-
1
-
-
0003188315
-
-
M.S. Bartlett, J. R. Stat. Soc. Ser. A 120, 48 (1957); B. M. Bolkerand B. T. Grenfell, Proc. R. Soc. London Ser. B 251, 75 (1993).
-
(1957)
J. R. Stat. Soc. Ser. A
, vol.120
, pp. 48
-
-
Bartlett, M.S.1
-
4
-
-
0013923546
-
-
F. L. Black, J. Theor. Biol. 11, 207 (1966); A. P. Cliff, P. Haggett, J. K. Ord, G. R. Versey, Spatial Diffusion: An Historical Geography of Epidemics in an Island Community (Cambridge Univ. Press, Cambridge, 1981).
-
(1966)
J. Theor. Biol.
, vol.11
, pp. 207
-
-
Black, F.L.1
-
5
-
-
84976060851
-
-
Cambridge Univ. Press, Cambridge
-
F. L. Black, J. Theor. Biol. 11, 207 (1966); A. P. Cliff, P. Haggett, J. K. Ord, G. R. Versey, Spatial Diffusion: An Historical Geography of Epidemics in an Island Community (Cambridge Univ. Press, Cambridge, 1981).
-
(1981)
Spatial Diffusion: An Historical Geography of Epidemics in An Island Community
-
-
Cliff, A.P.1
Haggett, P.2
Ord, J.K.3
Versey, G.R.4
-
11
-
-
0021690803
-
-
P. E. M. Fine and J. A. Clarkson, Int. J. Epidemiol. 11, 5 (1982); J. L. Aron and I. B. Schwartz J. Theor. Biol. 110, 665 (1984).
-
(1984)
J. Theor. Biol.
, vol.110
, pp. 665
-
-
Aron, J.L.1
Schwartz, I.B.2
-
14
-
-
0001152032
-
-
B. T. Grenfell, A. Kleczkowski, S. P. Ellner, B. M. Bolker, Philos. Trans. R. Soc. London Ser. A 348, 515 (1994).
-
(1994)
Philos. Trans. R. Soc. London Ser. A
, vol.348
, pp. 515
-
-
Grenfell, B.T.1
Kleczkowski, A.2
Ellner, S.P.3
Bolker, B.M.4
-
15
-
-
0029310524
-
-
B. T. Grenfell, A. Kleczkowski, C. A. Gilligan, B. M. Bolker, Star. Methods Med. Res. 4, 160 (1995).
-
(1995)
Star. Methods Med. Res.
, vol.4
, pp. 160
-
-
Grenfell, B.T.1
Kleczkowski, A.2
Gilligan, C.A.3
Bolker, B.M.4
-
17
-
-
14444284214
-
-
note
-
2 is decreased during school holidays. The WAIFW matrix (for both the RAS and PRAS models) is estimated by obtaining the best fit to the average biennial cycle from the England and Wales data. Full details are given in (12, 13).
-
-
-
-
18
-
-
77957182038
-
-
R. M. Anderson and R. M. May, IMA J. Math. Appl. Med. Biol. 1,233 (1984); R. M. May and R. M. Anderson, Math. Biosci. 72, 83 (1984); B. M. Bolker and B. T. Grenfell, Philos. Trans. R. Soc. London Ser. B 348, 309 (1995).
-
(1984)
IMA J. Math. Appl. Med. Biol.
, vol.1
, pp. 233
-
-
Anderson, R.M.1
May, R.M.2
-
19
-
-
0021529194
-
-
R. M. Anderson and R. M. May, IMA J. Math. Appl. Med. Biol. 1,233 (1984); R. M. May and R. M. Anderson, Math. Biosci. 72, 83 (1984); B. M. Bolker and B. T. Grenfell, Philos. Trans. R. Soc. London Ser. B 348, 309 (1995).
-
(1984)
Math. Biosci.
, vol.72
, pp. 83
-
-
May, R.M.1
Anderson, R.M.2
-
20
-
-
0029654470
-
-
R. M. Anderson and R. M. May, IMA J. Math. Appl. Med. Biol. 1,233 (1984); R. M. May and R. M. Anderson, Math. Biosci. 72, 83 (1984); B. M. Bolker and B. T. Grenfell, Philos. Trans. R. Soc. London Ser. B 348, 309 (1995).
-
(1995)
Philos. Trans. R. Soc. London Ser. B
, vol.348
, pp. 309
-
-
Bolker, B.M.1
Grenfell, B.T.2
-
24
-
-
0028670078
-
-
preprint
-
R. Engbert and F. R. Drepper, Chaos Solitons Fractals 4, 1147 (1994); N. M. Ferguson, preprint (1996).
-
(1996)
-
-
Ferguson, N.M.1
-
25
-
-
14444270230
-
-
note
-
1 be the probability distribution functions of times in the two classes, then (ignoring mortality in the exposed and infectious classes) the standard SEIR model can be replaced by two time-delayed differential equations equations presented where equation presented γ = βSI, m is the birth and death rate, and N is the population size. Although Eqs. 1 are useful from a mathematical perspective (23), for computational simplicity we further subdivide the E and I classes, so that individuals move into a new subclass after short time intervals. Deterministic simulations using these two methods give identical results.
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-
-
-
26
-
-
50449154711
-
-
R. E. Hope Simpson, Lancet ii, 549 (1952); N. J. T. Bailey, Biometrika 43, 15 (1956).
-
(1952)
Lancet
, vol.2
, pp. 549
-
-
Hope Simpson, R.E.1
-
27
-
-
50449154711
-
-
R. E. Hope Simpson, Lancet ii, 549 (1952); N. J. T. Bailey, Biometrika 43, 15 (1956).
-
(1956)
Biometrika
, vol.43
, pp. 15
-
-
Bailey, N.J.T.1
-
29
-
-
0016061590
-
-
N. J. T. Bailey, The Mathematical Theory of lnfectious Diseases (Griffin, London, 1975); F. C. Hoppensteadt, J. Franklin Inst. 297, 325 (1974); Z. Grossman, Theor. Popul. Biol. 18, 204 (1980).
-
(1974)
J. Franklin Inst.
, vol.297
, pp. 325
-
-
Hoppensteadt, F.C.1
-
30
-
-
0019075237
-
-
N. J. T. Bailey, The Mathematical Theory of lnfectious Diseases (Griffin, London, 1975); F. C. Hoppensteadt, J. Franklin Inst. 297, 325 (1974); Z. Grossman, Theor. Popul. Biol. 18, 204 (1980).
-
(1980)
Theor. Popul. Biol.
, vol.18
, pp. 204
-
-
Grossman, Z.1
-
32
-
-
14444273098
-
-
note
-
0. This in turn leads to greater stochasticity and more extinctions, which can be highlighted by examining ℙ(O), the probability that an infectious individual will not produce any secondary cases (Fig. 3B) equation presented
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-
-
-
34
-
-
0021283858
-
-
_, Nature 310, 224 (1984).
-
(1984)
Nature
, vol.310
, pp. 224
-
-
-
35
-
-
14444272857
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note
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We thank B. Bolker, S. Ellner, P. Harvey, and A. Kleczkowski for stimulating discussions. This research was supported by the Wellcome Trust and the Royal Society.
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