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Host population structure and the evolution of parasites

Host population structure and the evolution of parasites. Mike Boots. Our Infectious Diseases. Theory on the evolution of parasites. Evolutionary game theory ‘Adaptive Dynamics’ Can strains invade when rare? Generally a simple haploid genetic assumption Small mutations

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Host population structure and the evolution of parasites

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  1. Host population structure and the evolution of parasites Mike Boots

  2. Our Infectious Diseases

  3. Theory on the evolution of parasites • Evolutionary game theory • ‘Adaptive Dynamics’ • Can strains invade when rare? • Generally a simple haploid genetic assumption • Small mutations • Ecological feedbacks

  4. Theory on the evolution of parasites • Infectivity is maximised • Infectious period maximised • Mortality due to infection (virulence) minimised • Recovery rate minimised • Trade-offs related to exploitation of the host explain variation

  5. Virulence as a cost to transmission Transmission Virulence

  6. S I Natural Mortality + Virulence Natural Mortality Transmission Reproduction Lattice Models (Spatial structure within populations) S S S S S I S I I

  7. Simulation results for the evolution of transmission with individuals on a lattice where interactions are all local Mean Transmission TIME Max transmission = 150 No trade-offs between transmission and virulence

  8. I S Global Infection (L) I S Local Infection (1-L) Intermediate Levels of Spatial Structure

  9. 5 4 3 2 1 0 0.0 0.2 0.4 0.6 0.8 1.0 Maximum virulence Mean Virulence Linear trade-off with virulence and transmission L (Proportion of global infection)

  10. event conditional prob that I is a neighbour of an S site in an SI pair = # neighbours (fixed) transmission rate Host Parasite models between local and mean-field Pair-wise Approximation: differential equations for pair densities eg, PSI(t) =prob randomly chosen pair is in state SI

  11. Host Parasite models between local and mean-field Pair-wise Approximation: differential equations for pair densities PSI(t) =prob randomly chosen pair is in state SI eg, event =

  12. Host Parasite models between local and mean-field Pair-wise Approximation: differential equations for pair densities PSI(t) =prob randomly chosen pair is in state SI eg, LI event prob that a site is infected (1-LI) = proportion of global infection LI=0 (local), LI=1 (mean-field)

  13. Host Parasite models between local and mean-field • Derive correlation Eqns: for each pair and singleton from states S, I, R and 0 (empty sites). with params 0<LI,Lr<1 for global proportions of reproduction for pathogen and host. • Pair closure: determine qI/SI in terms of qI/S (from Monte Carlo sims). • Analysis:Stability analysis (long term behaviours) • Bifurcation analysis, continuation (limit cycles)

  14. Local density of infecteds Virulence Transmission Background Mortality Global density of susceptibles Invasion Condition > 0 J is a mutant strain I is the resident strain Hat notation denotes quasi steady state

  15. Pairwise Invasion Plots (Linear trade-off between transmission and virulence)

  16. Does the analysis agree with the simulations? • Yes: There is an ES virulence with spatial structure and maximization with global infection • Yes: The ES virulence increases as the proportion of global infection increases • But: The ESS is lost before L=1.0 • Weak selection gradients mean this is not seen when simulation is run for a set time period

  17. The ESS is lost

  18. Bistability

  19. Bistability

  20. Standard assumption of the evolution of virulence theory Transmission Virulence The role of trade-off shape

  21. Simulation Approximation Evolution with a saturating trade-off in a spatial model

  22. S S S S R I R I I The role of recovery: The Spatial Susceptible Infected Removed (SIR) Model

  23. The role of recovery No recovery =0

  24. The role of recovery =0.1 Increased ES virulence Wider region of bistability

  25. The role of recovery =0.2 Bi-stability region reduces

  26. The role of recovery =0.3

  27. The role of recovery =0.4

  28. The role of recovery Max ES virulence increases Recovery rate

  29. Conclusions • Spatial structure crucial to evolutionary outcomes • Bi-stability leading to the possibility of dramatic shifts in virulence • Shapes of trade-offs are important • Approximate analysis is useful in spatial evolutionary models

  30. Collaborators • Akira Sasaki (Kyushu University) • Masashi Kamo (Kyushu: Institute for risk management, Tsukuba) • Steve Webb

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