Stochastic analysis of a non-linear modal on the growth of terrorism
by
Surender Kumar
Research Scholar, Dept. of Statistics and Operations Research, K.U., Kurukshetra-136119
Coauthors: Usha Sharma (Chairperson, Dept. of Statistics and Operations Research, K.U., Kurukshetra-136119)

Over the last three decades terrorism has acquired global dimension and received a great deal of international attention in the recent past. The fear expressed by Hamilton & Hamilton in there investigation that terrorists may serve to precipitate the larger disaster of internal or external war or that terrorists themselves may become capable of wrecking havoc on a war like scale, became a reality on 11th September 2001. The world from Manhattan to Manila has been painted red. It is manifesting itself in the various form such as narco- terrorism, bio-terrorism, state terrorism cross border terrorism etc. A larger number of research papers and scores of books have been authored on the topic, however these studies are confined to conceptual qualitative description of the phenomenon. The quantitative expect of the phenomenon has been hardly attempted by the researchers . A class of stochastic models for social contagion has been suggested by Hamilton & Hamilton to apply for the modeling of terrorism. Usha Sharma & Mukesh Chawla have studied a stochastic model of periodically instigated terrorism as a non-homogeneous Poisson process involving periodic variation in the occurrence rate .

A close scrutiny of the phenomenon of terrorism shows that it is quite akin to the cancer growth in a bio-system .Both are anti-social in the sense that they destroy the very system in which they grow. A cancer is initiated by some carcinogens while the terrorism originates from sporadic violence, exploitation or false historical pride. Nature provides immune surveillance to a bio-system while civil societies build up their own security mechanism. Taking a clue from this remarkable similarity, in this piece of work, we have extended the bio-mathematical concepts used in the study of tumors and cancers, to the phenomenon of terrorism. We have proposed and examined a non-linear stochastic model for the growth of terrorism. Using linearization and random variable techniques, we have obtain generating function for the terrorism process represented by a random variable n(t), denoting the number of terrorists at time t. We have also obtained expression for the probability of ultimate control of the terrorism and in passing have noted that even in an almost crime and exploitation free country terrorism may grow with logrithmic distribution.

Date received: October 8, 2002