کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
4499811 1623998 2016 10 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
Solvability of implicit final size equations for SIR epidemic models
موضوعات مرتبط
علوم زیستی و بیوفناوری علوم کشاورزی و بیولوژیک علوم کشاورزی و بیولوژیک (عمومی)
پیش نمایش صفحه اول مقاله
Solvability of implicit final size equations for SIR epidemic models
چکیده انگلیسی


• Final size relations are derived for three SIR mean-field models.
• The uniqueness of the solution is proved and it is given by iteration of a fixed point equation.
• Final sizes from mean-field approximations are compared to those given by exact stochastic models.

Final epidemic size relations play a central role in mathematical epidemiology. These can be written in the form of an implicit equation which is not analytically solvable in most of the cases. While final size relations were derived for several complex models, including multiple infective stages and models in which the durations of stages are arbitrarily distributed, the solvability of those implicit equations have been less studied. In this paper the SIR homogeneous mean-field and pairwise models and the heterogeneous mean-field model are studied. It is proved that the implicit equation for the final epidemic size has a unique solution, and that through writing the implicit equation as a fixed point equation in a suitable form, the iteration of the fixed point equation converges to the unique solution. The Markovian SIR epidemic model on finite networks is also studied by using the generation-based approach. Explicit analytic formulas are derived for the final size distribution for line and star graphs of arbitrary size. Iterative formulas for the final size distribution enable us to study the accuracy of mean-field approximations for the complete graph.

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Mathematical Biosciences - Volume 282, December 2016, Pages 181–190
نویسندگان
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