Stochastic amplification in epidemics

Journal of the Royal Society Interface - Tập 4 Số 14 - Trang 575-582 - 2007
David Alonso1, Alan J. McKane2, Mercedes Pascual1
1Department of Ecology and Evolutionary Biology, University of Michigan830 North University Avenue, Ann Arbor, MI 48109-1048, USA
2Theory Group, School of Physics and Astronomy, University of ManchesterManchester M13 9PL, UK

Tóm tắt

The role of stochasticity and its interplay with nonlinearity are central current issues in studies of the complex population patterns observed in nature, including the pronounced oscillations of wildlife and infectious diseases. The dynamics of childhood diseases have provided influential case studies to develop and test mathematical models with practical application to epidemiology, but are also of general relevance to the central question of whether simple nonlinear systems can explain and predict the complex temporal and spatial patterns observed in nature outside laboratory conditions. Here, we present a stochastic theory for the major dynamical transitions in epidemics from regular to irregular cycles, which relies on the discrete nature of disease transmission and low spatial coupling. The full spectrum of stochastic fluctuations is derived analytically to show how the amplification of noise varies across these transitions. The changes in noise amplification and coherence appear robust to seasonal forcing, questioning the role of seasonality and its interplay with deterministic components of epidemiological models. Childhood diseases are shown to fall into regions of parameter space of high noise amplification. This type of ‘endogenous’ stochastic resonance may be relevant to population oscillations in nonlinear ecological systems in general.

Từ khóa


Tài liệu tham khảo

Bartlett M.S, 1957, Measles periodicity and community size, J. R. Stat. Soc. A, 120, 37

Bauch C.T, 2003, Interepidemic intervals in forced and unforced SEIR models, Fields Inst. Commun, 36, 33

10.1098/rspb.2003.2410

10.2307/3100023

10.1073/pnas.93.22.12648

10.1016/0378-4371(80)90207-1

10.1016/0378-4371(80)90208-3

10.1890/0012-9615(2002)072[0057:FPMIPN]2.0.CO;2

10.1006/tpbi.1994.1032

10.1073/pnas.0407293101

10.1126/science.287.5453.667

10.1016/0021-9991(76)90041-3

10.1038/nature03072

10.1890/0012-9615(2002)072[0185:DOMESN]2.0.CO;2

10.1046/j.1461-0248.2001.00220.x

10.1016/j.tree.2003.09.007

Hethcote H.W, 1998, Oscillations in an endemic model for pertussis, Can. Appl. Math. Q, 6, 61

Hethcote H.W, 1989, Applied mathematical ecology, 193, 10.1007/978-3-642-61317-3_8

10.1126/science.1086726

10.1016/S0167-2789(00)00187-1

Lloyd A.L, 2002, Spatiotemporal dynamics of epidemics: synchrony in metapopulation models, Math. Biosci, 5, 20

10.1126/science.287.5453.601

10.1103/PhysRevLett.94.218102

10.1890/0012-9658(1997)078[0653:ATRFMT]2.0.CO;2

Nisbet R.M& Gurney W.S.C Modelling fluctuating populations. 1982 New York NY:Wiley.

10.1126/science.2382131

10.1098/rspb.1991.0142

10.1126/science.286.5441.968

10.1086/339467

10.1038/355584a0

van Kampen N.G Stochastic processes in physics and chemistry. 1992 Amsterdam The Netherlands:Elsevier.

10.1086/422341

Thông tin
Thông tin xuất bản

Journal of the Royal Society Interface

Tập 4 Số 14

575-582

Thông tin tác giả