| Summary: | Complex Networks can adequately describe many systems that we find in our lives. For example: the network of communications, the way people organize socially, the biological structures animals and plants, and epidemiological systems. In particular, the study of epidemic models in Complex Networks call the attention because its proximity with reality. Such models give a good explanation of how epidemic diseases spread in a network of individuals. This dissertation studied through computer simulation, the process of spreading an epidemic of theoretical physics using tools. Study the critical properties of the Contact Process (CP) and the Contact SIS (Susceptible-Infected-Susceptible) models. The objective of this study is to analyze the results through computer simulation, where we check the type of transition that occurred in both epidemic processes, and also study the critical properties of these models. Using Monte Carlo method (MC), we studied the behavior of the above-mentioned models in the Apollonius network. We simulate the two models for different network sizes and for several generations of an Apollonius network. In the contact process, the model has a representation of the competition between healthy and infected individuals within a given system which leads to a continuous phase transition between active and inactive states. The critical exponents β/ν and 1/ν are calculated. In the SIS model, the spread of the disease occurs by the direct contact between infected and healthy individuals. In each step time, each healthy individual is infected with some disease rate λ and each infected individual is cured with a cure rate equal to 1. In the evolution of system the disease density is the order parameter. For the SIS model, we estimate the critical exponents β=ν, ν, γ0=ν e β. Based on results from the literature, we conclude that the models studied PC and SIS, the network of Apollonius, are in the universality class of Directed Percolation Field for Medium Scale Free network.
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