Insights sobre criticalidade e universalidade do modelo calazar em redes regulares 1D

Abstract

This study investigated the propagation of Leishmaniasis (Kala-azar) using the Diffusive Epidemic Model (PED) on a one-dimensional network. The objective was to analyze the disease dynamics, focusing on the critical properties of the model obtained in this simulation, namely the critical transition point (pc ≈ 2.480) between active and inactive phases and the critical exponents β/ν ≈ 0.213, γ/ν ≈ 0.72, 1/ν ≈ 0.40. To obtain these results, diffusion rates were considered for Mosquitoes (DA = DB = 0.50), Dogs (DA = DB = 0.25) and Humans (DA = DB = 0) for different network sizes. The results confirmed that the system exhibits a continuous phase transition between the inactive and active phases of the infection. The universality class of the model needs further investigation, as the critical properties do not align with the Directed Percolation class. It is worth noting the potential of Statistical Physics in understanding out-of-equilibrium phenomena, as explored in this study. However, the one-dimensional model and fixed diffusion rates are limitations that simplify reality. For future work, it is suggested to expand the model to complex networks and investigate different diffusion rates, as well as include other epidemiological and socioeconomic factors. The application to other infectious diseases is also a promising avenue to consolidate the contribution of Statistical Physics to public health.