The paper considers how cardinal exponential B-splines can be applied in solving singularly perturbed boundary problems. The exponential nature and the multiresolution property of these splines are essential for an accurate simulation of a singular behavior of some differential equation solutions. Based on the knowledge that the most of exponential B-spline properties coincide with those of polynomial splines (smoothness, compact support, positivity, partition of unity, reconstruction of polynomials, recursion for derivatives), one novel algorithm is proposed. It merges two well known approaches for solving such problems, fitted operator and fitted mesh methods. The exponential B-spline basis is adapted for an interval because a considered problem is solved on a bounded domain.

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A bioterrorist attacks usually cause epidemics of panic in a targeted population. We have presented epidemiologic aspect of this phenomenon as a three-component model--host, information on an attack and social network. We have proposed a mathematical model of panic and counter-measures as the function of time in a population exposed to a bioterrorist attack. The model comprises ordinary differential equations and graphically presented combinations of the equations parameters. Clinically, we have presented a model through a sequence of psychic conditions and disorders initiated by an act of bioterrorism. This model might be helpful for an attacked community to timely and properly apply counter-measures and to minimize human mental suffering during a bioterrorist attack.

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