Epidemiology
Mathematics, statistics, computer science, …
CODES and LANGUAGES
fishy.com.br
www.epischisto.org
Statistical epidemiology - (spatial and temporal frequency)
Mathematical epidemiology - (temporal dynamics)
Computational epidemiology - (spatial dynamics)
Genetic epidemiology - (genetic factors)
Codes
Languages
Machines
Epidemiologistas devem ter conhecimentos
de [Naomar, 2006,
]:
http://www.livrariaodontosites.com.br/produtos_descricao.asp?lang=pt_br&codigo_produto=66
•SAÚDE PÚBLICA – devido a ênfase na prevenção de enfermidades.
•MEDICINA CLÍNICA – devido a ênfase na classificação das doenças
e seus diagnósticos.
•FISIOPATOLOGIA – devido a necessidade de entender mecanismos
biológicos básicos da doença.
•ESTATÍSTICA – devido a necessidade de quantificar a freqüência
das doenças e sua relação com os antecedentes.
•CIÊNCIAS SOCIAIS – devido a necessidade de entender o contexto
social no qual a doença ocorre e se apresenta.
What is statistics for epidemiologists?
a code! so “statistical epidemiology” is a redundancy...
• a bit of philosophy of languages and codes...
Discrete versus continuous codes
Alphabet
Numbers
Languages
e 2012?
a bit of history, before…
• http://library.thinkquest.org/22584/emh1000
.htm
resume…
•
•
•
•
•
•
•
•
1650 BC – Papiro by Ahmes – Fractions
600 – 300 BC – Thales and Euclides – Geometry
1200 – Fibonacci – Series
16th - Father of arithmetic by Widmann – Symbols and x^3
+ mx = n
17th – 1654 – Probability and Newton - Leibniz Calculus
and symbols
18th - Bernoulli´s differential equations, needles of Buffon
http://mste.illinois.edu/reese/buffon/bufjava.html
19th – Gauss, Cauchy, Poincaré, Cantor, Boole…
20th – …
[An Introduction to the History of Mathematics by Howard Eves.]
Epidemiologistas devem ter conhecimentos
de que códigos e linguagens [Epischisto,
2012]:
???????????????
• tudo de 2006 + ...?
•http://en.wikipedia.org/wiki/Epidemic_model
•??? Livro Naomar ´onicio´... Capítulo modelos...
Mathematical epidemiology!
and what else?...
another code… Moving Things
Around
WHAT are
these systems?
Self-Reproducing Automata
History...
Cellular Spaces
• John von Neumann, 40´s, but...
[Ulam, Stanislaw 1952]
Calculating Spaces
[von Neumann, John, 1968]
[Zuse, Konrad, 1970]
[Burks, Arthur (ed.) Essays on Cellular
Automata, Univ. Ill, 1970]
[Holland, John, 1966]
A famous and simple one:
Game of Life
• Take a look at this applet
– http://www.bitstorm.org/gameoflife/
• MATHEMATICAL GAMES
The fantastic combinations of John Conway's new solitaire
game "life"
• Scientific American, 223 (October 1970): 120-123.
some codes by machines...
• 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 is a code by machine...
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
Biology
Psicology
Physics
Computing
Mathematics
Arqueology
...
and
Epidemiology?
Statistical epidemiology - (spatial and temporal frequency)
Mathematical epidemiology - (temporal dynamics)
Computational epidemiology - (spatial dynamics)
Genetic epidemiology - (genetic factors)
Codes
Languages
Machines
We have tried with
ANKOS…
Some codes...
cellular automata and
epidemiology
Population
Disease
Parameters
Vaccination
Demographics
Interaction
factors
Distances
Data
Sets
Visualization
a cellular automaton
Cellular 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|+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
a
b
1 km
simulation space, a 10x10 square grid
the dynamics
(3a)
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):
dN
N
 rN (1  )
dt
C
(1)
(3b)
C
N (t ) 
C  N 0  rt
1
e
N0
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).
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
dS
=  p·S·MI + αR
dt
dI
= pH ·S·MI  χI
dt
dR
= χI  αR
dt
dM S
=  pM ·I·MS  rM S
dt
dM I
= pM ·I·MS  rM I
dt
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, pH)
I -> R (if treated (1-α), χ)
Molluscs
S -> I (infected human contact, pM)
the algorithm – like the GAME OF LIFE!
Main
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.
4.
5.
6.
7.
Choose a cell in the world;
Call the “Events” process;
Return the individual to his original cell after the infection phase;
Choose a cell in the world;
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.
Events process
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.
simulations
Temporal
evolution
Color Legend
I = 100%
80% ≤ I < 100%
60% ≤ I < 80%
40% ≤ I < 60%
20% ≤ I < 40%
0% ≤ I < 20%
(I = percentage of
infected humans)
Day 26
Day 43
Day 106
Day 132
Day 88
Day 365
“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”
Simulations – previsibility...
2012
2017
2022
2027
Color 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
Statistical epidemiology - (spatial and temporal frequency)
Mathematical epidemiology - (temporal dynamics)
Computational epidemiology - (spatial dynamics)
Genetic epidemiology in
(genetic factors)
Codes?
Languages?
Machines?
Schistosomiasis???? -
Thanks a lot!
jones.albuquerque