Application of Error Control Software to ODE and PDE-based Epidemiological Models
  
           Connor Tannahill  and  Paul Muir
  
ABSTRACT
Epidemiological models provide powerful tools for predicting the spread of a disease and understanding the dynamics which effect its transmission through a population. In this report, we describe time dependent and time-space dependent compartmental epidemic models and the application of adaptive error control numerical software to approximate their solutions.

Software that implements adaptive error control returns an approximate solution for which an associated error estimate  satisfies a  user-prescribed tolerance; this has two important advantages: (i) the user can have reasonable confidence that the numerical solution has an error that is consistent with the requested tolerance, and (ii) the cost of the computation is consistent with the requested accuracy.

Several examples of time dependent ODE based models are solved within the Scilab problem solving environment to compute error controlled  solutions. A number of time-space PDE based epidemic models are solved using BACOLI, a recently developed FORTRAN B-spline collocation software package which provides adaptive spatial and temporal error control. We compare the numerical results from several previously published models with those obtained using  our error control software based approach. We find that in some cases, the numerical results published are inconsistent with those we obtained, and that these discrepancies may be due uncontrolled error in the original numerical solutions.