Aggregation, blowup, and collapse: the abc's of taxis in reinforced random walks
SIAM Journal on Applied Mathematics
Simulation and the Monte Carlo Method (Wiley Series in Probability and Statistics)
Simulation and the Monte Carlo Method (Wiley Series in Probability and Statistics)
Discrete and continuous approaches to modeling cell movement in the presence of a foreign stimulus
Computers & Mathematics with Applications
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Populations interact in a wide variety of ways: through cooperation, competition, or predation. In this work we consider two interacting populations, individuals and a stimulus. Individuals move in response to the stimulus population while the stimulus only diffuses. Both populations grow while the stimulus population is being depleted by the individuals. In order to account for the random nature of the system, an individual-based model (IBM) is first developed and then upscaled into a continuous partial differential equation (PDE) model by considering transition probabilities of the individuals at each site. Finally, a set of numerical experiments is presented showing very good agreement between the IBM and the PDE model.