# Dynamics of measles epidemics: scaling noise, determinism, and predictability with the tsir model

##### Citations

1,304 citations

### Cites background from "Dynamics of measles epidemics: scal..."

...This is vividly illustrated by the dynamics of measles, a communicable childhood disease that represents one of the most comprehensively studied data sets in population ecology (e.g. Bjørnstad et al. 2002; Grenfell et al. 2002; Fig....

[...]

1,248 citations

906 citations

684 citations

### Cites background or methods from "Dynamics of measles epidemics: scal..."

...These extensions of the simple compartmental framework have included age-specific contact patterns and heterogeneities induced by spatial structure (Ball et al. 1997; Bjørnstad et al. 2002; Grenfell et al. 2002), but they do not allow for individual-level resolution....

[...]

...Bjornstad and Grenfell have developed the time-series SIR (TSIR) framework to model seasonal changes in contact patterns that influence the spread of measles (Bjørnstad et al. 2002; Grenfell et al. 2002)....

[...]

555 citations

### Cites background or methods from "Dynamics of measles epidemics: scal..."

...In the companion paper (Grenfell et al. 2002), we show that the model is able to describe and regenerate the quantitative and qualitative properties of the different types of dynamics in these 60 cities....

[...]

...We have also checked that the dynamic behavior of the 10-d model corresponds to that of the 14-d model—annual cycles for high birth rates and/or low seasonality and biannual cycles for low birth rates and/or high seasonality (Grenfell et al. 2002)....

[...]

...…of the de-Ï2/I mographic stochasticity (see Materials and methods: The model: Scaling of rates and parameters), indicate that there is a threshold shortly after epidemic take off where the dynamics are approximately ‘‘deterministic’’ (in all but the smallest communities; see Grenfell et al. 2002)....

[...]

...In a companion paper (Grenfell et al. 2002) we show how the TSIR model captures the long-term dynamical behavior of measles, and discuss how the balance between noise and determinism scales in this highly nonlinear ecological system....

[...]

...In the companion paper (Grenfell et al. 2002), we show that this simple modeling framework for measles is capable of reproducing highly predictable fluctuations in large populations, and recurring episodic outbreaks in small populations....

[...]

##### References

7,675 citations

### "Dynamics of measles epidemics: scal..." refers background or methods in this paper

...The characteristic time scale of the chain is 2 wk (corresponding roughly to the sum of incubation and infectious periods for the infection; Anderson and May 1991)....

[...]

...…closely match the well known biennial cycles of measles in the UK (and many other developed countries) during the 1950s and 1960s (Fine and Clarkson 1982, Anderson et al. 1984, Black 1984, Schenzle 1984, Anderson and May 1991, Cliff et al. 1993, Bolker and Grenfell 1995, Grenfell and Harwood 1997)....

[...]

...This form of prediction can have an important applied dimension since such shifts are often directly or indirectly anthropogenic in origin; relating, for example, to the effects of global warming (Fan et al. 1998) or vaccination (Anderson and May 1991)....

[...]

...This is a discrete-time nonlinear stochastic analogue of the well-known SIR (Susceptible–Infected–Recovered) model (Dietz and Schenzle 1985, Anderson and May 1991, Finkenstädt and Grenfell 2000, Bjørnstad et al. 2002)....

[...]

...1 follows directly from the extensive theoretical literature on childhood-disease dynamic modeling (see reviews in Anderson and May 1991, Grenfell and Dobson 1995, Mollison 1995)....

[...]

5,083 citations

### "Dynamics of measles epidemics: scal..." refers background in this paper

...A key issue in population dynamics is the relative importance of low-dimensional nonlinear deterministic forces and the, often high-dimensional, irregularities which we label as stochasticity (May 1973, Royama 1992, Ellner and Turchin 1995, Sugihara 1995, Stenseth et al. 1996, Leirs et al. 1997)....

[...]

1,652 citations

1,199 citations

### "Dynamics of measles epidemics: scal..." refers background in this paper

...A key issue in population dynamics is the relative importance of low-dimensional nonlinear deterministic forces and the, often high-dimensional, irregularities which we label as stochasticity (May 1973, Royama 1992, Ellner and Turchin 1995, Sugihara 1995, Stenseth et al. 1996, Leirs et al. 1997)....

[...]