In the thesis, we introduce and study different approaches of modelling zombie epidemic. We model the apocalypse of zombies, who came into the population through an outbreak of an epidemic, with the use of assumptions based on popular zombie movies. We introduce and analyse the basic zombie model, determine steady states of the model and their stability. We expand our model by adding different compartments to the model, such as state of latency, quarantine and vaccination. In the thesis we introduce some other approaches for modelling the apocalypse of zombies. We begin with a model based on Lotka-Volterra predator-prey model and illustrate the periodic oscillations of the number of zombies and humans in population. Furthermore, we consider more aggressive approach in facing the zombie threat and try to answer the question whether the humanity survives. We describe the interactions between populations using an analogy with chemical reactions. We formulate a new model and consider whether the size of initial population affects the outcome of epidemic. As a strategy for surviving the zombie epidemic we propose the model in which we build a community. At the end we use diffusion to describe the movement of zombies and calculate how much time we have before getting caught by a zombie.
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