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

Elements of Computational Epidemiologya cellular automata framework for computational epidemiology

www.epischisto.org

fishy.com.br

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

we need 3 steps to understand and colaborate with

ANKOS in EpiSchisto...

1stLet´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– http://www.bitstorm.org/gameoflife/

• MATHEMATICAL GAMESThe fantastic combinations of John Conway's new solitaire game "life"

• Scientific American, 223 (October 1970): 120-123.

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

some patterns...

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

Rule 30 - 1000 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 seashells, like the ones in Conus and Cymbiola genus, are generated by natural CA.

http://www.answers.com/topic/cellular-automaton

arts

What can we do with these “systems”?

MUSIC?

Let´s take a bit of time with this site– http://tones.wolfram.com/

CA music generator

What else?

The Crucial Experiment – Stephen Wolfram, 1986

22.000 BC

Arts

BiologyPsicologyPhysicsComputingMathematicsArqueology...

andEpidemiology?

challenges…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 We have tried with ANKOS!ANKOS!

results...

endemic area!??

results...

How?

2ndLet´s define

(formally and briefly) to answer

in the correct form...

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|+1Z (for automaton, which has cells “with memory”)

– Z|N|Z (for automaton, which has “memoryless” cells)

Cellular automata - Cellular automata - generic models for complex systemsgeneric 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.

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.

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– http://www.bitstorm.org/gameoflife/

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…SchistosomiasisCarne de Vaca – GO Ponta do Canoé!

2006 – 2007, data collect in-loco

2006 – 2007, data collect in-loco

http://200.17.137.109:8081/xiscanoe/infra-estrutura/expedicoes

Figure 1.

Adjusted Pre lavence

0to 10 (3)10to

20 (32)

20to 30 (11)30to 50 (3)

Stream

Prevalence per 100 hab

0 to 1 (15)1 20 (17)

20 60 (14)60 80 (2)80 100 (1)

Breeding sites

to

to

toto

water-collecting tank

R iacho D oce

1a. P revalence 1b. Adjusted Prevalence

Male Female Total

Age group Pop1 Posit2 Prev3 Pop Posit Prev Pop Posit Prev

up to 9 99 7 7.1 100 3 3.0 199 10 5.0

10 to 19 109 26 23.9 99 24 24.2 208 50 24.0

20 to 29 76 31 40.8 90 21 23.3 166 52 31.3

30 to 39 88 18 20.5 103 23 22.3 191 41 21.5

>= 40* 141 14 9.9 168 18 10.7 310 32 10.3

unreported 16 3 18.8 10 2 20.0 26 5 19.2

Total 529 99 18.71 570 91 15.96 1100 190 17.3

* No information on sex for one individual. 1 population. 2 Number of positives. 3 Prevalence per 100 inhabitants.

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

2008 – 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. 19-24.http://dx.doi.org/10.1590/S0073-47212010000100003

Collecting Sites

Alive Dead Positive to S. mansoni

% de infection

I 0 0II 1707 129 4 0,23III 297 198 0 0IV 0 0V 0 0VI 0 0VII 2355 322 37 1,57VIII 76 125 3 3,95IX 0 0Total 4435 774 44 0,99

2009-2010, modelling with 15 real parameters (?)

Paremeter Ranges (avg) How were obtained?

Susceptible human population 0-23 social inquires (Paredes et al, 2010)

Infected human population 0-23 croposcological inquires (Paredes et al, 2010)

Recovered population of humans 0-23 social inquires (Paredes et al, 2010)

Rate of mobility of humans 0-26% social inquires (Paredes et al, 2010)

Rate of mobility of molluscs 0-2% malacological research (Souza et al, 2010)

Population of healthy molluscs 0-1302 malacological research (Souza et al, 2010)

Population of infected molluscs 0-11 malacological research (Souza et al, 2010)

Area susceptible to flooding 0-45%LAMEPE - Meteorological Laboratory of Pernambuco (lamepe, 2008) and environmental inquires (Souza et al, 2010)

Connection to other cells 0-100%LAMEPE - Meteorological Laboratory of Pernambuco (lamepe, 2008) and environmental inquires (Souza et al, 2010)

Rate of human infection 0-100% croposcological inquires and social inquires (Paredes et al, 2010)

Rate of human re-infection 0-100% croposcological inquires and social inquires (Paredes et al, 2010)

Recovery rate 0-100% croposcological inquires and social inquires (Paredes et al, 2010)

Mollusc infection rate 0-100% malacological research (Souza et al, 2010)

Rate of sanitation 0-93% social and environmental inquires (Souza et al, 2010)

Rainfall of the area 39-389mm LAMEPE - Meteorological Laboratory of Pernambuco (Lamepe, 2008)

From one year (population 1 snapshot, molluscs 12 snapshots)without previous historical...

a cellular automatonCellular automaton A is a set of four objects

A = <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|+1Z (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

a b

1 km

a ba b

1 km

simulation space, a 10x10 square grid

the dynamics

Mollusk population dynamicsa 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): )1(

C

NrN

dt

dN

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: MS (for susceptible mollusk) and MI (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).

rteN

NCC

tN

0

01)(

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)

αRχI=dt

dR

χI·S·Mp=dt

dI

αR+p·S·M=dt

dS

IH

I

ISMI

SSMS

rM·I·Mp=dt

dM

rM·I·Mp=dt

dM

(3a)

(3b)

Cells and infection forces

statesblack: 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 forcesHumanS -> I (infected molluscs contact, pH)I -> R (if treated (1-α), χ)

MolluscsS -> I (infected human contact, pM)

the algorithm – like the GAME OF LIFE!

1. Choose a cell in the world; 2. For each human in the cell perform a random walk weighted by the “probability of movement" defined

at each site.

Repeat these steps for every cell in the world. Then update data.

3. Choose a cell in the world; 4. Call the “Events” process; 5. Return the individual to his original cell after the infection phase; 6. Choose a cell in the world; 7. For the mollusk population in that cell, perform a diffusion process weighted by the “rate of movement"

defined at each site;

Repeat these steps for every cell in the world. Then update data.

1. Increase the population of mollusks using the growth model described in Section 3.1; 2. Compute the transition between population compartments of humans using the set of equations (3b)

defined in Section 3.2; 3. Compute the transition between population compartments of humans using the set of equations (3a)

defined in Section 3.2;

Update local data of the spatial cell.

Events process

Main

S – SuscetibleI – InfectedR - Recuperate

coding... 4 DRISTIBUIÇÃO DAS CHUVAS Dados retirado da estação Goiana interpolacaoDados InterpolationdadosChuva;chuvaAreaAlagada A, d :a matrizAux A; Fori 1, i Dimensions A 1 , i ,

Forj 1, j Dimensions A 2 , j , a i, j A i, j interpolacaoDados d 200 ; Returna PlotinterpolacaoDadosx, x, 1, 365, Epilog MapPoint, dadosChuva, AxesOrigin 1, 0, AxesLabel dias, mm³ ,ColorFunction Function x, y , Huey

Grafico ilustrativo da distribuição das chuvas durante o ano

rain

people

molusks

rivers

5 CRESCIMENTO DOS MOLUSCOS Função de Crescimento Populacional:Modelo de Verhulst nt, n0, l, k : If n0 l n0 Ek t 0, Return0, l n0 n0 l n0 Ek t função que retorna o número limite de molusco por celula limiteMoluscoi, j : areaAlagada i, j 40; Limite da população em função do ambiente constanteMolusco 0.02; constante de crescimento area alagavel de cada celula

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)

simulationsDay 26 Day 43 Day 88

Day 106 Day 132 Day 365Color Legend

I = 100%80% ≤ I < 100%60% ≤ I < 80%40% ≤ I < 60%20% ≤ I < 40%0% ≤ I < 20%

(I = percentage of infected humans)

Temporal evolution

Day 26Day 26 Day 43Day 43 Day 88Day 88

Day 106Day 106 Day 132Day 132 Day 365Day 365Color Legend

I = 100%80% ≤ I < 100%60% ≤ I < 80%40% ≤ I < 60%20% ≤ I < 40%0% ≤ I < 20%

(I = percentage of infected humans)

Temporal evolution “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...

2012 2017 2022 2027Color legend

I = 100%80% ≤ I < 100%60% ≤ I < 80%40% ≤ I < 60%20% ≤ I < 40%0% ≤ I < 20%

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

3rdhow to learn to do

these systems?

Projects epichisto.org

Projectshttp://200.17.137.109:8081/xiscanoe/projeto

Graduate Projectshttp://200.17.137.109:8081/xiscanoe/projeto/graduate-projects

PIBIC projects???

Courses – free, but...

http://200.17.137.109:8081/xiscanoe/courses-1

where

• PPGIA - UFRPE

• MPES - Cesar.edu

• BSI - ufrpe

Where can I obtain $$ to finance my ideas with these systems

Let´s look this text:– http://0357464.netsolhost.com/WordPress/

2012/05/30/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: http://200.17.137.109:8081/xiscanoe/courses-1/mentoring– “How can I do this?” …

• DEADLINE: 06.set.2012

Thanks a lot!

jones.albuquerque