Processo epidêmico mediado por vetores e processo epidêmico no modelo SIS em rede complexa: um estudo das propriedades críticas

Abstract

Since 1990, epidemic spread has been the subject of many studies based on statistical physics methods. The dynamics of these epidemic processes, typically unbalanced, consist of competition for active (infected hosts) and inactive (uninfected hosts) health status. The transition between these active (epidemic) and inactive (non-epidemic) states allows the analysis of the critical point and exponents of the system (universality class). In this thesis the critical properties of two epidemic systems are investigated: The first composed of two population species that are human with uninfected hosts (H) and infected hosts (Hi) and that of vectors composed of non-infected vectors infected (V ) and infected vectors (Vi), which spread independently in a one-dimensional network, with the rate D, following a dynamic probability rule, where the cure rates of vectors and individuals are respectively φ and λ. A second epidemic system, known as susceptible infected susceptible (SIS), in a complex network with high aggregation factor and contamination rate λ. Both models were simulated using the Monte Carlo method to obtain the data and a finite-size scale analysis allowed the critical properties to be estimated. For the first model, the critical point was obtained for fifteen combinations between the rates of cure of vectors and hosts and fit into the universality class of diffusive epidemic processes, exponents z = ν = 2 and β/ν = 0.11(2). For the second model, the critical point was λc = 0.068(9) and the exponents were: β/ν = 0.88(4), 1/ν = 0.25(4) and γ/ν = 0.51. This information can contribute to the methodologies employed by epidemiology in the fight against infectious diseases.