Evolution of Parasites and Diseases

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Evolution of Parasites and Diseases

• The Red Queen to Alice
• It takes all the running you can do to stay in
  the same place

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Dynamical Models for Parasites and Diseases

• SIR Models (Microparasites)
• SI Models (HIV)

Figure 12.28
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Alternative Models for Parasites and Diseases
Figure 12.30 Rabies and Foxes
Figure 12.32 Macroparasites
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Many Dynamical Interactions Possible
Pathogen Productivity
Figure 12.29
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Not everyone needs vaccination
Pc 1 1/R0
Critical Vavvination Percentage
Basic Reproductive Rate (infected hosts)
Figure 12.23
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Parasites are everywhere and strike fast
Figure 12.16
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Parasites spread faster in dense hosts
Figure 12.6
8
Parasites are usually aggregated
Negative binomial Distributions
Gut nematode of foxes
Human head lice
Figure 12.10
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Parasites obey distribution laws
Number of parasites per host
Figure 12.11
infected hosts
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Parasites incur a fitness cost
Yearling males
Yearling males
Adult males
Adult males
Figure 12.19
Arrival breedinggrounds of pied fly catcher
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Resistance and Immunity are costly
Figure 12.20
Number of buds of susceptible and resistant
lettuce
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Virulence is subject to natural selection
Is intermediate virulence optimal?
Myxoma virus in rabbits
Figure 12.34
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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)
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Basic Microparasite Models (Comp. p. 88)
Exercise 1 bc
For a disease to spread, we need
dY/dt ?XY (? b ?) Y gt 0 (9)
During invasion Y Z 0 ? X N
? NT (? b ?)/ ? (18)
? dN/dt dX/dt NT 0 ? (a - b)N 0
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Duration of immunity (1/?)
NT has been variable through human evolution
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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
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HIV-AIDS The first equation
dN/dt N (? - ?) (? (1 - ? )?) (Y/N)
(1)

• per capita birth rate
• fraction infected children surviving
• ? natural mortality rate
• ? HIV induced mortality rate

Equivalent to dN/dt ? (X ? Y) - ? (X Y) -
? Y
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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)
(2)
Equivalent to dY/dt ? XY (c/N) (? ?) Y
? transmission rate C average rate of
aquiring partners C/N proportion of population
being a sexual partner
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HIV-AIDS
dN/dt N (? - ?) (? (1 - ? )?) (Y/N) (1)
dY/dt Y (?c - ? - ?) - ?c (Y/N)
(2)

• (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

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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?