Macroparasites and Metapopulations For Muggles Beth Boulton - - PowerPoint PPT Presentation

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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

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Macroparasites and Metapopulations Parasites and time travel

Macroparasites and Metapopulations

For Muggles Beth Boulton

University of Bath

08/06/16

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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

ften 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

f these problems

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Macroparasites and Metapopulations Parasites and time travel

Lifecycle

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Macroparasites and Metapopulations Parasites and time travel

Ode to our forefathers12

dH dt = (a − b)H − αP. dP dt = λP(t)H(t) H0 + H(t) − (b + µ)P(t) − αHE[i2] dP dt = λPH H0 + H − (b + µ + α)P − α(k + 1)P2 kH

1Anderson and May 1978. 2May and Anderson 1978.

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Macroparasites and Metapopulations Parasites and time travel

#So Random3

dPm(t) dt = −(µH(t) + αm + (1 − h0)φ + µMm)Pm(t) + µM(m + 1)Pm+1(t) + φ

Pm−c(t)hc ∂Q(t; z) ∂t = (φ(h(z)−1)+αE(M(t)))Q(t; z)−((α+µM)z −µM)∂Q(t; z) ∂z

3Isham 1995.

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Macroparasites and Metapopulations There has to be a better way

Lets get Meta4

dL dt =

βM2

i − µLL − NφL2

dMi dt = ρφL2 − µMMi − DMM2

4Keeling 2000.

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Macroparasites and Metapopulations There has to be a better way

A moment like this

dL dt = Nβ(VM + M) − µLL − DLL

2 − NφL 2

dM dt = ρφL

2 − µMM − DM(VM + M 2)

dVM dt = ρφL

2(2M + 1) − µM(2VM − M)

− DM(2TM + 2M

3 + 6M(VM) − VM − M 2)

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Macroparasites and Metapopulations There has to be a better way

What does a numerical Dalek say? - Approximate!

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Macroparasites and Metapopulations There has to be a better way

Vive la resistance

dMi

dt = ρφLss(Lss + Lsr + Lrr) − µMMi

− DMMi

ss((Mi ss + Mi sr + Mi rr))

dMi

dt = ρφLsr(Lss + Lsr + Lrr) − µMMi

− DMMi

ss((Mi ss + Mi sr + Mi rr))

dMi

dt = ρφLrr(Lss + Lsr + Lrr) − µMMi

− DMMi

rr((Mi ss + Mi sr + Mi rr))

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Macroparasites and Metapopulations There has to be a better way

and the beat goes on...

dLss dt = −(µL + DL(Lss + Lsr + Lrr))Lss − Nφ(Lss + Lsr + Lrr)Lss + β

((Mi

ss)2 + 1

2Mi

ssMi sr + 1

4(Mi

sr)2)

dLsr dt = −(µL + DL(Lss + Lsr + Lrr))Lsr − Nφ(Lss + Lsr + Lrr)Lsr + β

(Mi

ssMi rr + 1

2(Mi

ssMi sr + Mi srMi rr + (Mi sr)2))

dLrr dt = −(µL + DL(Lss + Lsr + Lrr))Lrr − Nφ(Lss + Lsr + Lrr)Lss + β

((Mi

rr)2 + 1

2Mi

rrMi sr + 1

4(Mi

sr)2)

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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

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Macroparasites and Metapopulations Where do we go from here?

You thought I’d forgotten...

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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.