Abstract
The main goal of this work is to propose a mathematical model, based on two-dimensional cellular automata (CA), to simulate an infectious disease outbreak. Specifically, we revisit the general deterministic SEIR (Susceptible Exposed Infectious Recovered) model by adding terms describing the spatial spreading of disease. The state of each cell is a 4-tuple where each component represents the portion of each compartment in the cell at a given time step. We emphasis the role of the basic reproduction number and its relation with some spatial characteristics of CA models. We study in particular, the impact of the neighborhood structure in relation to the spread of such infectious diseases. The presented model will serve as a basis to simulate real epidemics and will also be concerned with the control problem where efficient strategies for disease spread have to be investigated.
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