# Abba Gumel

### (Department of Mathematics, University of Manitoba)

*Dynamically-Consistent Finite-difference Methods for Epidemic Models*

Date | Monday, November 30, 2009 |
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Models for the transmission dynamics of human diseases are often formulated in the form of systems of non-linear differential equations. The (typically) large size and high nonlinearity of some of these systems make their analytical solutions difficult or impossible to obtain in closed form. Consequently, robust numerical methods must be used to obtain their approximate solutions. This talk addresses the problem and challenges of designing discrete-time models (finite-difference methods) that are dynamically-consistent with the continuous-time disease transmission models they approximate (in particular, the preservation of some of the key dynamical properties of the continuous-time models, such as positivity, boundedness, bifurcations etc.).