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 Pathogen Productivity Figure Depression

Not everyone needs vaccination P c = 1 – 1/R 0 Figure Basic Reproductive Rate (infected hosts) Critical Vavvination Percentage

Parasites are everywhere and strike fast Figure 12.16

Parasites spread faster in dense hosts Figure 12.6

Parasites are usually aggregated Figure Negative binomial Distributions Gut nematode of foxesHuman head lice

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

Parasites incur a fitness cost Figure Arrival breedinggrounds of pied fly catcher Adult males Yearling 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 Myxoma 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)  N T = (  + b + )/  (18)   X > (  + b + )  X > (  + b + )/  During invasion Y = Z = 0  X = N  dN/dt = dX/dt N T = 0  (a - b)N = 0 Exercise 1 b+c

Duration of immunity (1/  ) N T 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 rate 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?