A deep learning based surrogate model for the parameter identification problem in probabilistic cellular automaton epidemic models.

BACKGROUND AND OBJECTIVE: an accurate estimation of the epidemiological model coefficients helps understand the basic principles of disease spreading. Some studies showed that dozens of hours are needed to simulate the traditional probabilistic cellular automaton (PCA) model, and dozens of hours are spent for a fine-tuning of the system. Here, we propose a deep learning-based surrogate model to mimic a PCA model to reduce the simulations' computational time, maintaining an equivalent precision in the estimates. METHOD: we consider PCA models based on regular lattices of different sizes to generate training data sets varying the parameters related to individuals' movement in the lattice and the disease infectivity. These parameters are the input variables for training the surrogate model, and the outputs parameters to be fitted are the percentages of susceptible and infected individuals at the steady-state, the basic reproduction number R0, the peak value and the peak instant of infected individuals, I(τ) and τ, respectively. RESULTS: The proposed surrogate model can predict all the output variables with a low relative error. The surrogate model's training time is independent of the size of the lattice, and the time for evaluating a solution by the surrogate model is low and independent of the lattice size. CONCLUSIONS: The surrogate model provides a fast simulation time for a generic Susceptible-Infected-Removed (SIR) model in a PCA, which is helpful for tuning the model before final simulations, supporting the initial search for inverse problems of parameters estimation in SIR models and providing a satisfactory estimation of the output variables for large populations.

Disease spreading in complex networks: A numerical study with Principal Component Analysis.

Disease spreading models need a population model to organize how individuals are distributed over space and how they are connected. Usually, disease agent (bacteria, virus) passes between individuals through these connections and an epidemic outbreak may occur. Here, complex networks models, like Erdös-Rényi, Small-World, Scale-Free and Barábasi-Albert will be used for modeling a population, since they are used for social networks; and the disease will be modeled by a SIR (Susceptible-Infected-Recovered) model. The objective of this work is, regardless of the network/population model, analyze which topological parameters are more relevant for a disease success or failure. Therefore, the SIR model is simulated in a wide range of each network model and a first analysis is done. By using data from all simulations, an investigation with Principal Component Analysis (PCA) is done in order to find the most relevant topological and disease parameters.