ur - yeakel lab
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13¥Host defenses and parasite counter-defenses h a i r
w i l d f l a x u s . Rustpathogen-
Aug#
) and ra te o f pg reproductionis:-###.." ' " ' " '" " " " ' " "
perpostde
(reproductive
geneo v e r c o m e
what a r e t h e ecological effectso f pansies
parasites?
-e x ) American
Chestnut Blight
1904 4 bi l l ion
-reduced ranges , g y p a fewindividuals÷;÷÷.............
f squirrelpopulations
✓ extinction 7 mo t h app.
A Deer, CoopersHawks, Cougars,
bobcats
i f nematodesGrousepopulations
E t i . E m- el imination o f nematode
parasites does n o t
eliminate cycles but changes t h e i r amplitudes
D.is/q%fffIII#ofµ host individuals w i n
a population• Assume
that
pathogen dynamicssusceptible
⑤N I G RO a r e much faster=
t h e n hos t pop.Infected - =-
dynamicsRecovered n o lifetime immunity s + I + p = N
= - w h e n should w eexpect
s = Density o fsusceptible
individualsa disease
t o spread w i t h i n
[ I = Density ofInfected individuals a population
- For a disease tospread, 5 individuals must
encounte r Iindividuals
Encounter r a t eshould b e proportional
t o 5 - I
- Disease transmission i s ①S Iu p s i s the transmission
r a t e
-
I f D i s e a s e transmission i s p s I
then I s t h e density of infectedindividuals I should grow up ①S I
when shou l d t h e d i s e a s e b e
d¥= PEI - 8 I expected t o spread?4 Recovery
rate
✓ dat> 0 ?
⑤ psi-8I 7 0
S t = ¥ 135¥> 8171351¥ ↳threshold value of thedensity
' I Gpg
of susceptibleindividuals ps> 8
when s t > I f the diseasespreads .gypIM
w
when S t <Fgthe disease
does
not spread
i f recovery r a t edqI=psI-8#i s h igher, t h e n
- ÷:÷÷÷, S T i s l a r g e rS t =
¥3
✓ (if t h e transmissionDisease growth:
S T > ¥r a p e i s higher,
t h e "
Disease decline:5 T < I soc¥t¥8 s p i s smaller
Addsomerealism
of l i n et h a t
individuals
r e c o v e r a t a fixed r a t eµ§¥, t h e n
theatamount
§§'become
infected v i a contact
a r e infectedi s Ig
[a n d have lifetime
immunity ,
weM'"" To t a l number of individuals
i s constant:
sizeo f
compartments
overE N N e s t I t R
X = theforceofinionper-capita r a t e a t w h i c h susceptible indiv iduals
acquire infection.⑧ BAO 7 i s n o t constant. . .
t h e m o r e
infected individualsthere a r e , t h e greater t h e force
of infection.X I )
Let's considert h e function 2 ( I )
Composed o f 1) transmissionr a t e 13 ← Le]
2) Interactiont e r m : proportion of infectious
individuals IN =STIFF
days
=
-7475=-13%5H I T 13¥
§¥=
MCI) S - R I = pins - 8 I pandemic
offs
= r t
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