Modelling the 1985 influenza epidemic in France

Abstract

The Rvachev-Baroyan-Longini model is a space-time predictive model of the spread of influenza epidemics. It has been applied to 128 cities of the USSR, and more recently, to forecasting the spread of the pandemic of 1968-1969 throughout 52 large cities. It is a deterministic, mass-action, space and time continuous model. The model has been applied to the simulation of the influenza epidemic of 1984-1985 in the 22 French Metropolitan districts and results are presented. Estimates of the parameters of the model were made using the French Communicable Diseases Network data. These parameters are the contact rate, a, (estimate = 0.55) which is the number of people with whom an infectious individual will make contact daily sufficient to pass infection and the infectious period, 1/b, estimated as 2.49 days. The mean annual railroad passenger traffic from district i to district j varies from 0 to 1,991,000 persons depending on the districts. The computer spread of the epidemic is presented on weekly maps. Results are also presented on district charts, giving the size of district epidemics and the time of peak of the epidemic. The precision of the computer fittings was judged satisfactory by the calculated size of peak differing from the real one by less than 100 per cent, in 17 out of 18 districts, and by the calculated time of peak differing from the observed by less than two weeks in 14 out of 18 districts. Although precision could be improved with more detailed information about passenger traffic, the French use of the model has been satisfactory.

Seasonal influenza in the United States, France, and Australia: transmission and prospects for control

“…While this is the first study to systematically estimate the reproduction numbers of influenza for multiple inter-pandemic seasons in different countries, our results are in overall agreement with a previous study reporting an estimate of 1.5 for a single A/H3N2 season in France [12]. An earlier study proposed estimates higher than ours (range 1.4-2.6) for several consecutive influenza seasons in England and Wales [15,16], however the exact quantity measured in this work remains controversial [14,31].…”

“…Past studies have estimated the reproduction number of individual influenza seasons, in particular for pandemics [11][12][13][14][15][16][17][18][19]. However, no study has yet reported estimates of the reproduction number for several countries and consecutive influenza seasons in the interpandemic period, where a fraction of the population is immune due to previous influenza exposure or vaccination.…”

Spreading dynamics on heterogeneous populations: Multitype network approach

“…Multi-type models are difficult to deal with and are generally tackled using multi-agent simulations [2,4,5,16,17,18]. The advantage of multi-agent simulations is that we can consider several details and study their impact on the spreading dynamics.…”

Pre-symptomatic Influenza Transmission, Surveillance, and School Closings: Implications for Novel Influenza A (H1N1)

“…Since the viral shedding measurements range over many orders of magnitude, assigning threshold values is justified. Although the efficiency of viral shedding for transmission from asymptomatic hosts is unknown ( [11]), the contribution of pre-symptomatic infectious children to transmission may be critical in school settings. Formulas for the epidemic reproduction number R 0 and the daily and cumulative epidemic attack percentages AR under these assumptions are given in the Appendix.…”

“…We specify the parameters of the model at baseline (Table 1) with values supported by studies of past influenza epidemics ( [5], [6], [11], [15]) as well as recent reports of the current epidemic, with extrapolation to the context of schoolchildren ( [14]). An advantage of this approach is that its parameterization is relatively manageable within a range of acceptable values, which can be adjusted as new information develops.…”