Terrorist population dynamics model.

A system that includes a number of terrorist cells is considered. The cells can consist of one or more terrorists. The current number of terrorist cells is further denoted by N(t), where t is a current time counted from any appropriate origin. The objective is to find the evolution of the system in terms of N(t) and some interpretable parameters, such as the initial number of the terrorist cells N0=N(0), the cell disabling rate constant lambda (or the cell half-life t1/2), and the rate of formation of new cells P. The cost-effectiveness analysis, performed in the framework of the model, reveals that the effectiveness of disabling a terrorist cell is getting worse after 2-3 half-lives of a cell, which shows that if the anti-terrorist actions have not reached their goal during that time, the respective policy should be considered for revision, using the risk assessment consideration. Another important issue raised concerns balancing the efforts related to counterterrorism actions inside the system and the efforts protecting its borders. The respective data analysis is suggested and illustrated using simulated data.

Simple bounds on cumulative intensity functions of renewal and G-renewal processes with increasing failure rate underlying distributions.

The article considers point processes most commonly used in reliability and risk analysis. Short-term and long-term behavior for the point processes used as models for repairable systems(1) are introduced. As opposed to the long term, the term short term implies that a process is observed during an interval limited by a time close to the mean (or the median) of the respective underlying distribution. A new simple upper bound is proposed on the cumulative intensity function of the renewal process and G-renewal process with an increasing failure rate underlying distribution. The new bound is compared with some known bounds for the renewal process. Finally, a formal definition of "a boundary point" between the short-term repairable system behavior and long-term behavior is introduced. This point can also be used as a lower time limit beyond which the "long-term" Barlow and Proschan bound for the renewal process with NBUE underlying distribution could be effectively applied.