Evolution of Parasites and Diseases
• The Red Queen to Alice:
• It takes all the running you can do to stay in the same place
Dynamical Models for Parasites and Diseases
• SIR Models (Microparasites)
• SI Models (HIV)
Figure 12.28
Alternative Models for Parasites and Diseases
Figure 12.30: Rabies and FoxesFigure 12.32: Macroparasites
Many Dynamical Interactions Possible
Path
og
en P
rod
uct
ivit
y
Figure 12.29
Dep
ress
ion
Not everyone needs vaccination
Pc = 1 – 1/R0
Figure 12.23Basic Reproductive Rate (infected hosts)
Cri
tica
l V
avvin
ati
on
Perc
en
tag
e
Parasites are everywhere and strike fast
Figure 12.16
Parasites spread faster in dense hosts
Figure 12.6
Parasites are usually aggregated
Figure 12.10
Negative binomial Distributions
Gut nematode of foxes Human head lice
Parasites obey distribution ”laws”
Figure 12.11% infected hosts
Nu
mb
er
of
para
site
s p
er
host
Parasites incur a fitness cost
Figure 12.19 Arrival breedinggrounds of pied fly catcher
Adult males
Yearling malesYearling males
Adult males
Resistance and Immunity are costly
Figure 12.20Number of buds of susceptible and resistant lettuce
Virulence is subject to natural selection
Figure 12.34Myxoma virus in rabbits
Is intermediate virulence optimal?
Basic Microparasite Models (Comp. p. 88)
dX/dt = a(X + Y + Z) – bX - XY + Z (8)
dY/dt = XY – ( + b + ) Y (9)
dZ/dt = Y – (b +) Z (10)
dN/dt = (a – b)N - Y = rN - Y (11)
+
Exercise 1a
Basic Microparasite Models (Comp. p. 88)
For a disease to spread, we need
dY/dt = XY – ( + b + ) Y > 0 (9)
NT = ( + b + )/ (18)
X > ( + b + ) X > ( + b + )/
During invasion Y = Z = 0 X = N
dN/dt = dX/dt NT = 0 (a - b)N = 0
Exercise 1 b+c
Duration of immunity (1/)
NT has been variable through human evolution
HIV-AIDS
dN/dt = N{ ( - ) – ( + (1 - )) (Y/N)} (1)
dY/dt = Y{ (c - - ) - c (Y/N)} (2)
No Immune Class (Z) so that X = N - Y
HIV-AIDS: The first equation
dN/dt = N{ ( - ) – ( + (1 - )) (Y/N)} (1)
Equivalent to:dN/dt = (X + Y) - (X + Y) - Y
= per capita birth rate = fraction infected children surviving= natural mortality rate = HIV induced mortality rate
HIV-AIDS: The second equation
dY/dt = Y{ (c - - ) - c (Y/N)} (2)
= per capita birth rate = fraction infected children surviving= natural mortality rate = HIV induced mortality rate
Equivalent to:dY/dt = XY (c/N) – ( + ) Y
= transmission rateC = average rate of aquiring partnersC/N = proportion of population being a sexual partner
HIV-AIDS
dN/dt = N{ ( - ) – ( + (1 - )) (Y/N)} (1)
dY/dt = Y{ (c - - ) - c (Y/N)} (2)
(1)+ (2) on page 104 are completely equivalent with (8) + (9) on page 88 if infected children (vertical transmission) and sexual transmission are taken into account
Issues to be discussed
• What are the population-dynamical and evolutionary characterizes of flu and HIV?
• Why does flu ”cycle” (outbreak epidemics) and HIV not?
• Why is AIDS so devastating?• How well did the predictions of the 1988
HIV model hold up?• Will AIDS medicine help in Africa?