This is intended to provide a set of self-contained examples, much like the Mudd math fun facts which demonstrate mathematics through biological examples.
Divide population into 3 or more groups. Number of infections in one generation is mapped to next generation through matrix multiplication. After short time, proportion of infections in each generation is same.
This is an eigenvector. The eigenvalue happens to be the dominant eigenvalue. This corresponds to the power method.
Perron-Frobenius guarantees the existence of a dominant positive eigenvalue.
Divide population into 3 or more groups. Number of infections in one generation is mapped to next generation through matrix multiplication. After short time, proportion of infections in each generation is same.
This is an eigenvector. The eigenvalue happens to be the dominant eigenvalue. This corresponds to the power method.
Perron-Frobenius guarantees the existence of a dominant positive eigenvalue.