We all have to deal with the coronavirus epidemic. Many strategies have been put in place to try to contain the disease, with varying success.

I will present an SIR-type mathematical model to predict the state of the epidemic. The effect of distancing, isolation of exposed individuals and treatment of symptoms will be compared.

I will begin with a simple explanation of SIR models, then discuss a PDE model and its resolution.

In this talk, we consider the Cucker-Smale flocking model involving both singularity and noise. We first show the local strong well-posedness for the system, in which the communication weight is locally Lipschitz beyond the origin. Then, for the special case that the communication weight has a strong singularity at the origin, we establish the global well-posedness by showing the finite time collision-avoidance. Finally, we study the large time behavior of the system when the communication weight is of zero lower bound. The conditional flocking emerges for the case of constant noise intensity, while the unconditional flocking emerges for various time-varying intensities and long-range communications.