# 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

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topJoshua 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 -

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