Modeling And Optimization Theory And Applications

Mathematics is publishing a Special Issue to honor Prof. Sally McClean on the occasion of her semi-retirement and in recognition of her important research contributions. Sally Ida McClean was born in Belfast and received her first degree, an M.A. in Mathematics, from the University of Oxford in 1970. She earned an M.Sc. in Mathematical Statistics and Operations Research from Cardiff University in 1972, and completed her Ph.D. in 1976 at Ulster University at Coleraine. Her contribution to mathematical modeling in healthcare planning is enormous, and, in particular, her studies on improving the wellbeing of the elderly are greatly respected amongst her peers. She is currently a Professor of Mathematics at Ulster University. Her main research interests are in Stochastic Modeling and Optimization for Healthcare Planning and Computer Science. Stochastic processes are some of the most important tools in many areas of science, such as biology, operational research, the social sciences, stochastic finance, etc. Important characteristics in these areas evolve with time in a relatively random way, and since stochastic processes are mainly sequences or families of random variables, in which their index represents time, they are the natural tool to use. The theory and applications of stochastic processes emerged in the genesis of one of the richest ones, that is, Brownian motion. This was rather unexpected since Brownian motion is a beautiful object which is at the same time a martingale, a Gaussian process, a diffusion, a Levy process, a Markov process, etc.—concepts that were discovered quite latter in the evolution of time.

Over the past decade, significant progress has been made in the theory and applications of pharmacodynamics of antimicrobial agents. On the basis of pharmacokinetic-pharmacodynamic modeling concepts it has become possible to describe and predict the time course of antimicrobial effects under normal and pathophysiological conditions. The study of pharmacokinetic-pharmacodynamic relationships can be of considerable value in understanding drug action, defining optimal dosing regimens, and in making predictions under new or changing pre-clinical and clinical circumstances.