Modelos epidemiológicos para físicos

Referências para o paper sobre gripe suína que estou escrevendo:

Modeling epidemics using cellular automata

doi:10.1016/j.amc.2006.06.126 

S. Hoya Whitea, , A. Martín del Reyb, , and G. Rodríguez Sánchezc,

aDepartment of Applied Mathematics, E.T.S.I.I., Universidad de Salamanca, Avda. Fernández Ballesteros 2, 37700-Béjar, Salamanca, Spain

bDepartment of Applied Mathematics, E.P.S. de Ávila, Universidad de Salamanca, C/ Hornos Caleros 50, 05003-Ávila, Spain

cDepartment of Applied Mathematics, E.P.S. de Zamora, Universidad de Salamanca, Avda. Requejo 33, 49022-Zamora, Spain

Available online 15 September 2006.

Abstract

The main goal of this work is to introduce a theoretical model, based on cellular automata, to simulate epidemic spreading. Specifically, it divides the population into three classes: susceptible, infected and recovered, and the state of each cell stands for the portion of these classes of individuals in the cell at every step of time. The effect of population vaccination is also considered. The proposed model can serve as a basis for the development of other algorithms to simulate real epidemics based on real data.

Keywords: Cellular automata; Epidemic spreading; Mathematical modeling; Rectangular lattices; SIR model

Modelling SIR-type epidemics by ODEs, PDEs, difference equations and cellular automata – A comparative study

doi:10.1016/j.simpat.2008.05.015  

G. Schneckenreithera, , , N. Poppera, b, G. Zaunera, b and F. Breiteneckera

aInstitute for Analysis and Scientific Computing, Vienna University of Technology, Wiedner Hauptstraße 8-10, 1040 Vienna, Austria

b‘Die Drahtwarenhandlung’ – Simulation Services, Neustiftgasse 57-59, 1070 Vienna, Austria

Received 16 December 2007; revised 21 April 2008; accepted 26 May 2008. Available online 6 June 2008.

Abstract

The Kermack–McKendrick susceptible-infected-recovered (SIR) model describes the dynamics of epidemics in a cumulative way. This contribution compares different approaches for introducing spatial patterns into these dynamics. The applied techniques cover lattice gas cellular automata (LGCA), stochastic cellular automata (SCA) and partial differential equations (PDE). Even though these methods involve distinct types of spatial interaction, it can be shown, that consistent qualitative and quantitative model behaviour can be obtained by means of parameter adaptions and slight technical modifications. These modifications are motivated by stochastic analysis of distributed interaction (PDE, SCA) and diffusion dynamics (LGCA) as well as prevailing physical analogies. The law of large numbers permits to approximate stochastic contacts by distributed interaction. Diffusion of particles can be approximated through empiric adjustment of a Gaussian diffusion distribution.

Keywords: Susceptible-infected-recovered model; Lattice gas cellular automaton; Stochastic cellular automaton; Partial differential equation; Diffusion distribution

An Infectious Disease Outbreak Simulator Based on the Cellular Automata Paradigm

Sangeeta Venkatachalam1 and Armin R. Mikler1 

(1) Department of Computer Science, University of North Texas, Denton, TX 76207, USA

Abstract

In this paper, we propose the use of Cellular Automata paradigm to simulate an infectious disease outbreak. The simulator facilitates the study of dynamics of epidemics of different infectious diseases, and has been applied to study the effects of spread vaccination and ring vaccination strategies. Fundamentally the simulator loosely simulates SIR (Susceptible Infected Removed) and SEIR (Susceptible Exposed Infected Removed). The Geo-spatial model with global interaction and our approach of global stochastic cellular automata are also discussed. The global stochastic cellular automata takes into account the demography, culture of a region. The simulator can be used to study the dynamics of disease epidemics over large geographic regions. We analyze the effects of distances and interaction on the spread of various diseases.