N 70%

→

u r

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