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The use of extrinsic stimulation to control activity in neuronal networks i.e., neurocontrol, is a key problem in control engineering and neuroscience. Here, we study the general problem of selective spiking in a population of neurons. The goal is to use an input stimulus in order to induce a spike in a specific neuron of a population while keeping all others suppressed. We formulate a strict version...
For a SIR model with time-varying population that accounts for deaths from a disease, the optimal control problem to limit the spread of the disease through vaccination and treatment is studied. It is shown that singular controls play an important role in the structure of optimal vaccination schedules whereas optimal treatment schedules follow a bang-bang structure of on-off strategies.
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