Ring vaccination

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Abstract
Based on the description of an outbreak of foot-and-mouth disease (FMD), a particle model is developed describing the most important properties of this epidemic. Also control measures (mass and ring vaccination) are implemented. This model shows the expected behavior in simulations. Since it is impossible to treat this model analytically, we use ideas of branching processes on two levels to derive a caricature of the particle model. In simulations it is shown that this caricature exhibits similar behavior as the particle system. It is possible to analyze the caricature and, in this way, to obtain expressions for the most important quantities like the reproduction number or the expected final number of infected individuals etc. In this way mass vaccination and ring vaccination can be compared and control strategies can be optimized.

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