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Nondeterministic and Stochastic Cellular Automata and Virus Dynamics

We discuss topological dynamical properties of stochastic cellular automata and nondeterministic cellular automata in the context of virus dynamics models. We consider surjectivity and topological transitivity, and we apply our definitions and results to existing models of dynamics that exhibit different behavior and capture properties of HIV and Ebola virus, labelling the behavior as H-dynamics (surjective and topologically transitive) and E-dynamics (neither).