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2 International Journal of Applied Mathematics and Computer Science

2 2009

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Verified solution method for population epidemiology models with uncertainty

Enszer J. A., Stadtherr M. A.

International Journal of Applied Mathematics and Computer Science

2009

Vol. 19, no 3

501-512

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.

Verified methods for computing Pareto sets: General algorithmic analysis

G.-Tóth B., Kreinovich V.

International Journal of Applied Mathematics and Computer Science

2009

Vol. 19, no 3

369-380

In many engineering problems, we face multi-objective optimization, with several objective functions f1, . . . , fn. We want to provide the user with the Pareto set-a set of all possible solutions x which cannot be improved in all categories (i.e., for which fj (x') fj (x) for all j and fj(x') > fj(x) for some j is impossible). The user should be able to select an appropriate trade-off between, say, cost and durability. We extend the general results about (verified) algorithmic computability of maxima locations to show that Pareto sets can also be computed.