Automata Network Simulator Applied to theEpidemiology of Urban Dengue Fever

Paper’s Authors:Henrique F. Gagliardi, Fabrcio A.B. da Silva and Domingos Alves

Presented by: Hector Cuesta Arvizu

Center for Computational Epidemiology and Response AnalysisUniversity of North Texas

September 19, 2011Hector Cuesta (CeCERA) Automata Network Simulator Urban Dengue Fever September 19, 2011 1 / 17

Outline

Introduction (why this is important?).

Dengue Fever.

Cellular Automata (...the computational part).

Model (Epidemiology of Urban Dengue Fever).

Automata Network Simulator.

Conclusions.

Hector Cuesta (CeCERA) Automata Network Simulator Urban Dengue Fever September 19, 2011 2 / 17

Introduction

Why is this important?

Dengue Fever are the most common mosquito-borne viral disease inthe world.

Globally, there are an estimated 50 to 100 million cases of DengueFever.

2.5 billion people are at risk world-wide, in most tropical countries.

In the last 20 years, Dengue transmission and frequency of dengueepidemics has increase greatly.

It can be fatal.

Hector Cuesta (CeCERA) Automata Network Simulator Urban Dengue Fever September 19, 2011 3 / 17

Dengue Fever

Dengue Fever

What is Dengue Fever?

Dengue fever is an illness caused by infection with a virus transmittedby the ”Aedes Aegipty” mosquito.

Facts:

ARthropod-BOrne viruses (Arbovirues).Typically, people infected with dengue virus are asymptomatic (80%) oronly have mild symptoms such as an uncomplicated feverDengue fever virus (DENV) is an RNA virus of the family Flaviviridae.The incubation period (time between exposure and onset of symptoms)ranges from 3 to 14 days.

Hector Cuesta (CeCERA) Automata Network Simulator Urban Dengue Fever September 19, 2011 4 / 17

Dengue Fever

Dengue Fever

Transmission

A human may only become infected by Aedes Aegypti bite and amosquito only becomes infected by biting an infected human.

Facts:

Only the female mosquito feeds on blood, this is because they need theprotein found in the blood to produce eggs.On average mosquito can lay about 300 eggs during its life span of 14to 21 days.Dengue can also be transmitted via infected blood products andthrough organ donation.

Hector Cuesta (CeCERA) Automata Network Simulator Urban Dengue Fever September 19, 2011 5 / 17

Dengue Fever

Dengue Fever

The problem statement.

The reason for this approach is that cellular automata have asignificant role in epidemic modeling because each individual, or cell,or small region of space ”updates” itself independently (in parallel)allowing for the concurrent development of several epidemic spatialclusters, defining its new state based on the current state of itssurrounding cells (locality) and on some shared laws of change [2,5].

Hector Cuesta (CeCERA) Automata Network Simulator Urban Dengue Fever September 19, 2011 6 / 17

Cellular Automata

Cellular Automata

What is a Cellular Automata?

Discrete model studied in computability theory and mathematics for anon-linear problems.

Facts:

It consist of an infinite, regular grid of cells, each in one of a finitenumber of states.The grid can be any finite number of dimensions.Each cell is a particular individual.

Hector Cuesta (CeCERA) Automata Network Simulator Urban Dengue Fever September 19, 2011 7 / 17

Cellular Automata

Cellular Automata

Neighbourhood

The Neighbourhood is a selection of cells relative to some specifiedand does not change.

Each cell has the same rules for updating based on the values in thisneighbourhood.

Each time the rules are applied to the whole grid a new generation isproduce.

Local an Global Neighborhoods, Von Newmnan and Moore Neighborhood

Hector Cuesta (CeCERA) Automata Network Simulator Urban Dengue Fever September 19, 2011 8 / 17

Model

Model

The Epidemic Cellular Automata Model for Dengue

The goal of this model is to describe the dynamics of the denguetransmission in a virtual urban environment.

Dengue model, which is a human-vector interaction model

The schematic model of Dengue spreading representing the stage of thedisease for both populations, where thick edges represent the interaction

among population(mosquito bite) and the thin ones the internaltransmission of states in each model.

Hector Cuesta (CeCERA) Automata Network Simulator Urban Dengue Fever September 19, 2011 9 / 17

Model

Model

Iterative rules between these two cellular automata

The local and global influences are show in this figure. The pointedsquares represent the mosquitoes affected by the local and globalhuman infective influence. The same kind of influence occurring inthis bottom-up interactions also occurs for the vector-humans in atop-down sense at each simulation update.

Hector Cuesta (CeCERA) Automata Network Simulator Urban Dengue Fever September 19, 2011 10 / 17

Model

Model

The probability ps of any susceptible individual become infective

1.- Any susceptible individual may become infected with probability ps

2.- An infected individual becomes infective after an average latencytime (TE)

3.- Infective individual are removed deterministically from thesystem(becoming immune) after an infectious period (t > 0), which isconsidered as a constant for all infected human individuals andinfinity to the mosquito population.

4.- Once in the removed class, the individual participate only passivelyin the spreading of the infection by a period of immunity larger thanthe complete epidemic process.

ps = ΓpG + ΛpL;ΓandΛ are weight’s

Hector Cuesta (CeCERA) Automata Network Simulator Urban Dengue Fever September 19, 2011 11 / 17

Model

Model

The resulting probabilities to each population are as follow

Human:

pL = 1− (1− λm)nIm and pG = phNmi (t)

Nm

Mosquito:

pL = 1− (1− λh)nIh and pG = pmNhi (t)

Nh

p = Susceptible individual in General

λ = Susceptible local individual

nIh = Number of infected mosquito in Moore neighbourhood

Hector Cuesta (CeCERA) Automata Network Simulator Urban Dengue Fever September 19, 2011 12 / 17

Automata Network Simulator

Automata Network Simulator

Automata Network Simulator

The main contribution of this paper is to present a software systemthat incorporates a general probabilistic cellular automata model.

Technological Choices:

C++ (as a programming language)OpenGL (to create grid animations during simulations)

Modules:

The specification module.The simulation module.The visualization module.The analysis module.

Hector Cuesta (CeCERA) Automata Network Simulator Urban Dengue Fever September 19, 2011 13 / 17

Automata Network Simulator

Automata Network Simulator

Analysis module

The Status and the Graphic windows of the analysis module.

Hector Cuesta (CeCERA) Automata Network Simulator Urban Dengue Fever September 19, 2011 14 / 17

Automata Network Simulator

Automata Network Simulator

Simulator module

In (a) we see a simulation with the orthogonal view and in(b) the perspective view, where the bottom grid represents the humanpopulation while the top grid represents the vector population.

Hector Cuesta (CeCERA) Automata Network Simulator Urban Dengue Fever September 19, 2011 15 / 17

Conclusions

Conclusions and Future Work

Conclusions and Future Work

Help you understand how to the disease spreads and see differentoutcomes.

Future Work: Seasonality and Geographical information.

A simulation of the Dengue model over Santos city map, a southeastcostal Brazilian city which epidemic historical data will also be used in

future studyHector Cuesta (CeCERA) Automata Network Simulator Urban Dengue Fever September 19, 2011 16 / 17

Conclusions

Questions??

Questions ???

Hector Cuesta (CeCERA) Automata Network Simulator Urban Dengue Fever September 19, 2011 17 / 17