Verified solution method for population epidemiology models with uncertainty

Joshua A. Enszer; Mark A. Stadtherr

International Journal of Applied Mathematics and Computer Science (2009)

  • Volume: 19, Issue: 3, page 501-512
  • ISSN: 1641-876X

Abstract

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Epidemiological models can be used to study the impact of an infection within a population. These models often involve parameters that are not known with certainty. Using a method for verified solution of nonlinear dynamic models, we can bound the disease trajectories that are possible for given bounds on the uncertain parameters. The method is based on the use of an interval Taylor series to represent dependence on time and the use of Taylor models to represent dependence on uncertain parameters and/or initial conditions. The use of this method in epidemiology is demonstrated using the SIRS model, and other variations of Kermack-McKendrick models, including the case of time-dependent transmission.

How to cite

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Joshua A. Enszer, and Mark A. Stadtherr. "Verified solution method for population epidemiology models with uncertainty." International Journal of Applied Mathematics and Computer Science 19.3 (2009): 501-512. <http://eudml.org/doc/207951>.

@article{JoshuaA2009,
abstract = {Epidemiological models can be used to study the impact of an infection within a population. These models often involve parameters that are not known with certainty. Using a method for verified solution of nonlinear dynamic models, we can bound the disease trajectories that are possible for given bounds on the uncertain parameters. The method is based on the use of an interval Taylor series to represent dependence on time and the use of Taylor models to represent dependence on uncertain parameters and/or initial conditions. The use of this method in epidemiology is demonstrated using the SIRS model, and other variations of Kermack-McKendrick models, including the case of time-dependent transmission.},
author = {Joshua A. Enszer, Mark A. Stadtherr},
journal = {International Journal of Applied Mathematics and Computer Science},
keywords = {nonlinear dynamics; epidemiology; interval analysis; verified computing; ordinary differential equations},
language = {eng},
number = {3},
pages = {501-512},
title = {Verified solution method for population epidemiology models with uncertainty},
url = {http://eudml.org/doc/207951},
volume = {19},
year = {2009},
}

TY - JOUR
AU - Joshua A. Enszer
AU - Mark A. Stadtherr
TI - Verified solution method for population epidemiology models with uncertainty
JO - International Journal of Applied Mathematics and Computer Science
PY - 2009
VL - 19
IS - 3
SP - 501
EP - 512
AB - Epidemiological models can be used to study the impact of an infection within a population. These models often involve parameters that are not known with certainty. Using a method for verified solution of nonlinear dynamic models, we can bound the disease trajectories that are possible for given bounds on the uncertain parameters. The method is based on the use of an interval Taylor series to represent dependence on time and the use of Taylor models to represent dependence on uncertain parameters and/or initial conditions. The use of this method in epidemiology is demonstrated using the SIRS model, and other variations of Kermack-McKendrick models, including the case of time-dependent transmission.
LA - eng
KW - nonlinear dynamics; epidemiology; interval analysis; verified computing; ordinary differential equations
UR - http://eudml.org/doc/207951
ER -

References

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