Faculty of Science Distinguished Lecture Series looks at renewal equations in population biology

A Department of Mathematics & Statistics lecture series with Utrecht University Professor Odo Diekmann will look at renewal equations in population biology.

Odo Diekmann

The IRC, LIAM and Fields-CQAM MfPH Distinguished Lecture Series in the Faculty of Science will run Mondays and Wednesdays from 9:30 a.m. to noon, June 5 to 19 at 227 Kinsmen Building, Keele Campus.

Delay differential equations and renewal equations are rules for extending a function of time towards the future based on the (assumed to be) known past. A dynamical system is defined by shifting along the extended function.

The lecture series will focus on:

• modelling considerations: how physiologically structured population models lead to renewal equations;

• bifurcation analysis: steady states, stability (criteria in terms of the position of the roots of a characteristic equation in the complex plane), and transcritical, saddlenode and Hopf bifurcation;

• numerical bifurcation analysis: reduction to ODE via approximation by polynomials and subsequent use of ODE tools;

• derivation of biological insights by interpretation of the results of a mathematical analysis of models; and

• case studies: age structure and demography, cannibalism, Nicholson’s blowflies, size structure and Daphnia (waterfleas), infectious diseases, waning and boosting of immunity.

Diekmann is with the Mathematical Institute at Utrecht University. He is the author of several books, including Mathematical Tools for Understanding Infectious Disease Dynamics.

For more information, view the poster.