Epidemics and Bootstrap Percolation in Square Lattice

This lecture covers the spread of epidemics in different models such as SI, SIR, and SIS on complete graphs, focusing on the Kolmogorov equation and probability generating functions. It also explores the concept of Bootstrap Percolation, where nodes need a threshold of active neighbors to become active, with applications in physics and social networks. The instructor discusses the Bootstrap Percolation by Culling method, where inactive nodes remain inactive forever, and the network evolves until a perfect rectangle or all vertices become inactive. The lecture concludes with examples and analyses of diffusion Bootstrap Percolation on contact graphs and random regular graphs.