Transições de fase e fenômenos críticos do modelo epidêmico difusivo calazar 1d

Abstract

The study of phase transitions and critical phenomena in systems out of thermodynamic equilibrium has gained prominence, particularly in the modeling of complex processes such as the propagation of epidemics. Spatially explicit stochastic models, such as the Diffusive Epidemic Process (DEP), allow the investigation of the interaction between reaction and diffusion and its impact on the critical behavior of the system. Inspired by the DEP and with relevance to the dynamics of diseases such as visceral leishmaniasis (kala-azar), this work addresses physical phenomena associated with systems such as the contact process, which can be interpreted as a model of epidemiological transmission. Both physical systems and epidemics are out of equilibrium systems, sharing universal critical properties, such as phase transitions and critical exponents. In this context, in order to understand the spread of an epidemic, as visceral leishmaniasis (VL) is an endemic disease on five continents, caused by protozoa of the genus \textit{Leishmania}, we use the epidemic model introduced by Harris, which describes the dynamics of propagation in a network of connections between individuals, represented as sites in a network. Each individual can be in one of two states: susceptible (healthy) or infected. Transmission occurs by direct contact: if a neighbor is infected, there is a defined probability of contamination, proportional to the number of neighboring sites. This process can have two states at the end, which are active and absorbent, where in one the epidemic does not cease completely and in the other all individuals remain susceptible. Thus, the propagation of epidemics by direct contact allows us to explore physical properties such as phase transitions, criticality and critical exponents, characterizing the different possible states of the system.