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J. P. Caulkins, D. Grass, G. Tragler, G. Feichtinger:
"Optimizing counter-terror operations: Should one fight fire with "fire" or "water"?";
Computers & Operations Research, 35 (2008), 6; S. 1874 - 1885.

This paper deals dynamically with the question of how recruitment to terror organizations is influenced by counter-terror operations. This is done within an optimal control model, where the key state is the (relative) number of terrorists and the key controls are two types of counter-terror tactics, one ("water") that does not and one ("fire") that does provoke recruitment of new terrorists. The model is nonlinear and does not admit analytical solutions, but an efficient numerical implementation of Pontryagin's minimum principle allows for solution with base case parameters and considerable sensitivity analysis. Generally, this model yields two different steady states, one where the terror organization is nearly eradicated and one with a high number of terrorists. Whereas water strategies are used at almost any time, it can be optimal not to use fire strategies if the number of terrorists is below a certain threshold.

Optimal dynamic control; Terrorism; Counter-terror; Epidemic modeling

http://dx.doi.org/10.1016/j.cor.2006.09.017