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

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en P

rod

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Figure 12.29

Dep

ress

ion

Not everyone needs vaccination

Pc = 1 – 1/R0

Figure 12.23Basic Reproductive Rate (infected hosts)

Cri

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avvin

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Perc

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tag

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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

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of

para

site

s p

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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?