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quancol . ........ . . . ... ... ... ... ... ... ... www.quanticol.eu Spatial Representations and Analysis Techniques Part II: Analysis Vashti Galpin University of Edinburgh Bertinoro 22 June 2016 SFM-16 1 / 60 quancol .

  1. quan�col . ........ . . . ... ... ... ... ... ... ... SIR model on 12x12 grid Stochastic: full connectivity www.quanticol.eu Initial values: S ( i ) (0) = 49 , I ( i ) (0) = 1 , R ( i ) (0) = 0 Parameters: k = 0 . 011, r = 0 . 1, m s = m i = 0 . 00001 SFM-16 10 / 60

  2. quan�col . ........ . . . ... ... ... ... ... ... ... SIR model on 12x12 grid Stochastic: von Neumann neighbourhood www.quanticol.eu Initial values: S ( i ) (0) = 49 , I ( i ) (0) = 1 , R ( i ) (0) = 0 Parameters: k = 0 . 011, r = 0 . 1, m s = m i = 0 . 00001 SFM-16 11 / 60

  3. quan�col . ........ . . . ... ... ... ... ... ... ... SIR model on 12x12 grid Stochastic: von Neumann neighbourhood www.quanticol.eu Initial values: S ( i ) (0) = 49 , I ( i ) (0) = 1 , R ( i ) (0) = 0 Parameters: k = 0 . 011, r = 0 . 1, m s = m i = 0 . 00001 SFM-16 11 / 60

  4. quan�col . ........ . . . ... ... ... ... ... ... ... SIR model on 12x12 grid Stochastic: von Neumann neighbourhood www.quanticol.eu Initial values: S ( i ) (0) = 49 , I ( i ) (0) = 1 , R ( i ) (0) = 0 Parameters: k = 0 . 011, r = 0 . 1, m s = m i = 0 . 00001 SFM-16 11 / 60

  5. quan�col . ........ . . . ... ... ... ... ... ... ... SIR model on 12x12 grid Stochastic: von Neumann neighbourhood www.quanticol.eu Initial values: S ( i ) (0) = 49 , I ( i ) (0) = 1 , R ( i ) (0) = 0 Parameters: k = 0 . 011, r = 0 . 1, m s = m i = 0 . 00001 SFM-16 11 / 60

  6. quan�col . ........ . . . ... ... ... ... ... ... ... SIR model on 12x12 grid Stochastic: von Neumann neighbourhood www.quanticol.eu Initial values: S ( i ) (0) = 49 , I ( i ) (0) = 1 , R ( i ) (0) = 0 Parameters: k = 0 . 011, r = 0 . 1, m s = m i = 0 . 00001 SFM-16 11 / 60

  7. quan�col . ........ . . . ... ... ... ... ... ... ... SIR model on 12x12 grid Stochastic: von Neumann neighbourhood www.quanticol.eu Initial values: S ( i ) (0) = 49 , I ( i ) (0) = 1 , R ( i ) (0) = 0 Parameters: k = 0 . 011, r = 0 . 1, m s = m i = 0 . 00001 SFM-16 11 / 60

  8. quan�col . ........ . . . ... ... ... ... ... ... ... SIR model on 12x12 grid Stochastic: von Neumann neighbourhood www.quanticol.eu Initial values: S ( i ) (0) = 49 , I ( i ) (0) = 1 , R ( i ) (0) = 0 Parameters: k = 0 . 011, r = 0 . 1, m s = m i = 0 . 00001 SFM-16 11 / 60

  9. quan�col . ........ . . . ... ... ... ... ... ... ... SIR model on 12x12 grid Stochastic: von Neumann neighbourhood www.quanticol.eu Initial values: S ( i ) (0) = 49 , I ( i ) (0) = 1 , R ( i ) (0) = 0 Parameters: k = 0 . 011, r = 0 . 1, m s = m i = 0 . 00001 SFM-16 11 / 60

  10. quan�col . ........ . . . ... ... ... ... ... ... ... SIR model on 12x12 grid Stochastic: von Neumann neighbourhood www.quanticol.eu Initial values: S ( i ) (0) = 49 , I ( i ) (0) = 1 , R ( i ) (0) = 0 Parameters: k = 0 . 011, r = 0 . 1, m s = m i = 0 . 00001 SFM-16 11 / 60

  11. quan�col . ........ . . . ... ... ... ... ... ... ... SIR model on 12x12 grid Stochastic: von Neumann neighbourhood www.quanticol.eu Initial values: S ( i ) (0) = 49 , I ( i ) (0) = 1 , R ( i ) (0) = 0 Parameters: k = 0 . 011, r = 0 . 1, m s = m i = 0 . 00001 SFM-16 11 / 60

  12. quan�col . ........ . . . ... ... ... ... ... ... ... SIR model on 12x12 grid Stochastic: von Neumann neighbourhood www.quanticol.eu Initial values: S ( i ) (0) = 49 , I ( i ) (0) = 1 , R ( i ) (0) = 0 Parameters: k = 0 . 011, r = 0 . 1, m s = m i = 0 . 00001 SFM-16 11 / 60

  13. quan�col . ........ . . . ... ... ... ... ... ... ... SIR model on 12x12 grid Deterministic: full connectivity www.quanticol.eu Initial values: S ( i ) (0) = 49 , I ( i ) (0) = 1 , R ( i ) (0) = 0 Parameters: k = 0 . 011, r = 0 . 1, m s = m i = 0 . 00001 SFM-16 12 / 60

  14. quan�col . ........ . . . ... ... ... ... ... ... ... SIR model on 12x12 grid Deterministic: full connectivity www.quanticol.eu Initial values: S ( i ) (0) = 49 , I ( i ) (0) = 1 , R ( i ) (0) = 0 Parameters: k = 0 . 011, r = 0 . 1, m s = m i = 0 . 00001 SFM-16 12 / 60

  15. quan�col . ........ . . . ... ... ... ... ... ... ... SIR model on 12x12 grid Deterministic: full connectivity www.quanticol.eu Initial values: S ( i ) (0) = 49 , I ( i ) (0) = 1 , R ( i ) (0) = 0 Parameters: k = 0 . 011, r = 0 . 1, m s = m i = 0 . 00001 SFM-16 12 / 60

  16. quan�col . ........ . . . ... ... ... ... ... ... ... SIR model on 12x12 grid Deterministic: full connectivity www.quanticol.eu Initial values: S ( i ) (0) = 49 , I ( i ) (0) = 1 , R ( i ) (0) = 0 Parameters: k = 0 . 011, r = 0 . 1, m s = m i = 0 . 00001 SFM-16 12 / 60

  17. quan�col . ........ . . . ... ... ... ... ... ... ... SIR model on 12x12 grid Deterministic: full connectivity www.quanticol.eu Initial values: S ( i ) (0) = 49 , I ( i ) (0) = 1 , R ( i ) (0) = 0 Parameters: k = 0 . 011, r = 0 . 1, m s = m i = 0 . 00001 SFM-16 12 / 60

  18. quan�col . ........ . . . ... ... ... ... ... ... ... SIR model on 12x12 grid Deterministic: full connectivity www.quanticol.eu Initial values: S ( i ) (0) = 49 , I ( i ) (0) = 1 , R ( i ) (0) = 0 Parameters: k = 0 . 011, r = 0 . 1, m s = m i = 0 . 00001 SFM-16 12 / 60

  19. quan�col . ........ . . . ... ... ... ... ... ... ... SIR model on 12x12 grid Deterministic: full connectivity www.quanticol.eu Initial values: S ( i ) (0) = 49 , I ( i ) (0) = 1 , R ( i ) (0) = 0 Parameters: k = 0 . 011, r = 0 . 1, m s = m i = 0 . 00001 SFM-16 12 / 60

  20. quan�col . ........ . . . ... ... ... ... ... ... ... SIR model on 12x12 grid Deterministic: full connectivity www.quanticol.eu Initial values: S ( i ) (0) = 49 , I ( i ) (0) = 1 , R ( i ) (0) = 0 Parameters: k = 0 . 011, r = 0 . 1, m s = m i = 0 . 00001 SFM-16 12 / 60

  21. quan�col . ........ . . . ... ... ... ... ... ... ... SIR model on 12x12 grid Deterministic: full connectivity www.quanticol.eu Initial values: S ( i ) (0) = 49 , I ( i ) (0) = 1 , R ( i ) (0) = 0 Parameters: k = 0 . 011, r = 0 . 1, m s = m i = 0 . 00001 SFM-16 12 / 60

  22. quan�col . ........ . . . ... ... ... ... ... ... ... SIR model on 12x12 grid Deterministic: full connectivity www.quanticol.eu Initial values: S ( i ) (0) = 49 , I ( i ) (0) = 1 , R ( i ) (0) = 0 Parameters: k = 0 . 011, r = 0 . 1, m s = m i = 0 . 00001 SFM-16 12 / 60

  23. quan�col . ........ . . . ... ... ... ... ... ... ... SIR model on 12x12 grid Deterministic: full connectivity www.quanticol.eu Initial values: S ( i ) (0) = 49 , I ( i ) (0) = 1 , R ( i ) (0) = 0 Parameters: k = 0 . 011, r = 0 . 1, m s = m i = 0 . 00001 SFM-16 12 / 60

  24. quan�col . ........ . . . ... ... ... ... ... ... ... SIR model on 12x12 grid Stochastic simulations www.quanticol.eu Initial values: S ( i ) (0) = 49 , I ( i ) (0) = 1 , R ( i ) (0) = 0 Parameters: k = 0 . 011, r = 0 . 1, m s = m i = 0 . 00001 No connectivity Von Neumann full connectivity neighbourhood SFM-16 13 / 60

  25. quan�col . ........ . . . ... ... ... ... ... ... ... SIR model on 12x12 grid Stochastic simulations www.quanticol.eu Initial values: S ( i ) (0) = 49 , I ( i ) (0) = 1 , R ( i ) (0) = 0 Parameters: k = 0 . 011, r = 0 . 1, m s = m i = 0 . 00001 100 <S>: no connectivity <I>: no connectivity <R>: no connectivity <S>: von Neumann 80 <I>: von Neumann <R>: von Neumann <S>: full connectivity spatial average <I>: full connectivity 60 <R>: full connectivity 40 20 0 0 20 40 60 80 100 time SFM-16 14 / 60

  26. quan�col . ........ . . . ... ... ... ... ... ... ... SIR model on 30x30 grid Stochastic: von Neumann neighbourhood www.quanticol.eu Initial values: S ( i ) (0) = 30 , I ( i ) (0) = 10 , R ( i ) (0) = 0 Parameters: k = 0 . 01, r = 0 . 2, m s = m i = 0 . 05 SFM-16 15 / 60

  27. quan�col . ........ . . . ... ... ... ... ... ... ... SIR model on 30x30 grid Stochastic: von Neumann neighbourhood www.quanticol.eu Initial values: S ( i ) (0) = 30 , I ( i ) (0) = 10 , R ( i ) (0) = 0 Parameters: k = 0 . 01, r = 0 . 2, m s = m i = 0 . 05 SFM-16 15 / 60

  28. quan�col . ........ . . . ... ... ... ... ... ... ... SIR model on 30x30 grid Stochastic: von Neumann neighbourhood www.quanticol.eu Initial values: S ( i ) (0) = 30 , I ( i ) (0) = 10 , R ( i ) (0) = 0 Parameters: k = 0 . 01, r = 0 . 2, m s = m i = 0 . 05 SFM-16 15 / 60

  29. quan�col . ........ . . . ... ... ... ... ... ... ... SIR model on 30x30 grid Stochastic: von Neumann neighbourhood www.quanticol.eu Initial values: S ( i ) (0) = 30 , I ( i ) (0) = 10 , R ( i ) (0) = 0 Parameters: k = 0 . 01, r = 0 . 2, m s = m i = 0 . 05 SFM-16 15 / 60

  30. quan�col . ........ . . . ... ... ... ... ... ... ... SIR model on 30x30 grid Stochastic: von Neumann neighbourhood www.quanticol.eu Initial values: S ( i ) (0) = 30 , I ( i ) (0) = 10 , R ( i ) (0) = 0 Parameters: k = 0 . 01, r = 0 . 2, m s = m i = 0 . 05 SFM-16 15 / 60

  31. quan�col . ........ . . . ... ... ... ... ... ... ... SIR model on 30x30 grid Stochastic: von Neumann neighbourhood www.quanticol.eu Initial values: S ( i ) (0) = 30 , I ( i ) (0) = 10 , R ( i ) (0) = 0 Parameters: k = 0 . 01, r = 0 . 2, m s = m i = 0 . 05 SFM-16 15 / 60

  32. quan�col . ........ . . . ... ... ... ... ... ... ... SIR model on 30x30 grid Stochastic: von Neumann neighbourhood www.quanticol.eu Initial values: S ( i ) (0) = 30 , I ( i ) (0) = 10 , R ( i ) (0) = 0 Parameters: k = 0 . 01, r = 0 . 2, m s = m i = 0 . 05 SFM-16 15 / 60

  33. quan�col . ........ . . . ... ... ... ... ... ... ... SIR model on 30x30 grid Stochastic: von Neumann neighbourhood www.quanticol.eu Initial values: S ( i ) (0) = 30 , I ( i ) (0) = 10 , R ( i ) (0) = 0 Parameters: k = 0 . 01, r = 0 . 2, m s = m i = 0 . 05 SFM-16 15 / 60

  34. quan�col . ........ . . . ... ... ... ... ... ... ... SIR model on 30x30 grid Stochastic: von Neumann neighbourhood www.quanticol.eu Initial values: S ( i ) (0) = 30 , I ( i ) (0) = 10 , R ( i ) (0) = 0 Parameters: k = 0 . 01, r = 0 . 2, m s = m i = 0 . 05 SFM-16 15 / 60

  35. quan�col . ........ . . . ... ... ... ... ... ... ... SIR model on 30x30 grid Stochastic: von Neumann neighbourhood www.quanticol.eu Initial values: S ( i ) (0) = 30 , I ( i ) (0) = 10 , R ( i ) (0) = 0 Parameters: k = 0 . 01, r = 0 . 2, m s = m i = 0 . 05 SFM-16 15 / 60

  36. quan�col . ........ . . . ... ... ... ... ... ... ... SIR model on 30x30 grid Stochastic: von Neumann neighbourhood www.quanticol.eu Initial values: S ( i ) (0) = 30 , I ( i ) (0) = 10 , R ( i ) (0) = 0 Parameters: k = 0 . 01, r = 0 . 2, m s = m i = 0 . 05 SFM-16 15 / 60

  37. quan�col . ........ . . . ... ... ... ... ... ... ... SIR model on 30x30 grid Stochastic: von Neumann neighbourhood www.quanticol.eu Initial values: S ( i ) (0) = 30 , I ( i ) (0) = 0 , R ( i ) (0) = 0 except border, I ( i ) (0) = 10 Parameters: k = 0 . 01, r = 0 . 2, m s = m i = 0 . 05 SFM-16 16 / 60

  38. quan�col . ........ . . . ... ... ... ... ... ... ... SIR model on 30x30 grid Stochastic: von Neumann neighbourhood www.quanticol.eu Initial values: S ( i ) (0) = 30 , I ( i ) (0) = 0 , R ( i ) (0) = 0 except border, I ( i ) (0) = 10 Parameters: k = 0 . 01, r = 0 . 2, m s = m i = 0 . 05 SFM-16 16 / 60

  39. quan�col . ........ . . . ... ... ... ... ... ... ... SIR model on 30x30 grid Stochastic: von Neumann neighbourhood www.quanticol.eu Initial values: S ( i ) (0) = 30 , I ( i ) (0) = 0 , R ( i ) (0) = 0 except border, I ( i ) (0) = 10 Parameters: k = 0 . 01, r = 0 . 2, m s = m i = 0 . 05 SFM-16 16 / 60

  40. quan�col . ........ . . . ... ... ... ... ... ... ... SIR model on 30x30 grid Stochastic: von Neumann neighbourhood www.quanticol.eu Initial values: S ( i ) (0) = 30 , I ( i ) (0) = 0 , R ( i ) (0) = 0 except border, I ( i ) (0) = 10 Parameters: k = 0 . 01, r = 0 . 2, m s = m i = 0 . 05 SFM-16 16 / 60

  41. quan�col . ........ . . . ... ... ... ... ... ... ... SIR model on 30x30 grid Stochastic: von Neumann neighbourhood www.quanticol.eu Initial values: S ( i ) (0) = 30 , I ( i ) (0) = 0 , R ( i ) (0) = 0 except border, I ( i ) (0) = 10 Parameters: k = 0 . 01, r = 0 . 2, m s = m i = 0 . 05 SFM-16 16 / 60

  42. quan�col . ........ . . . ... ... ... ... ... ... ... SIR model on 30x30 grid Stochastic: von Neumann neighbourhood www.quanticol.eu Initial values: S ( i ) (0) = 30 , I ( i ) (0) = 0 , R ( i ) (0) = 0 except border, I ( i ) (0) = 10 Parameters: k = 0 . 01, r = 0 . 2, m s = m i = 0 . 05 SFM-16 16 / 60

  43. quan�col . ........ . . . ... ... ... ... ... ... ... SIR model on 30x30 grid Stochastic: von Neumann neighbourhood www.quanticol.eu Initial values: S ( i ) (0) = 30 , I ( i ) (0) = 0 , R ( i ) (0) = 0 except border, I ( i ) (0) = 10 Parameters: k = 0 . 01, r = 0 . 2, m s = m i = 0 . 05 SFM-16 16 / 60

  44. quan�col . ........ . . . ... ... ... ... ... ... ... SIR model on 30x30 grid Stochastic: von Neumann neighbourhood www.quanticol.eu Initial values: S ( i ) (0) = 30 , I ( i ) (0) = 0 , R ( i ) (0) = 0 except border, I ( i ) (0) = 10 Parameters: k = 0 . 01, r = 0 . 2, m s = m i = 0 . 05 SFM-16 16 / 60

  45. quan�col . ........ . . . ... ... ... ... ... ... ... SIR model on 30x30 grid Stochastic: von Neumann neighbourhood www.quanticol.eu Initial values: S ( i ) (0) = 30 , I ( i ) (0) = 0 , R ( i ) (0) = 0 except border, I ( i ) (0) = 10 Parameters: k = 0 . 01, r = 0 . 2, m s = m i = 0 . 05 SFM-16 16 / 60

  46. quan�col . ........ . . . ... ... ... ... ... ... ... SIR model on 30x30 grid Stochastic: von Neumann neighbourhood www.quanticol.eu Initial values: S ( i ) (0) = 30 , I ( i ) (0) = 0 , R ( i ) (0) = 0 except border, I ( i ) (0) = 10 Parameters: k = 0 . 01, r = 0 . 2, m s = m i = 0 . 05 SFM-16 16 / 60

  47. quan�col . ........ . . . ... ... ... ... ... ... ... SIR model on 30x30 grid Stochastic: von Neumann neighbourhood www.quanticol.eu Initial values: S ( i ) (0) = 30 , I ( i ) (0) = 0 , R ( i ) (0) = 0 except border, I ( i ) (0) = 10 Parameters: k = 0 . 01, r = 0 . 2, m s = m i = 0 . 05 SFM-16 16 / 60

  48. quan�col . ........ . . . ... ... ... ... ... ... ... SIR model on 30x30 grid Stochastic: von Neumann neighbourhood www.quanticol.eu Initial values: S ( i ) (0) = 30 , I ( i ) (0) = 0 , R ( i ) (0) = 0 except border, I ( i ) (0) = 10 Parameters: k = 0 . 01, r = 0 . 2, m s = m i = 0 . 05 SFM-16 16 / 60

  49. quan�col . ........ . . . ... ... ... ... ... ... ... SIR model on 30x30 grid Stochastic: von Neumann neighbourhood www.quanticol.eu Initial values: S ( i ) (0) = 30 , I ( i ) (0) = 0 , R ( i ) (0) = 0 except border, I ( i ) (0) = 10 Parameters: k = 0 . 01, r = 0 . 2, m s = m i = 0 . 05 SFM-16 16 / 60

  50. quan�col . ........ . . . ... ... ... ... ... ... ... SIR model on 30x30 grid Stochastic: von Neumann neighbourhood www.quanticol.eu Initial values: S ( i ) (0) = 30 , I ( i ) (0) = 0 , R ( i ) (0) = 0 except border, I ( i ) (0) = 10 Parameters: k = 0 . 01, r = 0 . 2, m s = m i = 0 . 05 SFM-16 16 / 60

  51. quan�col . ........ . . . ... ... ... ... ... ... ... SIR model on 30x30 grid Stochastic: von Neumann neighbourhood www.quanticol.eu Initial values: S ( i ) (0) = 30 , I ( i ) (0) = 0 , R ( i ) (0) = 0 except border, I ( i ) (0) = 10 Parameters: k = 0 . 01, r = 0 . 2, m s = m i = 0 . 05 SFM-16 16 / 60

  52. quan�col . ........ . . . ... ... ... ... ... ... ... SIR model on 30x30 grid Stochastic: von Neumann neighbourhood www.quanticol.eu Initial values: S ( i ) (0) = 30 , I ( i ) (0) = 0 , R ( i ) (0) = 0 except border, I ( i ) (0) = 10 Parameters: k = 0 . 01, r = 0 . 2, m s = m i = 0 . 05 SFM-16 16 / 60

  53. quan�col . ........ . . . ... ... ... ... ... ... ... SIR model on 30x30 grid Stochastic: von Neumann neighbourhood www.quanticol.eu Initial values: S ( i ) (0) = 30 , I ( i ) (0) = 10 , R ( i ) (0) = 0 Parameters: k = 0 . 01, r = 0 . 2, m s = m i = 0 . 05 except bottom third k = 0 . 05 SFM-16 17 / 60

  54. quan�col . ........ . . . ... ... ... ... ... ... ... SIR model on 30x30 grid Stochastic: von Neumann neighbourhood www.quanticol.eu Initial values: S ( i ) (0) = 30 , I ( i ) (0) = 10 , R ( i ) (0) = 0 Parameters: k = 0 . 01, r = 0 . 2, m s = m i = 0 . 05 except bottom third k = 0 . 05 SFM-16 17 / 60

  55. quan�col . ........ . . . ... ... ... ... ... ... ... SIR model on 30x30 grid Stochastic: von Neumann neighbourhood www.quanticol.eu Initial values: S ( i ) (0) = 30 , I ( i ) (0) = 10 , R ( i ) (0) = 0 Parameters: k = 0 . 01, r = 0 . 2, m s = m i = 0 . 05 except bottom third k = 0 . 05 SFM-16 17 / 60

  56. quan�col . ........ . . . ... ... ... ... ... ... ... SIR model on 30x30 grid Stochastic: von Neumann neighbourhood www.quanticol.eu Initial values: S ( i ) (0) = 30 , I ( i ) (0) = 10 , R ( i ) (0) = 0 Parameters: k = 0 . 01, r = 0 . 2, m s = m i = 0 . 05 except bottom third k = 0 . 05 SFM-16 17 / 60

  57. quan�col . ........ . . . ... ... ... ... ... ... ... SIR model on 30x30 grid Stochastic: von Neumann neighbourhood www.quanticol.eu Initial values: S ( i ) (0) = 30 , I ( i ) (0) = 10 , R ( i ) (0) = 0 Parameters: k = 0 . 01, r = 0 . 2, m s = m i = 0 . 05 except bottom third k = 0 . 05 SFM-16 17 / 60

  58. quan�col . ........ . . . ... ... ... ... ... ... ... SIR model on 30x30 grid Stochastic: von Neumann neighbourhood www.quanticol.eu Initial values: S ( i ) (0) = 30 , I ( i ) (0) = 10 , R ( i ) (0) = 0 Parameters: k = 0 . 01, r = 0 . 2, m s = m i = 0 . 05 except bottom third k = 0 . 05 SFM-16 17 / 60

  59. quan�col . ........ . . . ... ... ... ... ... ... ... SIR model on 30x30 grid Stochastic: von Neumann neighbourhood www.quanticol.eu Initial values: S ( i ) (0) = 30 , I ( i ) (0) = 10 , R ( i ) (0) = 0 Parameters: k = 0 . 01, r = 0 . 2, m s = m i = 0 . 05 except bottom third k = 0 . 05 SFM-16 17 / 60

  60. quan�col . ........ . . . ... ... ... ... ... ... ... SIR model on 30x30 grid Stochastic: von Neumann neighbourhood www.quanticol.eu Initial values: S ( i ) (0) = 30 , I ( i ) (0) = 10 , R ( i ) (0) = 0 Parameters: k = 0 . 01, r = 0 . 2, m s = m i = 0 . 05 except bottom third k = 0 . 05 SFM-16 17 / 60

  61. quan�col . ........ . . . ... ... ... ... ... ... ... SIR model on 30x30 grid Stochastic: von Neumann neighbourhood www.quanticol.eu Initial values: S ( i ) (0) = 30 , I ( i ) (0) = 10 , R ( i ) (0) = 0 Parameters: k = 0 . 01, r = 0 . 2, m s = m i = 0 . 05 except bottom third k = 0 . 05 SFM-16 17 / 60

  62. quan�col . ........ . . . ... ... ... ... ... ... ... SIR model on 30x30 grid Stochastic: von Neumann neighbourhood www.quanticol.eu Initial values: S ( i ) (0) = 30 , I ( i ) (0) = 10 , R ( i ) (0) = 0 Parameters: k = 0 . 01, r = 0 . 2, m s = m i = 0 . 05 except bottom third k = 0 . 05 SFM-16 17 / 60

  63. quan�col . ........ . . . ... ... ... ... ... ... ... SIR model on 30x30 grid Stochastic: von Neumann neighbourhood www.quanticol.eu Initial values: S ( i ) (0) = 30 , I ( i ) (0) = 10 , R ( i ) (0) = 0 Parameters: k = 0 . 01, r = 0 . 2, m s = m i = 0 . 05 except bottom third k = 0 . 05 SFM-16 17 / 60

  64. quan�col . ........ . . . ... ... ... ... ... ... ... SIR model on 30x30 grid Stochastic: von Neumann neighbourhood www.quanticol.eu Initial values: S ( i ) (0) = 30 , I ( i ) (0) = 10 , R ( i ) (0) = 0 Parameters: k = 0 . 01, r = 0 . 2, m s = m i = 0 . 05 except bottom third m i = 0 . 001 SFM-16 18 / 60

  65. quan�col . ........ . . . ... ... ... ... ... ... ... SIR model on 30x30 grid Stochastic: von Neumann neighbourhood www.quanticol.eu Initial values: S ( i ) (0) = 30 , I ( i ) (0) = 10 , R ( i ) (0) = 0 Parameters: k = 0 . 01, r = 0 . 2, m s = m i = 0 . 05 except bottom third m i = 0 . 001 SFM-16 18 / 60

  66. quan�col . ........ . . . ... ... ... ... ... ... ... SIR model on 30x30 grid Stochastic: von Neumann neighbourhood www.quanticol.eu Initial values: S ( i ) (0) = 30 , I ( i ) (0) = 10 , R ( i ) (0) = 0 Parameters: k = 0 . 01, r = 0 . 2, m s = m i = 0 . 05 except bottom third m i = 0 . 001 SFM-16 18 / 60

  67. quan�col . ........ . . . ... ... ... ... ... ... ... SIR model on 30x30 grid Stochastic: von Neumann neighbourhood www.quanticol.eu Initial values: S ( i ) (0) = 30 , I ( i ) (0) = 10 , R ( i ) (0) = 0 Parameters: k = 0 . 01, r = 0 . 2, m s = m i = 0 . 05 except bottom third m i = 0 . 001 SFM-16 18 / 60

  68. quan�col . ........ . . . ... ... ... ... ... ... ... SIR model on 30x30 grid Stochastic: von Neumann neighbourhood www.quanticol.eu Initial values: S ( i ) (0) = 30 , I ( i ) (0) = 10 , R ( i ) (0) = 0 Parameters: k = 0 . 01, r = 0 . 2, m s = m i = 0 . 05 except bottom third m i = 0 . 001 SFM-16 18 / 60

  69. quan�col . ........ . . . ... ... ... ... ... ... ... SIR model on 30x30 grid Stochastic: von Neumann neighbourhood www.quanticol.eu Initial values: S ( i ) (0) = 30 , I ( i ) (0) = 10 , R ( i ) (0) = 0 Parameters: k = 0 . 01, r = 0 . 2, m s = m i = 0 . 05 except bottom third m i = 0 . 001 SFM-16 18 / 60

  70. quan�col . ........ . . . ... ... ... ... ... ... ... SIR model on 30x30 grid Stochastic: von Neumann neighbourhood www.quanticol.eu Initial values: S ( i ) (0) = 30 , I ( i ) (0) = 10 , R ( i ) (0) = 0 Parameters: k = 0 . 01, r = 0 . 2, m s = m i = 0 . 05 except bottom third m i = 0 . 001 SFM-16 18 / 60

  71. quan�col . ........ . . . ... ... ... ... ... ... ... SIR model on 30x30 grid Stochastic: von Neumann neighbourhood www.quanticol.eu Initial values: S ( i ) (0) = 30 , I ( i ) (0) = 10 , R ( i ) (0) = 0 Parameters: k = 0 . 01, r = 0 . 2, m s = m i = 0 . 05 except bottom third m i = 0 . 001 SFM-16 18 / 60

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