Verified Solution Method for Population Epidemiology Models with Uncertainty

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.

Biomathematics and Interval Analysis: A Prosperous Marriage

“…For such variables one can construct interval bounds on the bases of feedback relations depending only on measurable (in real time) variables, so-called interval observers, see, e.g., [10], [11], [12], [15]. Several American researchers investigate bifurcations related to dynamical bio-processes pointing attention to cases when the type of the equilibrium points of sensitive dynamical processes may change with the uncertainties of the input coefficients [8], [9], [14]. Other American researchers apply interval and fuzzy methods to various application areas related to biology and medicine [18], [19].…”