Strategies for containing a global influenza pandemic
Introduction
As the emergence of SARS illustrated, international travel may be significantly affected by news of a potential pandemic. Mathematical modelling can be used to investigate how such changes impact the global spread of infectious agents. The aim of this study was to develop a computer simulation of the global spread of a new pandemic influenza strain and to evaluate the potential impact of preventive and control measures.
Recent mathematical models addressing pandemic influenza have focused on the containment of an emerging pandemic at a very early stage [1], [2] or the exposure within a community to a virus from an isolated source [3]. Stopping the spread of a novel influenza virus with pandemic-potential at a very early stage is definitely the best strategy to manage a pandemic. However, this strategy may fail, in which case the problem would no longer be how to stop viral spread from a unique and well-identified source, but how to protect world's population from the constant risk of introduction or re-introduction of the virus over a period of many months.
Although an important area of research, few studies have directly explored the global diffusion of infectious agents by air travel. The paucity of research is primarily due to the lack of adequate air transportation data. The seminal work in this field is the model of Rvachev and Longini [4], [5], [6]. Using a mathematical model, they reconstructed the spread of the 1968–1969 influenza pandemic through a network of 52 cities, assuming the virus spread from Hong Kong through regular air transportation. Similar applications have been developed to forecast the temporal and geographic spread of influenza at a global scale using updated transportation data [7], or at local or regional scales in France [8] and Europe [9].
Here, we refined the Rvachev and Longini model to include different types of interventions for prevention and control (vaccination, antiviral therapy, isolation of infectious individuals and reduction of air travel) at either local or global levels, and at different times during the evolution of the pandemic. The results of such simulations provide insights into the best way to implement control measures to limit the spread of the first wave of a pandemic influenza.
Section snippets
Mathematical model
The dynamic model used in this study was initially published by Rvachev and Longini [4], [5], [6] and updated and refined later by Grais et al. [7]. It simulates the global spread of a pandemic through a worldwide network of 52 major cities and includes the seasonal pattern of influenza. A compartmental deterministic (SEIR) model simulates the epidemic at the city level, with all cities connected by an air traffic matrix. The air traffic matrix and information concerning city populations used
Scenario S1
In absence of control measures, it would take less than 5 months for the epidemic threshold to be reached in all 52 cities. The first wave of the pandemic would be over in 7 months (Fig. 1). Geographic proximity to Hong Kong and the geographic zone affected the time to reach the epidemic threshold in each city: it took an average of 44 days after Hong Kong in southern zone cities, 56 days in the tropical cities and 89 days in northern cities. Seasonality was the strongest of the two factors.
Discussion
The results of the simulations presented here confirm that if a pandemic influenza strain cannot be contained within its country of origin, it will become much more difficult to control. A realistic objective will then be to limit its impact rather than stopping it. Many diffusion scenarios are possible, depending notably on seasonality, virus transmissibility, and the geographic origin of the pandemic. A detailed and accurate prediction of such an event is therefore quite impossible,
Acknowledgment
This research was partially funded by Sanofi-Pasteur.
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