Macroparasites and Metapopulations Parasites and time travel Macroparasites and Metapopulations For Muggles Beth Boulton University of Bath 08/06/16
Macroparasites and Metapopulations Parasites and time travel Parasites: Introducing the complex little blighters Parasites have more complex lifecycles than standard diseases and as a result aren’t often spread through direct contact. Parasitic infections also aren’t as clear cut as infected or not We need to try and formulate models that account for both of these problems
Macroparasites and Metapopulations Parasites and time travel Lifecycle
Macroparasites and Metapopulations Parasites and time travel Ode to our forefathers 12 dH dt = ( a − b ) H − α P . dt = λ P ( t ) H ( t ) dP H 0 + H ( t ) − ( b + µ ) P ( t ) − α H E [ i 2 ] H 0 + H − ( b + µ + α ) P − α ( k + 1) P 2 dP λ PH dt = kH 1 Anderson and May 1978. 2 May and Anderson 1978.
Macroparasites and Metapopulations Parasites and time travel #So Random 3 dP m ( t ) = − ( µ H ( t ) + α m + (1 − h 0 ) φ + µ M m ) P m ( t ) dt m � + µ M ( m + 1) P m +1 ( t ) + φ P m − c ( t ) h c c =1 ∂ Q ( t ; z ) = ( φ ( h ( z ) − 1)+ α E ( M ( t ))) Q ( t ; z ) − (( α + µ M ) z − µ M ) ∂ Q ( t ; z ) ∂ t ∂ z 3 Isham 1995.
Macroparasites and Metapopulations There has to be a better way Lets get Meta 4 N dL � β M 2 i − µ L L − N φ L 2 dt = i =1 dM i = ρφ L 2 − µ M M i − D M M 2 i dt 4 Keeling 2000.
Macroparasites and Metapopulations There has to be a better way A moment like this dL 2 − N φ L 2 dt = N β ( V M + M ) − µ L L − D L L dM 2 − µ M M − D M ( V M + M 2 ) dt = ρφ L dV M 2 (2 M + 1) − µ M (2 V M − M ) = ρφ L dt 3 + 6 M ( V M ) − V M − M 2 ) − D M (2 T M + 2 M
Macroparasites and Metapopulations There has to be a better way What does a numerical Dalek say? - Approximate!
Macroparasites and Metapopulations There has to be a better way Vive la resistance dM i ss = ρφ L ss ( L ss + L sr + L rr ) − µ M M i ss dt − D M M i ss (( M i ss + M i sr + M i rr )) dM i rs = ρφ L sr ( L ss + L sr + L rr ) − µ M M i sr dt − D M M i ss (( M i ss + M i sr + M i rr )) dM i rr = ρφ L rr ( L ss + L sr + L rr ) − µ M M i ss dt − D M M i rr (( M i ss + M i sr + M i rr ))
Macroparasites and Metapopulations There has to be a better way and the beat goes on... dL ss = − ( µ L + D L ( L ss + L sr + L rr )) L ss − N φ ( L ss + L sr + L rr ) L ss dt N ss ) 2 + 1 sr + 1 � sr ) 2 ) (( M i 2 M i ss M i 4( M i + β i =1 dL sr = − ( µ L + D L ( L ss + L sr + L rr )) L sr − N φ ( L ss + L sr + L rr ) L sr dt N rr + 1 � ( M i ss M i 2( M i ss M i sr + M i sr M i rr + ( M i sr ) 2 )) + β i =1 dL rr = − ( µ L + D L ( L ss + L sr + L rr )) L rr − N φ ( L ss + L sr + L rr ) L ss dt N rr ) 2 + 1 sr + 1 � (( M i 2 M i rr M i 4( M i sr ) 2 ) + β i =1
Macroparasites and Metapopulations Where do we go from here? Back to the future To try and find data which may lead to a more appropriate moment closure To incorporate treatment into the model To study the effects of optimised control on a treated population
Macroparasites and Metapopulations Where do we go from here? You thought I’d forgotten...
Macroparasites and Metapopulations Where do we go from here? Anderson, Roy M and Robert M May (1978). “Regulation and stability of host-parasite population interactions: I. Regulatory processes”. In: The Journal of Animal Ecology , pp. 219–247. cliniciansbrief.com. url : https://static1.squarespace.com/static/5339ac7ae4b04189ff520c9b/t/57d2e7069f7456d0a2b451b2/1473439502394/ . drclark.net. url : ww.drclark.net/the-essentials/beginners/parasites . fusic.com. url : http://dcp7ymsjupfx3.cloudfront.net/songs/a-moment-like-this/images/big_landscape.jpg?salt=9a043a . gnosticwarrior.com. url : https://s-media-cache-ak0.pinimg.com/736x/1b/7e/a7/1b7ea797ae7021a02097fa0e0a85eb08.jpg . Isham, Valerie (1995). “Stochastic models of host-macroparasite interaction”. In: The Annals of Applied Probability , pp. 720–740. Keeling, Matt J (2000). “Metapopulation moments: coupling, stochasticity and persistence”. In: Journal of Animal Ecology 69.5, pp. 725–736. May, Robert M and Roy M Anderson (1978). “Regulation and stability of host-parasite population interactions: II. Destabilizing processes”. In: The Journal of Animal Ecology , pp. 249–267. Munroe, Randall. Hofstadter . url : https://xkcd.com/917/ . unknown. url : https://s-media-cache-ak0.pinimg.com/originals/b3/b1/a5/b3b1a5127b90e3ac7eb0e45dd51466fb.jpg .
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