### Abstract

Language | English |
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Pages | 49-60 |

Journal | Journal of Theoretical Biology |

Volume | 367 |

DOIs | |

Status | Published - 21 Feb 2015 |

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**The exclusion problem in seasonally forced epidemiological systems.** / Greenman, J. V.; Adams, B.

Research output: Contribution to journal › Article

*Journal of Theoretical Biology*, vol. 367, pp. 49-60. DOI: 10.1016/j.jtbi.2014.11.011

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TY - JOUR

T1 - The exclusion problem in seasonally forced epidemiological systems

AU - Greenman,J. V.

AU - Adams,B.

PY - 2015/2/21

Y1 - 2015/2/21

N2 - 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.

AB - 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.

UR - http://dx.doi.org/10.1016/j.jtbi.2014.11.011

U2 - 10.1016/j.jtbi.2014.11.011

DO - 10.1016/j.jtbi.2014.11.011

M3 - Article

VL - 367

SP - 49

EP - 60

JO - Journal of Theoretical Biology

T2 - Journal of Theoretical Biology

JF - Journal of Theoretical Biology

SN - 0022-5193

ER -