Zombies are a popular figure in pop culture/entertainment and they are usually portrayed as being brought about through an outbreak or epidemic. Consequently, we model a zombie attack, using biological assumptions based on popular zombie movies. We introduce a basic model for zombie infection, determine equilibria and their stability, and illustrate the outcome with numerical solutions. We then refine the model to introduce a latent period of zombification, whereby humans are infected, but not infectious, before becoming undead. We then modify the model to include the effects of possible quarantine or a cure. Finally, we examine the impact of regular, impulsive reductions in the number of zombies and derive conditions under which eradication can occur. We show that only quick, aggressive attacks can stave off the doomsday scenario: the collapse of society as zombies overtake us all.
During my study leave in 2018 I have applied nonlinear stability analysis techniques to the Douglas-Rachford Algorithm, with the aim of shedding light on the interesting non-convex case, where convergence is often observed but seldom proven. The Douglas-Rachford Algorithm can solve optimisation and feasibility problems, provably converges weakly to solutions in the convex case, and constitutes a practical heuristic in non-convex cases. Lyapunov functions are stability certificates for difference inclusions in nonlinear stability analysis. Some other recent nonlinear stability results are showcased as well.