title: The exclusion problem in seasonally forced epidemiological systems.
abstract: The pathogen exclusion problem is the problem of finding control measures that will exclude a pathogen from an ecological system or, if the system is already disease-free, maintain it in that state. To solve this problem we work within a holistic control theory framework which is consistent with conventional theory for simple systems (where there is no external forcing and constant controls) and seamlessly generalises to complex systems that are subject to multiple component seasonal forcing and targeted variable controls. We develop, customise and integrate a range of numerical and algebraic procedures that provide a coherent methodology powerful enough to solve the exclusion problem in the general case. An important aspect of our solution procedure is its two-stage structure which reveals the epidemiological consequences of the controls used for exclusion. This information augments technical and economic considerations in the design of an acceptable exclusion strategy. Our methodology is used in two examples to show how time-varying controls can exploit the interference and reinforcement created by the external and internal lag structure and encourage the system to 'take over' some of the exclusion effort. On-off control switching, resonant amplification, optimality and controllability are important issues that emerge in the discussion.
authors.affiliation: Computing Science and Mathematics, University of Stirling, Stirling FK9 4LA, Scotland, UK. Electronic address: j.v.greenman@stir.ac.uk.
authors.forename: J V
authors.initials: JV
authors.lastname: Greenman
authors.affiliation: Department of Mathematical Sciences, University of Bath, Bath BA2 7AY, UK. Electronic address: b.adams@bath.ac.uk.
authors.forename: B
authors.initials: B
authors.lastname: Adams
mesh_terms: D000818:Animals; D003141:Communicable Diseases / Q000635:transmission; D016021:Epidemiologic Studies; D054884:Host-Pathogen Interactions / Q000276:immunology; D008954:Models, Biological; D012621:Seasons; D013997:Time Factors
keywords: Basic reproduction number R(0); Optimal scheduling; Phase control; Reservoir of infection; Resonance