Propriedades críticas e classe de universalidade do modelo calazar em uma rede quadrada

Abstract

In this work, we study the critical behavior of nonequilibrium systems using the Diffusive Epidemic Process (DEP) as a model. We analyze the system's temporal dynamics to understand the conditions under which it transitions from an inactive (disease-free) state to an active (infected) state on a two-dimensional lattice, using visceral leishmaniasis (Kala-azar)—a persistent challenge for Brazilian public health—as a real-world example. Our methodology combines computational simulations based on the Monte Carlo method on a square lattice, where each site can be occupied by particles of type A (healthy) or B (infected), which diffuse independently across the network at different rates (DA < DB, DA < DB, DA = DB). These particles interact according to rules representing contagion and recovery processes. We aim to identify the critical point (transition threshold) and employ finite-size scaling analysis to calculate key physical quantities, such as critical exponents. These results provide a clearer understanding of the type of phase transition occurring in the system and allow us to propose hypotheses about the universality class to which the model may belong. Our findings indicate a well-defined transition point between an inactive (non-infectious) phase and an active (infectious) phase. We conclude that the DEP is an effective model for representing disease spread in populations and that concepts from Statistical Physics can be successfully applied to real-world epidemiological problems.