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Determinants of periodicity in seasonally driven epidemics.
J Theor Biol. 2012 Mar 23; 305:88-95
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25 May 2012
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DOI: 10.3410/f.715947804.791302855
The main reason we like this paper is that it presents a quantitative approximation for the threshold points corresponding to a seasonal susceptible-infective-recovered (SIR) epidemiological model, at which recurrent epidemics switch from annual to biennial, from biennial to triennial, etc. These transitions...Continue reading
The main reason we like this paper is that it presents a quantitative approximation for the threshold points corresponding to a seasonal susceptible-infective-recovered (SIR) epidemiological model, at which recurrent epidemics switch from annual to biennial, from biennial to triennial, etc. These transitions have so far been explained only conceptually and graphically by looking at how the reproduction number of the disease varies in time.
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Krivan V and Berec L: F1000Prime Recommendation of [Uziel A and Stone L, J Theor Biol 2012, 305:88-95]. In F1000Prime, 25 May 2012; DOI: 10.3410/f.715947804.791302855. F1000Prime.com/715947804#eval791302855
F1000Prime Recommendations, Dissents and Comments for [Uziel A and Stone L, J Theor Biol 2012, 305:88-95]. In F1000Prime, 19 May 2013; F1000Prime.com/715947804
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Seasonality strongly affects the transmission and spatio-temporal dynamics of many infectious diseases, and is often an important cause for their recurrence. However, there are many open questions regarding the intricate relationship between seasonality and the complex dynamics of infectious diseases it gives rise to. For example, in the analysis of long-term time-series of childhood diseases, it is not clear why there are transitions from regimes with regular annual dynamics, to regimes in which epidemics occur every two or more years, and vice-versa. The classical seasonally-forced SIR epidemic model gives insights into these phenomena but due to its intrinsic nonlinearity and complex dynamics, the model is rarely amenable to detailed mathematical analysis. Making sensible approximations we analytically study the threshold (bifurcation) point of the forced SIR model where there is a switch from annual to biennial epidemics. We derive, for the first time, a simple equation that predicts the relationship between key epidemiological parameters near the bifurcation point. The relationship makes clear that, for realistic values of the parameters, the transition from biennial to annual dynamics will occur if either the birth-rate (μ) or basic reproductive ratio (R(0)) is increased sufficiently, or if the strength of seasonality (δ) is reduced sufficiently. These effects are confirmed in simulations studies and are also in accord with empirical observations. For example, the relationship may explain the correspondence between documented transitions in measles epidemics dynamics and concomitant changes in demographic and environmental factors.
Copyright © 2012 Elsevier Ltd. All rights reserved.
DOI: 10.1016/j.jtbi.2012.02.031
PMID: 22465112
