol.9
, pp. 65
-
-
Griffiths, D.A.1
-
15
-
-
0007632955
-
Multivariate birth-and-death processes as approximations to epidemic processes
-
Griffiths D.A. Multivariate birth-and-death processes as approximations to epidemic processes. Journal of Applied Probability 1973, 10:15.
-
(1973)
Journal of Applied Probability
, vol.10
, pp. 15
-
-
Griffiths, D.A.1
-
16
-
-
79954677689
-
The probability of extinction in a bovine respiratory syncytial virus epidemic model
-
Griffiths M., Greenhalgh D. The probability of extinction in a bovine respiratory syncytial virus epidemic model. Mathematical Biosciences 2011, 231:144.
-
(2011)
Mathematical Biosciences
, vol.231
, pp. 144
-
-
Griffiths, M.1
Greenhalgh, D.2
-
18
-
-
33847405628
-
The type-reproduction number T in models for infectious disease control
-
Heesterbeek J.A., Roberts M.G. The type-reproduction number T in models for infectious disease control. Mathematical Biosciences 2007, 206:3.
-
(2007)
Mathematical Biosciences
, vol.206
, pp. 3
-
-
Heesterbeek, J.A.1
Roberts, M.G.2
-
19
-
-
84864350554
-
On a new perspective of the basic reproduction number in heterogeneous environments
-
Inaba H. On a new perspective of the basic reproduction number in heterogeneous environments. Journal of Mathematical Biology 2012, 65:309.
-
(2012)
Journal of Mathematical Biology
, vol.65
, pp. 309
-
-
Inaba, H.1
-
20
-
-
0026360185
-
Reproduction number and thresholds in stochastic epidemic models I. Homogeneous populations
-
Jacquez J.A., O'Neill P. Reproduction number and thresholds in stochastic epidemic models I. Homogeneous populations. Mathematical Biosciences 1991, 107:161.
-
(1991)
Mathematical Biosciences
, vol.107
, pp. 161
-
-
Jacquez, J.A.1
O'Neill, P.2
-
22
-
-
0003730487
-
-
Academic Press, San Diego, New York, Boston
-
Karlin S., Taylor H.M. A First Course in Stochastic Processes 1975, Academic Press, San Diego, New York, Boston. second ed.
-
(1975)
A First Course in Stochastic Processes
-
-
Karlin, S.1
Taylor, H.M.2
-
23
-
-
0032518718
-
Effect of variability in infection period on the persistence and spatial spread of infectious diseases
-
Keeling M.J., Grenfell B.T. Effect of variability in infection period on the persistence and spatial spread of infectious diseases. Mathematical Biosciences 1998, 147:207.
-
(1998)
Mathematical Biosciences
, vol.147
, pp. 207
-
-
Keeling, M.J.1
Grenfell, B.T.2
-
25
-
-
0002232633
-
Solutions of ordinary differential equations as limits of pure jump Markov processes
-
Kurtz T.G. Solutions of ordinary differential equations as limits of pure jump Markov processes. Journal of Applied Probability 1970, 7:49.
-
(1970)
Journal of Applied Probability
, vol.7
, pp. 49
-
-
Kurtz, T.G.1
-
26
-
-
0001249058
-
Limit theorems for sequences of jump Markov processes approximating ordinary differential processes
-
Kurtz T.G. Limit theorems for sequences of jump Markov processes approximating ordinary differential processes. Journal of Applied Probability 1971, 8:344.
-
(1971)
Journal of Applied Probability
, vol.8
, pp. 344
-
-
Kurtz, T.G.1
-
27
-
-
0001455869
-
The relationship between stochastic and deterministic models for chemical reactions
-
Kurtz T.G. The relationship between stochastic and deterministic models for chemical reactions. Journal of Chemical Physics 1972, 57:2976.
-
(1972)
Journal of Chemical Physics
, vol.57
, pp. 2976
-
-
Kurtz, T.G.1
-
28
-
-
33646855146
-
A comparison of continuous and discrete-time West Nile virus models
-
Lewis M.A., Rencławowicz J., van den Driessche P., Wonham M. A comparison of continuous and discrete-time West Nile virus models. Bulletin of Mathematical Biology 2006, 68:491.
-
(2006)
Bulletin of Mathematical Biology
, vol.68
, pp. 491
-
-
Lewis, M.A.1
Rencławowicz, J.2
van den Driessche, P.3
Wonham, M.4
-
29
-
-
0036581212
-
Applications of Perron-Frobenius theory to population dynamics
-
Li C.-K., Schneider H. Applications of Perron-Frobenius theory to population dynamics. Journal of Mathematical Biology 2002, 44:450.
-
(2002)
Journal of Mathematical Biology
, vol.44
, pp. 450
-
-
Li, C.-K.1
Schneider, H.2
-
30
-
-
0034799244
-
Realistic distributions of infectious periods in epidemic models: changing patterns of persistence and dynamics
-
Lloyd A.L. Realistic distributions of infectious periods in epidemic models: changing patterns of persistence and dynamics. Theoretical Population Biology 2001, 60:59.
-
(2001)
Theoretical Population Biology
, vol.60
, pp. 59
-
-
Lloyd, A.L.1
-
32
-
-
84857795612
-
The basic reproduction number and the probability of extinction for a dynamic epidemic model
-
Neal P. The basic reproduction number and the probability of extinction for a dynamic epidemic model. Mathematical Biosciences 2012, 236:31.
-
(2012)
Mathematical Biosciences
, vol.236
, pp. 31
-
-
Neal, P.1
-
36
-
-
0036845274
-
Reproduction numbers and sub-threshold endemic equilibria for compartmental models of disease transmission
-
van den Driessche P., Watmough J. Reproduction numbers and sub-threshold endemic equilibria for compartmental models of disease transmission. Mathematical Biosciences 2002, 180:29.
-
(2002)
Mathematical Biosciences
, vol.180
, pp. 29
-
-
van den Driessche, P.1
Watmough, J.2
-
37
-
-
42249085379
-
Further notes on the basic reproduction number
-
Springer, Berlin, F. Brauer, P. van den Driessche, J. Wu (Eds.) Mathematical Epidemiology
-
van den Driessche P., Watmough J. Further notes on the basic reproduction number. Lecture Notes in Mathematics 2008, vol. 1945:159-178. Springer, Berlin. F. Brauer, P. van den Driessche, J. Wu (Eds.).
-
(2008)
Lecture Notes in Mathematics
, vol.1945
, pp. 159-178
-
-
van den Driessche, P.1
Watmough, J.2
-
38
-
-
77949699515
-
Impact of the infection period distribution on the epidemic spread in a metapopulation model
-
Vergu E., Busson H., Ezanno P. Impact of the infection period distribution on the epidemic spread in a metapopulation model. PLoS One 2010, 5:e9371.
-
(2010)
PLoS One
, vol.5
-
-
Vergu, E.1
Busson, H.2
Ezanno, P.3
-
39
-
-
0001236565
-
The outcome of a stochastic epidemic: a note on Bailey's paper
-
Whittle P. The outcome of a stochastic epidemic: a note on Bailey's paper. Biometrika 1955, 42:116.
-
(1955)
Biometrika
, vol.42
, pp. 116
-
-
Whittle, P.1
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