In this master thesis, mathematical modeling of the spread of infectious diseases is addressed using systems of first-order linear differential equations. The thesis presents an analysis of the basic SIR model, which describes the dynamics of transitions between susceptible, infected, and recovered individuals within a population. The model is extended by incorporating vaccination, allowing for the analysis of the impact of different vaccination strategies on disease containment. Furthermore, the model is adapted to include multiple pathogen variants, enabling a more comprehensive examination of epidemic scenarios. Numerical methods are applied to simulate the models, facilitating the exploration of key parameters such as vaccine efficacy, transmission rate, and vaccination coverage. The objective of this master thesis is to develop a mathematical tool that supports the planning of strategies for epidemic management.
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