Transcript Myxoma

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 Foxes
Figure 12.32: Macroparasites
Depression
Pathogen Productivity
Many Dynamical Interactions Possible
Figure 12.29
Critical Vavvination Percentage
Not everyone needs vaccination
Pc = 1 – 1/R0
Basic Reproductive Rate (infected hosts)
Figure 12.23
Parasites are everywhere and strike fast
Figure 12.16
Parasites spread faster in dense hosts
Figure 12.6
Parasites are usually aggregated
Negative binomial Distributions
Gut nematode of foxes
Human head lice
Figure 12.10
Number of parasites per host
Parasites obey distribution ”laws”
% infected hosts
Figure 12.11
Parasites incur a fitness cost
Yearling males
Adult males
Yearling males
Adult males
Arrival breedinggrounds of pied fly catcher
Figure 12.19
Resistance and Immunity are costly
Number of buds of susceptible and resistant lettuce
Figure 12.20
Virulence is subject to natural selection
Is intermediate
virulence optimal?
Myxoma virus in rabbits
Figure 12.34
Basic Microparasite Models (Comp. p. 88)
Exercise 1a
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)
Basic Microparasite Models (Comp. p. 88)
Exercise 1 b+c
For a disease to spread, we need
dY/dt = XY – ( + b + ) Y > 0
(9)
 X > ( + b + )  X > ( + b + )/ 
During invasion Y = Z = 0  X = N
 NT = ( + b + )/ 
(18)
 dN/dt = dX/dt NT = 0  (a - b)N = 0
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)}
No Immune Class (Z) so that X = N - Y
(2)
HIV-AIDS: The first equation
dN/dt = N{ ( - ) – ( + (1 -  )) (Y/N)}
 = per capita birth rate
 = fraction infected children surviving
= natural mortality rate
 = HIV induced mortality rate
Equivalent to:
dN/dt =  (X +  Y) -  (X + Y) -  Y
(1)
HIV-AIDS: The second equation
 = per capita birth rate
 = fraction infected children surviving
= natural mortality rate
 = HIV induced mortality rate
dY/dt = Y{ (c -  - ) - c (Y/N)}
Equivalent to:
dY/dt =  XY (c/N) – ( + ) Y
 = transmission rate
(2)
C = average rate of aquiring partners
C/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?