Filtro de partículas aplicado ao rastreamento e previsão de epidemias

Abstract

One of stochastic filtering objectives is to obtain more reliable and trustworthy data. Due to that characteristic, it was decided to apply some of the most well-known stochastic filtering methods to predicting and tracking epidemics. Through literature, three different models that represent populational dynamics in epidemics were obtained. The models are: SIS (Susceptible Infected Susceptible) model, SIR (Susceptible Infected Recovered) model and SEIR (Susceptible Exposed Infected Recovered) model. In all these cases, white noise was added to the data set in order to simulate a real measurement sample. Since the models are all non-linear, all the stochastic filters applied to the models are non-linear as well. This work is focused on the application of the Particle Filter to the aforementioned models. However, for matters of comparison, the Extended Kalman Filter was also implemented. Both filters were implemented using MATLAB software. The data obtained from the models was also generated in MATLAB, but through two different methods. The first method was with the data being generated based on the model itself, which was named Synthetic Generation. The second method was through a code written in MATLAB called MOSES (MATLAB-Based Open-Source Stochastic Epidemic Simulator), which was obtained from literature. Finally, só that all of the results that were obtained could be compared, the RMSE (Root Mean Squared Error) of each data set obtained through the stochastic filtering process. The results were within what was expected, with the Particle Filter outperforming de Extended Kalman Filter 4 out of 5 times.