Verified Solution of Nonlinear Dynamic Models in Epidemiology

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 the verified solution of nonlinear dynamic models we can bound the disease trajectories that are possible for given bounds on the uncertain parameters. The method used 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.

Analytic solution of the susceptible-infective epidemic model with state-dependent contact rates and different intervention policies

“…Therefore, there have been efforts to find verified (i.e., mathematically and computationally guaranteed) solutions of such systems of ODEs. For example, Enszer and Stadtherr 18 considered continuous epidemiological models that are systems of ODEs and formulated them as initial value problems (IVPs). They used interval methods (also called validated or verified methods) to find rigorous bounds on the solution of these systems of ODEs.…”