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  1. Emergent and re-emergent challenges in the theory of infectious diseases South Africa June, 2007 www.noveltp.com

  2. The theory of infectious diseases has a rich history Sir Ronald Ross 1857-1932

  3. But prediction is difficult • Disease systems are complex, characterized by nonlinearities and sudden flips image.guardian.co.uk/

  4. They also are complex adaptive systems, integrating phenomena at multiple scales lshtm.ac.uk www.who.int encarta.msn.com www.nobel.org

  5. Integrating these multiple scales is one major challenge • Pathogen • Host individual • Host population dynamics • Pathogen genetics • Host genetics • Vector

  6. Despite a century of elegant theory, new diseases emerge, old reemerge http://edie.cprost.sfu.ca/gcnet

  7. Significant management puzzles remain • Whom should we vaccinate? www.calcsea.org

  8. Whom should we vaccinate? • Those at greatest risk? www.nursingworld.org

  9. Whom should we vaccinate? • Or those who pose greatest risk to others? www-personal.umich.edu/~mejn

  10. Other management puzzles:Problems of the Commons • Individual benefits/costs vs. group benefits/costs • Vaccination • Antibiotic use • Hospitals and nursing homes vs. health-care providers vs. individuals These introduce game-theoretic problems

  11. Antibiotic resistance threatens the effectiveness of our most potent weapons against bacterial infections

  12. Lecture outline • Periodicities and fluctuations • Antibiotic resistance and other problems of the Commons

  13. Many important diseases exhibit oscillations on multiple temporal and spatial scales

  14. Measles in the U.K.; Grenfell et al. 2001 (Nature)

  15. Control must deal with temporal and spatial fluctuations

  16. Influenza global spread

  17. Influenza A reemerges year after year, despite the fact that infection leads to lifetime immunity to a strain

  18. U.S. mortality in the 20th century

  19. The “Spanish Flu” of 1918

  20. Bush, Fitch, Cox

  21. Timeseries of viral clusters

  22. Fluctuations in influenza A • Rapid replacement at level of individual strains • Gradual replacement at level of subtypes • Recurrence at level of clusters

  23. Standard SIR Model (No latency) SusceptibleS RemovedR Infectious I

  24. Simplest model recovered deaths

  25. For spread: Condition for spread in a naïve population ThusR0 is the #secondary/primary infection.

  26. Interpretation if threshold is exceeded 1. With no new recruits, outbreak and collapse • With new births, get stable equilibrium • Oscillations require a more complicated model

  27. Complications • New immigrants www.lareau.org H.M.S. Bounty

  28. Complications • New immigrants • Demography www.lareau.org

  29. Complications • New immigrants • Demography • Heterogeneous mixing patterns www.lareau.org

  30. Complications • New immigrants • Demography • Heterogeneous mixing patterns • Genetic changes in host www.lareau.org

  31. Complications • New immigrants • Demography • Heterogeneous mixing patterns • Genetic changes in host • Multiple strains/diseases www.lareau.org

  32. Complications • New immigrants • Demography • Heterogeneous mixing patterns • Genetic changes in host • Multiple strains/diseases • Vectors www.lareau.org

  33. Complications • New immigrants • Demography • Heterogeneous mixing patterns • Genetic changes in host • Multiple strains/diseases • Vectors www.lareau.org

  34. Oscillations • Stochastic factors • Seasonal forcing (e.g., in transmission rates) • Long periods of temporary immunity • Other explicit delays (e.g., incubation periods) • Age structure • Non-constant population size • Non-bilinear transmission coefficients • Interactions with other diseases/strains

  35. Oscillations • Stochastic factors • Seasonal forcing (e.g., in transmission rates) • Long periods of temporary immunity • Other explicit delays (e.g., incubation periods) • Age structure • Non-constant population size • Non-(bilinear) transmission coefficients • Interactions with other diseases/strains

  36. Oscillations • Stochastic factors • Seasonal forcing (e.g., in transmission rates) • Long periods of temporary immunity • Other explicit delays (e.g., incubation periods) • Age structure • Non-constant population size • Non-(bilinear) transmission coefficients • Interactions with other diseases/strains

  37. Oscillations • Stochastic factors • Seasonal forcing (e.g., in transmission rates) • Long periods of temporary immunity • Other explicit delays (e.g., incubation periods) • Age structure • Non-constant population size • Non-(bilinear) transmission coefficients • Interactions with other diseases/strains

  38. Oscillations • Seasonal forcing (e.g., in transmission rates) • Can interact with endogenous oscillations to produce chaos • Age structure • Creates implicit delays • Interactions with other diseases/strains • Includes, therefore, genetic change in pathogen

  39. Interacting strains or diseases Susceptible Infectious 1 Recovered 1 Infectious 2 Infectious 2 R1 Recovered 2 Infectious 1 Recovered 1,2 R2

  40. Understanding endogenous oscillations • Age-structured models can produce damped oscillations (Schenzele, Castillo-Chavez et al.) • Two-strain models can produce damped oscillations (Castillo-Chavez et al.) • Coupling these may lead to sustained periodic or other oscillations

  41. Summary:Understanding endogenous oscillations • Age-structure • Epidemiology • Genetics all have characteristic scales of oscillation that can interact with each other, and with seasonal forcing

  42. Lecture outline • Periodicities and fluctuations • Antibiotic resistance and other problems of the Commons

  43. Problems of The Commons • Fisheries • Aquifers • Pollution www.aisobservers.com

  44. Problems of The Commons • Fisheries • Aquifers • Pollution • Vaccines pubs.acs.org images.usatoday.com

  45. Problems of The Commons • Fisheries • Aquifers • Pollution • Vaccines • Antibiotics www.bath.ac.uk

  46. Antibiotic resistance is on the rise www.wellcome.ac.uk

  47. Would you deny your child antibiotics to maintain global effectiveness?