Chalmers Conferences, 9th European Conference on Mathematical and Theoretical Biology

The exclusion problem in seasonally forced eco-epidemiological systems
Jonathan Greenman

Last modified: 2014-06-12


The first objective is to solve the pathogen exclusion problem for systems with multiple host types and subject to multiple component periodic forcing.  A procedure based on a quadratic approximation in forcing strength is used to identify the mechanisms driving the distortions created by the forcing.  These mechanisms suggest ways in which system behaviour can be exploited to reduce the effort required to exclude the pathogen.  The importance of phase control is highlighted.  The methodology is extended by using time varying controls to find the least exclusion effort as the solution of an optimal scheduling problem.  Solutions can involve switching the control off for a time with the system ‘taking over’.  These methods can also be applied to the exclusion of predator, prey or host in eco-epidemiological systems to explore aspects of the impact of forcing on different forms of apparent competition.  The analysis of forcing is taken a step further by targeting the controls on specific groups of subpopulations in order to delve deeper into the mechanisms at work.  Finally we compare our explicit control theory approach to the exclusion problem with other approaches, including those involving the basic reproduction number.


phase control; apparent competition; optimal scheduling; basic reproduction number