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Evolution of Parasites and Diseases

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.

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Evolution of Parasites and Diseases

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  1. Evolution of Parasites and Diseases • The Red Queen to Alice: • It takes all the running you can do to stay in the same place

  2. Dynamical Models for Parasites and Diseases • SIR Models (Microparasites) • SI Models (HIV) Figure 12.28

  3. Alternative Models for Parasites and Diseases Figure 12.30: Rabies and Foxes Figure 12.32: Macroparasites

  4. Depression Many Dynamical Interactions Possible Pathogen Productivity Figure 12.29

  5. Not everyone needs vaccination Pc = 1 – 1/R0 Critical Vavvination Percentage Basic Reproductive Rate (infected hosts) Figure 12.23

  6. Parasites are everywhere and strike fast Figure 12.16

  7. 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

  9. Parasites obey distribution ”laws” Number of parasites per host % infected hosts Figure 12.11

  10. Parasites incur a fitness cost Yearling males Yearling males Adult males Adult males Figure 12.19 Arrival breedinggrounds of pied fly catcher

  11. Resistance and Immunity are costly Number of buds of susceptible and resistant lettuce Figure 12.20

  12. Virulence is subject to natural selection Is intermediate virulence optimal? Myxoma virus in rabbits Figure 12.34

  13. + dN/dt = (a – b)N - Y = rN - Y (11) 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)

  14.  X > ( + b + )  X > ( + b + )/  Basic Microparasite Models (Comp. p. 88) Exercise 1 b+c For a disease to spread, we need dY/dt = XY – ( + b + ) Y > 0 (9) During invasion Y = Z = 0  X = N  NT = ( + b + )/  (18)  dN/dt = dX/dt NT = 0  (a - b)N = 0

  15. Duration of immunity (1/) NT has been variable through human evolution

  16. 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

  17. 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

  18. 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

  19. 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

  20. 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?

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