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Elements of Computational Epidemiology

Elements of Computational Epidemiology a cellular automata framework for computational epidemiology. fishy.com.br. www.epischisto.org. Computational Epidemiology in the world. http://compepi.cs.uiowa.edu/ http://cerl.unt.edu/ http://healthmap.org/ceg/ http://www.ceal.psu.edu/

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Elements of Computational Epidemiology

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  1. Elements of Computational Epidemiology a cellular automata framework for computational epidemiology fishy.com.br www.epischisto.org

  2. Computational Epidemiology in the world • http://compepi.cs.uiowa.edu/ • http://cerl.unt.edu/ • http://healthmap.org/ceg/ • http://www.ceal.psu.edu/ • http://www.isi.it/research/computational-epidemiology-laboratory • http://www.epischisto.org

  3. we need 3 steps to understand and colaborate with ANKOS in EpiSchisto...

  4. 1stLet´s just look the natural behavior of some things...

  5. Gliders Interact …

  6. Smashing Gliders

  7. Moving Things Around

  8. WHAT are these systems?

  9. Self-Reproducing Automata History... Cellular Spaces • John von Neumann, 40´s, but... [Ulam, Stanislaw 1952] [von Neumann, John, 1968] [Zuse, Konrad, 1970] [Burks, Arthur (ed.) Essays on Cellular Automata, Univ. Ill, 1970] [Holland, John, 1966] Calculating Spaces

  10. A famous and simple one: Game of Life • Take a look at this applet • http://www.bitstorm.org/gameoflife/ • MATHEMATICAL GAMESThe fantastic combinations of John Conway's new solitaire game "life" • Scientific American, 223 (October 1970): 120-123.

  11. Let´s take some time with this applet to best understand a cellular automaton • http://www.bitstorm.org/gameoflife/

  12. some patterns... • A cell should be black whenever one or two, but not both, of its neighbors were black on the step before.

  13. Rule 30 - 1000 iterações

  14. Rule 110, 150 steps

  15. Flows in Rule 110!!

  16. Are these systems artificial ones?ANew Kind of Science! or ?

  17. natural biotic types Patterns of some seashells, like the ones in Conus and Cymbiola genus, are generated by natural CA. http://www.answers.com/topic/cellular-automaton

  18. arts

  19. What can we do with these “systems”?

  20. MUSIC? Let´s take a bit of time with this site • http://tones.wolfram.com/

  21. CA music generator

  22. What else?

  23. The Crucial Experiment – Stephen Wolfram, 1986 22.000 BC Arts Biology Psicology Physics Computing Mathematics Arqueology ... and Epidemiology?

  24. challenges… • Designing tools for investigate local disease clusters through simulation • What’s New? • Utilizing GIS and EPI information for modeling • Combining different simulation paradigms • Designing a tool kit to establish a computational epidemiology model Is it possible?

  25. We have tried with ANKOS!

  26. results...

  27. results... endemic area!??

  28. How?

  29. 2ndLet´s define (formally and briefly) to answer in the correct form...

  30. Definition of a Cellular Automaton Cellular automaton A is a set of four objectsA = <G, Z, N, f>, where • G– set of cells • Z– set of possible cells states • N – set, which describes cells neighborhood • f– transition function, rules of the automaton: • Z|N|+1Z (for automaton, which has cells “with memory”) • Z|N|Z (for automaton, which has “memoryless” cells)

  31. ΥC i ,j, C k ,l represents an interaction coefficient that controls all possible interactions between a cell Ci,j and its global neighborhood Gi,j. A function of inter-cell distance and cell population density. Cellular automata - generic models for complex systems Definition of a Fuzzy Set Neighborhood of cell Ci,j is global SCA Gi,j := {(Ck,l,ΥC i ,j, C k ,l) |for all Ck,l Є C, 0 ≤ Υ Ci,j, Ck,l≤1} C is a set of all cells in the CA.

  32. Two-DimensionalGrids Cells that have a common edge with the involved are named as “main neighbors” of the cell (are showed with hatching) The set of actual neighbors of the cell a, which can be found according to N, is denoted as N(a)

  33. Definition of the Rings Formally, if R(a, i) is a set of cells of i-th ring of cell a, then if N describes cells neighborhood as the set of its nearest neighbors, following formula will take place

  34. Rings for Grid of … Different rings are showed with hatching or color

  35. Definition of the Metrics Distance function D(a, b) for retrieving remoteness between cells a and b can be denoted as follows It is proved that this function satisfies to all metrics properties The notion of ring may be generalized for multi-dimensional grids and the distance function, given by last formula, will remain the same

  36. Disease Parameters Vaccination Population Demographics Interaction factors Visualization Data Sets cellular automata and epidemiology Distances

  37. modelling... world cells rules

  38. steps... • Cell Definition • World Definition • Simulating parameters • Transition Rules • Results? • Expansion of Diseases – endemic and epidemic aspects • Barriers

  39. Let´s return to the GAME of LIFE • http://www.bitstorm.org/gameoflife/

  40. Cell Definition • Each cell defines a familiar group • Parameters (states): • Carrying capacity; • Total population; • Susceptible subpopulation; • Infective population; • Recovered subpopulation.

  41. Simulating (cont.) • Neighbourhood radius; • Motion probability; • Immigration probability; • Birth rate; • Death rate; • Virus morbidity; • Vectored infection probability; • Contact infection probability; • Spontaneous infection probability; • Recovery probability; • Re-susceptible probability.

  42. How we do?

  43. A case study… Schistosomiasis Carne de Vaca – GO Ponta do Canoé!

  44. 2006 – 2007, data collect in-loco

  45. 2006 – 2007, data collect in-loco http://200.17.137.109:8081/xiscanoe/infra-estrutura/expedicoes

  46. 2008 – 2009, data analysis and reports...Parasitological exams on 1100 residents Spatial pattern, water use and risk levels associated with the transmission of schistosomiasis on the north coast of Pernambuco, Brazil. Cad. Saúde Pública vol.26 no.5 Rio de Janeiro May 2010. http://dx.doi.org/10.1590/S0102-311X2010000500023

  47. 2008 and 2009 data analysis and reports...Summary data for molluscscollected... Ecological aspects and malacological survey to identification of transmission risk' sites for schistosomiasis in Pernambuco North Coast, Brazil. Iheringia, Sér. Zool. 2010, vol.100, n.1, pp. 19-24. http://dx.doi.org/10.1590/S0073-47212010000100003

  48. 2009-2010, modellingwith15 real parameters (?) From one year (population 1 snapshot, molluscs 12 snapshots) without previous historical...

  49. a cellular automaton • Cellular automaton A is a set of four objectsA = <G, Z, N, f>, where • G– set of cells • Z– set of possible cells states • N – set, which describes cells neighborhood • f– transition function, rules of the automaton: • Z|N|+1Z (for automaton, which has cells “with memory”) • Z|N|Z (for automaton, which has “memoryless” cells) Moore Neighbourhood (in grey) of the cell marked with a dot in a 2D square grid

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