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A Branching Process Approximation of the Final Size of a Multitype Collective Reed-Frost Model |
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PP: 47-59 |
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Author(s) |
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A. Eseghir,
A. Kissami,
H. El Maroufy,
T. Ziad,
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Abstract |
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| We consider the asymptotic behavior of the final size of a multitype collective Reed-Frost process. This type of models was
introduced by [9] and include most known epidemic models of the type SIR (Susceptible, Infected, Removed) as special cases. Under
certain conditions, we show that, when the initial number of susceptible is very large and the initial number of infected individuals
is finite, the infection process behaves as a multitype Galton-Watson process. This fact is proved using a simple argument based on
Bernstein polynomials. We use this result to study the final size of the epidemic. |
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