Although population structure has long been recognized as relevant to the spread of infectious disease, traditional mathematical models have understated the role of nonhomogenous mixing in populations with geographical and social structure. Recently, a wide variety of spatial and network models have been proposed that incorporate various aspects of interaction structure among individuals. However, these more complex models necessarily suffer from limited tractability, rendering general conclusions difficult to draw. In seeking a compromise between parsimony and realism, we introduce a class of metapopulation models in which we assume homogeneous mixing holds within local contexts, and that these contexts are embedded in a nested hierarchy of successively larger domains. We model the movement of individuals between contexts via simple transport parameters and allow diseases to spread stochastically. Our model exhibits some important stylized features of real epidemics, including extreme size variation and temporal heterogeneity, that are difficult to characterize with traditional measures. In particular, our results suggest that when epidemics do occur the basic reproduction number R 0 may bear little relation to their final size. Informed by our model's behavior, we suggest measures for characterizing epidemic thresholds and discuss implications for the control of epidemics.

BackgroundMuch of the developing world, particularly sub-Saharan Africa, exhibits high levels of morbidity and mortality associated with diarrhea, acute respiratory infection, and malaria. With the increasing awareness that the aforementioned infectious diseases impose an enormous burden on developing countries, public health programs therein could benefit from parsimonious general-purpose forecasting methods to enhance infectious disease intervention. Unfortunately, these disease time-series often i) suffer from non-stationarity; ii) exhibit large inter-annual plus seasonal fluctuations; and, iii) require disease-specific tailoring of forecasting methods.Methodology/Principal FindingsIn this longitudinal retrospective (01/1996–06/2004) investigation, diarrhea, acute respiratory infection of the lower tract, and malaria consultation time-series are fitted with a general-purpose econometric method, namely the multiplicative Holt-Winters, to produce contemporaneous on-line forecasts for the district of Niono, Mali. This method accommodates seasonal, as well as inter-annual, fluctuations and produces reasonably accurate median 2- and 3-month horizon forecasts for these non-stationary time-series, i.e., 92% of the 24 time-series forecasts generated (2 forecast horizons, 3 diseases, and 4 age categories = 24 time-series forecasts) have mean absolute percentage errors circa 25%.Conclusions/SignificanceThe multiplicative Holt-Winters forecasting method: i) performs well across diseases with dramatically distinct transmission modes and hence it is a strong general-purpose forecasting method candidate for non-stationary epidemiological time-series; ii) obliquely captures prior non-linear interactions between climate and the aforementioned disease dynamics thus, obviating the need for more complex disease-specific climate-based parametric forecasting methods in the district of Niono; furthermore, iii) readily decomposes time-series into seasonal components thereby potentially assisting with programming of public health interventions, as well as monitoring of disease dynamics modification. Therefore, these forecasts could improve infectious diseases management in the district of Niono, Mali, and elsewhere in the Sahel.

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