Using GIS and CA to model the propagation of infectious ... · Using GIS and CA to study the Propagation of Infectious Diseases Epidemiology and CA (cont.) Lattice gas cellular automaton

Using GIS and CA to study the Propagation of Infec tious Diseases

Using GIS and CA to model the propagation of infectious

Diseases

"Everything should be made as simple as possible, but not simpler." A. Einstein

Joana Margarida

http://www.artificial-life.com/index.php

http://www.artificial-life.com/index.php


This study covers several fields:

Study and modelling of diffusion processes

Cellular automata (CA)

Spatial Epidemiology

Link between GIS and CA models


Diffusion study

•Concerns how fast and to what extent things grow, transfer and diffuse. (Banks, R. B., 1994)•

•The question is not why the processes take place, but the methodology involved in utilizing various frameworks for the analysis and display of data and how the resulting information can be used to

•Interpret and predict•Mathematical framework:

• N - magnitude of a growthing quantity• t - time• x -space direction• a - intrinsic growth coefficient•D - diffusion coefficient


Spatial Diffusion

•Propagation phenomena in time and space of a simple or complex element (Dauphiné, A, 1995)

•Macrodiffusion and Microdiffusion

•Diffusion processes:

•By contiguity without constraints

•Trought new hierarquies•

•With risk•

•Molecular•

•Particle Models: diffusion is represented by elements displacement*

•* Brownian movement

•Particle Models

•Aggregation Models

•Percolation Models

•Cellular Automata

•DLA and DBM

•DauphinéOttavi


Spatial Diffusion (cont.)(Cliff, A.D. ET AL, 1981)

•Expansion Diffusion

•Contagious Diffusion•Spatial Diffusion

•Relocation Diffusion

•Hierarquical Diffusion

http://www.spatial.maine.edu/ax/KEH_il

http://www.spatial.maine.edu/ax/KEH_il


•Why Study Epidemics?•Epidemics repeat themselves in time and space and so provide one data set upon wich calibrate the model and another data set upon wich test it.•Models of the spread of infectious diseases should be useful generally in the analysis of innovation and cultural diffusion patterns. (Cliff, A.D., ET AL, 1981)

Examples: a) spread of a wildfire, adoption of herbicides, b) migration, oxygen transfer across a water surface,...

Spatial Diffusion (cont.)

http://www.nczooeletrack.org/elephants/loomis_maps/

a) b)

http://www.nczooeletrack.org/elephants/loomis_maps/


Spatial Epidemiology

Analysis of the spatial/geographical distribution of the incidence of a disease (Lawson, A. B., 2001)

•Deterministic approach

•Epidemiological models

•Statistical approach

•CA approach

•Disease mapping

•Ecological analysis

•Disease clustering


Statistical ApproachDisease mapping - concerns the use of models to describe the overall disease distribution on the map (clean the map of extra noise).Ecological analysis -analysis of the relation between the spatial distribution of disease incidence and measured explanatory factors.Disease clustering -analysis of unusual aggregations of disease, assessing wether there are any areas of elevated incidence of disease within a map (general and especific clustering)

it is assumed that spatial and temporal clustering can be modelled explicity via a form of contact probability field wich will lead to clustering in space-time (purely descriptive models for spatial clusters of disease) (Lawson, A.B, 2001).

What about infectious diseases????

Incidence of Salmonellosis http://www.gisca.adelaide.edu.au/~cwright/graddip/communicable_diseases.html

WHOhttp://www.who.int/csr/mapping/

http://www.gisca.adelaide.edu.au/~cwright/graddip/communicable_diseases.html

http://www.who.int/csr/mapping/


Point based models and Count based models

Poisson Process

Statistical Approach (cont.)

Discrete Binomial distribution for a Poisson Processhttp://www.mathworld.wolfram.com/PoissonDistribution.html

http://www.mathworld.wolfram.com/PoissonDistribution.html


Bayesian approach incorporates random effects wich can describe unobserved features of the data: population strata random effects, region specific random effects, individual case random effects,...

Methods to incorporate autocorrelation in spatial data: krigging autoregressive (SAR) or conditional autoregressive models (CAR), Markov Random field models.

Effects peculiar to spatial problems: spatial correlated heteregoneity (analysis of spatial correlation) and random-object effects (stochastic geometry).

Statistical Approach (cont.)

The probability density of a vector random variable x, depends on a paremeter vector È as P(x|È). When a realisation of x is observed, we assume that a likelihood can be defined for the parameter vector.

Likelihood-based approach: values of parameters are based on the likelihood itselfBayesian approach: values of parameters are assumed to be governed by prior distributions.

Likelihood-based approach and Bayesian approach


Deterministic Approach•Mathematical models that lead to differential equations

•Epidemics model in a closed population

•r -infection rate•¾ - removal rate•ñ=¾/r (threshold value) S

0>ñ

Threshold Theorem of Epidemiology - When (S0 -ñ) is small compared to ñ, then the number of individuals

who ultimately contract the disease is aproximately 2(S0 ñ)

ODE's - assume there is an homogeneous mixing of types, in space.

(Banks, R. B., 1994, Burghes, D.N. ET AL, 1981)

•SI model for microparasites (G.A. DE LEO, A.P. Dodson)•http://hilbert.dartmouth.edu/~m4w02/syl2.htm

To study the geographical spread of epidemics: PDE's

N=N(x,y,z,t)

Still treat the population as continuous entity, and neglect the fact that populations are composed of single interacting individuals!! (Fuk´s, H. ET AL)

http://hilbert.dartmouth.edu/~m4w02/syl2.htm


Epidemiological Data -Types:

•Tricky!!•-excessive detail that can be useless•-confidentiality•- ecological fallacy (P. Elliot ET AL, 2000)

•-generally an aggregation of case event data•-aggregation increases the local sample size and avoids the need to use exact addresses•-Smoothing involved in counts yeld an invariance at regional level and disjunction between risk and location. •- ecological fallacy (P. Elliot ET AL, 2000)

•If there is case event data that should be used, and it is not recommended the lost of information by aggregation! (P. Elliot ET AL, 2000)

Point Data Count Data


Epidemiological Data -Sources:

Health Data statutory registration systems death (errors), and infectious diseases recording (incomplete).administrative systems (hospitals, admissions, prescriptions systems and general pratice) suplement only! specialised registers (disease registers or special surveys) better quality!

Population Datapopulation registerscensus datavital registration dataadministration dataspecial surveys

•Problems (Lawson, A.B., 2001):•diagnostic «fashion» changes over time•code differences in space and time•boundary changes (MAUP modifiable area unit problem)

•To be considered: edge effects and the scales of measurement (Lawson, A.B., 2001)

•Health Data and Population Data (Relative Risk Assessment)


Replicability

Requirements (Cliff, A.D. ET AL, 1981):Data Considered for this Study:

Stability over space and time

Observability

Isolation

Simplicity of transmission process

High level of data accuracy

Others


Data Considered for this Study:

Monthly numbers of reported cases of measles for each of the medical districts of Iceland (2 waves: 1896-1975, 1945-1970) and monthly estimates of the numbers of individuals at risk (S population*). SI model. (Cliff, A.D. ET AL, 1981).

•*Cohort Model

Centers for Disease Control and Prevention• http://www.cdc.gov/scientific.com- Surveillance: 121 cities mortality report: year, week, location (USA cities) (Cliff, A.D. ET AL, 1998)- HIV/AIDS surveillance report (morbidity data weekly, by city)- Surveillance Resources of infectious diseases - Lyme disease cases and population reported by state (1990-1999).- tuberculosis surveillance reports - tuberculosis cases and case rates, by year, by state.

Possible Sources:

http://www.cdc.gov/scientific.com


Cellular automata

Top Down - The relationships of interest are between variables that capture the global properties of a natural system.

Bottom up - Start from a description of local interactions. Analysis and computer simulation should produce, as emergent properties, the global relationships seen in the real world, without these being pre-programmed into the model!!

•An agent-based model is a bottom up model defined in terms of an algorithmic•description of the behaviour and interactions of individuals (Sumpter, D.J.T)

Artificial life, discrete event simulations, cellular automata,...

«Contrary from intuition, complexity can arise from simple rules» (Wolfram, S, 2002)

Traditional approach to systems study: assume that rules to explain the systems are based on traditional mathematics.Breaking the systems down to find their underlying parts can give us an a idea of how the components act together to produce some of the most obvious features of the overall behaviour!


Cellular Automata (cont.)Discrete dynamical systems whose behaviour is completely specified in terms of a local relation

(Toffoli ET AL, 1991)

System laws are local and uniform- Neighbourhoods: More, von Neumann, Margolus

- Rules: deterministic, probabilistic, voting

CA classes I, II, III, IV (in class IV moving structures are present that allow the comunnication of information))

With appropriate IC, class IV can mimic the behave of all sorts of systems ! (Wolfram, S., 2002)

Recent Progress of ca: Technological side: computers that can carry the directives of a CA model in a efficient way

conceptual side: we are learning how to construct discrete distributed models wich capture essential aspects of physical casuality

Virtues of CA:Inherently parallel: if we associate a processor with every N cells, we can multiply the size of the simulation indefinitly without increasing the time taken for each complete updating of the space.

Inherently local: locality of interconnection of simple processing elements can be translated into speed of operation (speed light constraint).


Plant epidemiology (Newton, A.C. ET AL) - in contrast to animal populations, plant populations are unable to mix freely, and whether an individual plant is healthy or diseased is often closely related to the state of other plants in its immediate neighbourhood.

Epidemiology and CA

Model for the spread of an aerially disseminated foliar disease in a mixed cultivar crop(A.C. Newton, G. Gibson & D. Cox)

The biology of the host-pathogen interactions is so complex that there is a tendency to allow models to become increasingly complex, making them computationally intensive, with many parameters, and difficult to analyse.

Good approach: simpler models which, nevertheless, have the ability to reproduce the behaviour of real systems.

Aplications

Wildlife diseases (Thulke H ET AL) - the host population is not homogeneously affected by the disease over time (the regional spatial pattern emerges from the particular disease dependent dynamics, on the level of the respective local units of infection).The disease dynamics within one local unit of infection is simply a finite number of finite states wich follow up according to time dependent transition probabilities and external stochastic.


Epidemiology and CA (cont.)

Lattice gas cellular automaton (LGCA) for a generic SIR (Fuk´s, H. ET AL) - Unlike models based on partial diferential equations the spread of the infection occurs due to the motion of individuals and their interactions.The model allows to investigate effects of spatial inhomogeneities in population, concentrations on the dynamics of epidemic processes and vaccination strategies.

Advantages of CA epidemic models:

- treat individuals in biological populations as discrete entities

- allow to introduce local stochasticity

- well suited for computer simulations

LGCA dynamics evolution under a uniform vaccination strategy (Fulk's, H. ET AL)

LGCA dynamics evolution under a barrier vaccination strategy (Fulk's, H. ET AL)


(My) CA model

•Assumptions •for model

•Formulate real model

•Formulate CA model

•Run CA model•

•Interpret solution

•Validate model•

•Use model to explain, predict, decide, design


Building a CA model: what is available?

Software Packages/Programming Languages for CA

SWARM - KENGEMAMLSTARLOGOCASECELLANG...

Programming Libraries for CA development

Integrating modelling toolkitBIOMESIMEXXtoys...

General Software Packages for Mathematical Models

Matlab - mapping toolboxScilabMathematica...

General GIS packages

GRASS - MAGICALArcGisIDRISI...

COM objects for GIS developmentMapObjectsArcObjects...


Solutions????

Programming a model and linking it to a GIS using I/O fileshttp://www.cobblestoneconcepts.com/ucgis2summer/liang/liang.htmhttp://www.gisdevelopment.net/aars/acrs/2000/ts12/ts12003.shtml

Developing the model inside the GIS using a scripting language

Developing the model outside the GIS using COM components (MapObjects, ArcObjects,...)http://www.casa.ucl.ac.uk/joanasimoes/

Are GIS capacities that relevant in this context????

Using CA software packages, mathematical packages or building an aplication from scratch

•Aplication using ESRI MapObjects http://www.casa.ucl.ac.uk/joanasimoes/•

Aplication using KENGE libraries for SWARMhttp://www.gis.usu.edu/swarm/•

http://www.cobblestoneconcepts.com/ucgis2summer/liang/liang.htm

http://www.gisdevelopment.net/aars/acrs/2000/ts12/ts12003.shtml

http://www.casa.ucl.ac.uk/joanasimoes/

http://www.casa.ucl.ac.uk/joanasimoes/

http://www.gis.usu.edu/swarm/


Geographic Resources Analysis Support System

http://grass.itc.it

GRASS is an open-source GIS distributed under the GNU license.It supports common vector and raster aplications, with enphasis on raster aplications.Provides environmental modelling such as CA for wildfire simulation.

Programming within GRASS: the open arquitecture of GRASS allows new functions to be implemented as native code rather than as scripts linking existing programs: this is essential to computationally intensive methods as simulation (Lake, M. W., 200)

There is a multiagent simulation extension for GRASS, created by Lake, M. W., (2000):MAGICAL - http://www.ucl.ac.uk/~tcrnmar/

•A Random Walk genotype generated by MAGICAL (genotypes determine agent activities) http://www.ucl.ac.uk/~tcrnmar/simulation/magical/examples/node1.html

http://www.ucl.ac.uk/~tcrnmar/

http://www.ucl.ac.uk/~tcrnmar/simulation/magical/examples/node1.html


Main url: http://www.joana.fr.fmMsc url: http://www.casa.ucl.ac.uk/joanasimoes

http://casoco.casa.ucl.ac.uk/joana/phd/phd.htm

Mail: [email protected]

This presentation is available on:

Contacts

http://www.joana.fr.fm/

http://www.casa.ucl.ac.uk/joanasimoes

mailto:[email protected]


References: Adami, Christoph. (1998) «Introduction to artificial life» - Springer/TELOS, New York. xviii, 374p.Chopard, B.; Droz,M.; (1998) «Cellular Automata Modelling of Physical Systems» section Aléa Saclay; Cambridge

University Press, UK. 341p.Wolfram, S.; (2002) «ANew Kind of Science», Wolfram Media INCToffoli; Margolus; (1991) «Cellular Automata Machines» MIT Press Series in scientific computation, USA. 259p.Cox, D. R. ; Anderson, R. M.; Hillier, Hilary C.; (1989) «Epidemiological and statistical aspects of the AIDS

epidemic»- Royal Society, London. 149p.Cliff, A.D, Hagget, P.; Smallman-Raynor, M. (1998) - «Deciphering Global Epidemics - Analytical approaches to the

disease records of world cities, 1888-1912”. Cambridge Studies in Historical Geography. Cambridge University Press. 470 p.

Cliff, A.D.; Hagget, P.; Ord, J.K.; Versey, G.R.; (1981) «Spatial Diffusion - An historical geography of epidemics in an island community» Cambridge University Press, Cambridge. 238p.

Diekmann, O.; Heesterbeek, J.A.P. (2000) «Mathematical Epidemiology of Infectious Diseases» model building, analysis and interpretation - Wiley series in Mathematical and Computational Biology; John Wiley & Sons, NY. 303p.

Lawson, Andrew. B.; (2001) «Statistical Methods in Spatial Epidemiology» Wiley series in probability and statistics. John Wiley & Sons, England.

P. Elliot, John Wakefield, Nicola Best, David Briggs (2000) «Spatial Epidemiology - Methods and Applications» , Oxforf University Press

Banks, Robert B. (1994) - «Growth and diffusion phenomena » mathematical frameworks and applications - Springer Verlag, USA. 428 p.

Gladwell, M.; (2000) «The Tipping Point - How litle things can make a big difference» Litle Brown and Company, USA. 279p.

Cliff, A.D.; Gould, P.R.; Hoare, A.G.; Thrift, N. J.; (1995) «Diffusing Geography» Blackwell Publishers Inc. 414p.Dauphiné, A.; (1995) «Chaos, Fractales et dynamiques en géographie» Glip RECLUS, Montepellier. 136p.Burghes, D.N.; Borrie, M.S.; (1981) - «Modelling with differential equations» - John Wiley & Sons. 172 p.Lake, M. W.; (2000) - «MAGICAL computer simulation of Mesolithic foraging». In Kohler, T. A. and Gumerman, G.

J., editors, Dynamics in Human and Primate Societies: Agent-Based Modelling of Social and Spatial Processes, pages 107-143. Oxford University Press, New York.

A.C. Newton, G. Gibson & D. Cox - «Understanding plant disease epidemics through mathematical modelling»Azra C. Ghani*, Neil M. Ferguson, Christl A. Donnelly, Thomas J. Hagenaars and Roy M. Anderson (1998) -

«Epidemiological determinants of the pattern and magnitude of the vCJD epidemic in UK »David J.T. Sumpter. « Models»• Thulke H H, Grimm V, Jeltsch F, Tischendorf L, M_uller T, Selhorst T, Staubach C, Wissel C«Cellular automata

in epidemiology - a modelling concept and a wildlife disease» Henryk Fuk´, Anna T. Lawniczak - «Individual-based lattice model for spatial spread of epidemics»


References (cont.):

http://www.maml.hu/ http://www.swarm.org/ http://sourceforge.net/projects/imt/ http://education.mit.edu/starlogo/starterpage.html http://wosx30.eco-station.uni-wuerzburg.de/~martin/biome/ http://www.iu.hio.no/~cell/ http://www.la.utexas.edu/lab/software/lib/simex/README.html http://www.vbi.vt.edu/~dana/ca/cellular.shtmlhttp://www.physics.mun.ca/~johnw/xtoys.html http://www.matlab.com http://www-rocq.inria.fr/scilab/ http://www.cobblestoneconcepts.com/ucgis2summer/liang/liang.htm http://www.stephenwolfram.com http://grass.itc.it http://www.geog.ucsb.edu/~kclarke/ucime/banff2000/78-mu-paper.htm http://www.gisdevelopment.net/aars/acrs/2000/ts12/ts12003.shtml http://www.gis.usu.edu/swarm/

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Using GIS and CA to model the propagation of infectious ... · Using GIS and CA to study the Propagation of Infectious Diseases Epidemiology and CA (cont.) Lattice gas cellular automaton