Elements of Computational Epidemiology a cellular automata framework for computational epidemiology fishy.com.br

Computational Epidemiology in the world epidemiology-laboratoryhttp:// epidemiology-laboratory

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

1st Let´s just look the natural behavior of some things...

Gliders Interact …

Smashing Gliders

Moving Things Around

WHAT are these systems?

History... 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] Cellular Spaces Calculating Spaces Self-Reproducing Automata

A famous and simple one: Game of Life Take a look at this applet – MATHEMATICAL GAMES The fantastic combinations of John Conway's new solitaire game "life" Scientific American, 223 (October 1970): Scientific American

Let´s take some time with this applet to best understand a cellular automaton –

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

Rule iterações

Rule 110, 150 steps

Flows in Rule 110!!

Are these systems artificial ones? A New Kind of Science! or ?

natural biotic types Patterns of some seashellsseashells, like the ones in Conus and Cymbiola genus, are generated by natural CA.Conus

arts

What can we do with these “systems”?

MUSIC? Let´s take a bit of time with this site –

CA music generator

What else?

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

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?

We have tried with ANKOS!

results...

endemic area!?? results...

How?

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

Definition of a Cellular Automaton Cellular automaton A is a set of four objects A =, 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)

Cellular automata - generic models for complex systems Definition of a Fuzzy Set Neighborhood of cell Ci,j is global SCA G i,j := {(C k,l, Υ C i,j, C k,l ) |for all C k,l Є C, 0 ≤ Υ C i,j, C k,l ≤ 1} C is a set of all cells in the CA. Υ C 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.

Two-Dimensional Grids 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)

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

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

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

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

modelling... world cells rules

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

Let´s return to the GAME of LIFE –

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

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.

How we do?

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

2006 – 2007, data collect in-loco

estrutura/expedicoes

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 – 2009, data analysis and reports... Parasitological exams on 1100 residents

2008 and 2009 data analysis and reports... Summary data for molluscs collected... 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

, modelling with 15 real parameters (?) From one year (population 1 snapshot, molluscs 12 snapshots) without previous historical...

a cellular automaton Cellular automaton A is a set of four objects A =, 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

one proposal: a top-down approach using a cellular automaton simulation space, a 10x10 square grid

the dynamics Mollusk population dynamics a growth model for the number of individuals (N) that considers the intrinsic growth rate (r) and the maximum sustainable yield or carrying capacity (C) defined at each site (Verhulst, 1838) : Human infection dynamics (SIR - SI) This model splits the human population into three compartments: S (for susceptible), I (for infectious) and R (for recovered and not susceptible to infection) and the snail population into two compartments: M S (for susceptible mollusk) and M I (for infectious mollusk). Socioeconomic and environmental factors environmental quality of the nine collection sites in Carne de Vaca, according to the criteria of Callisto et al (Souza et al, 2010). the model calculates the local increase of population using equation 1 and calculating N(t+1) out from N(t). The values for r and C are set at each site and each time step, using monthly meteorological inputs and considering the ecological quality of the habitat (1) (3a) (3b)

Cells and infection forces states black: rate of human infection = 100%; red: 80% ≤ rate of human infection < 100%; light red: 60% ≤ rate of human infection < 80%; yellow: 40% ≤ rate of human infection < 60%; light yellow: 20% ≤ rate of human infection < 40%; cyan: 0% ≤ rate of human infection < 20%. infection forces Human S -> I (infected molluscs contact, p H ) I -> R (if treated (1-α), χ) Molluscs S -> I (infected human contact, p M )

the algorithm – like the GAME OF LIFE! Events process Main

coding... rain people molusks rivers

sumulations Mathematica 7.0 (Mathematica, 2011) with a processor Intel i5 3GHz, 4MB Cache, 8GB RAM. Computational costs of a complete simulation when assuming a fixed world size (10x10 cells) and extent (365 time steps) and an increasing number of parameters being swept for rejection sampling (from 1 to 15)

simulations “according to the risk indicator, in the scattering diagram of Moran represented in the Box Map (Figure 2), indicated 18 areas of highest risk for the schistosomiasis, all located in the central sector of the village. Areas with lower risk and areas of intermediate risk for occurrence of the disease were located in the north and central portions with some irregularity in the distribution”

Fieldworks to calibrate...

Simulations – previsibility... Predictive scenarios generated with the parameter calibration of the year 2007 that show endemic schistosomiasis. I stands for the average percentage of infected humans per spatial cell predicted by the model

3rd how to learn to do these systems?

Projects epichisto.org Projects Graduate Projects PIBIC projects???

Courses – free, but...

where PPGIA - UFRPE MPES - Cesar.edu BSI - ufrpe

Where can I obtain $$ to finance my ideas with these systems Let´s look this text: – /05/30/graal-the-search-for-grand-algorithms- in-truly-global-software-markets/ /05/30/graal-the-search-for-grand-algorithms- in-truly-global-software-markets/ IKEWAI... RECIFE!

Home tasks To write a project to be executed during the class… template: s-1/mentoring s-1/mentoring –“How can I do this?” … DEADLINE: 06.set.2012

Thanks a lot! jones.albuquerque