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A STOCHASTIC EQUATION-BASED MODEL OF THE VALUE OF
INTERNATIONAL AIR-TRAVEL RESTRICTIONS FOR CONTROLLING PANDEMIC FLU
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In this Paper...
A stochastic, equation-based model for the spread of pandemic influenza is proposed
Results regarding the potential effectiveness of air travel restrictions as a disease control strategy are presented.
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Framework
A global network of cities connected by air travel is used.
Susceptible, Exposed, and Recovered can travel between cities.
Disease spreads within cities by contact between Susceptible and Infectious.
Outbreak in an uninfected city caused by Exposed travelers who become Infectious while in that city.
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Stochasticity
Two sources of stochasticity in this model: The daily number of infectious contacts
between Susceptible and Infectious persons The daily numbers of travelers between cities.
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The Model
Number of newly Exposed persons within a city on a particular day:
where λi is the infectious contact rate and T
i is the
total population of city i
λi (t) = λ (t, latitude
i)
Ei (0, t +1) chosen from a Poisson distribution
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The Model
With n cities in the model, the net number of travelers into and out of city i is then given by
pTij is the probability of traveling from city i to city j stochastic number of daily travelers to each
destination is drawn from a multinomial distribution
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Travel Restrictions
Travel restrictions are implemented by reducing the probability of all travel into or out of a given city by a pre-set percentage.
To prevent small fractions of Exposed travelers from prematurely initiating outbreaks in previously uninfected cities, if the net number of Exposed travelers to a city is below a threshold value, it is set equal to zero.
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Experiments
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Results – Population daily
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Results – Population cumulative
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Results – Volume daily
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Results – Volume cumulative