Mathematical modeling of infectious disease spread is crucial for understanding the dynamics of infection transmission in networks. Recent outbreaks of diseases such as COVID-19, SARS, and MERS have highlighted the need for precise mathematical models to predict the spread of diseases. Graph theory allows the simulation of various scenarios for infection transmission between individuals in social networks. The focus is on complete and star graphs, as well as their composites. The use of Markov chains is introduced, enabling the analysis of both single-step and multi-step probabilities of infection spread. Initially, the assumption that individuals cannot recover from the infection was used to simplify the calculations. A brief simulation was conducted to explore the possibility of recovery, both without and with immunity. This thesis contributes to the understanding of how network structures affect the spread of infectious diseases and how to design effective strategies for pandemic containment.
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