Understanding co-infection systems with multiple interacting strains remains difficult. High dimensionality and complex nonlinear feedbacks make the analytical study of such systems very challenging. When similar strains are similar, we can model trait variation as parameter perturbations, simplifying analysis. Applying singular perturbation theory to such a multi-strain system we have obtained the explicit collective dynamics in terms of fast (neutral) dynamics, and slow (non-neutral) dynamics. The slow dynamics are given by the replicator equation for strain frequencies, a key equation in evolutionary game theory, which in our case governs selection among N strains. In this talk, I will highlight some key features of this derivation, the use of the replicator equation to understand such a multi-strain system better, and discuss links with diversity data both in epidemiology and ecology.

The maximum likelihood problem for Hidden Markov Models is usually numerically solved by the Baum-Welch algorithm, which uses the Expectation-Maximization algorithm to find the estimates of the parameters. This algorithm has a recursion depth equal to the data sample size and cannot be computed in parallel, which limits the use of modern GPUs to speed up computation time. A new algorithm is proposed that provides the same estimates as the Baum-Welch algorithm, requiring about the same number of iterations, but is designed in such a way that it can be parallelized. As a consequence, it leads to a significant reduction in the computation time. We illustrate this by means of numerical examples, where we consider simulated data as well as real datasets.