student number: 9305872K M.Sc (Med) Dissertation - School of Physiology / Most performance assessments on athletes involve an excessive amount of testing procedures. The efficacy of these tests is not always apparent, and their application is not always practical. Elite male middle-distance runners (n=20) were used to assess the physiological determinants of 800 meter running performance. We used testing methods recommended by the South African Sports Commission, which included body composition, joint flexibility, muscular strength, -power and -endurance, as well as a Wingate test (anaerobic capacity) and an isokinetic evaluation. An assessment of maximal running speed and acceleration at distances up to 300 meters was conducted on a standard tartan track. In addition, maximal oxygen consumption (VO2max), running economy, onset of blood lactate accumulation (OBLA) and the maximal accumulated oxygen deficit (MAOD) were determined. Measured values were correlated with competitive performance times using the Pearson product-moment correlation technique, with the Bonferroni correction for multiple comparisons. Wingate mean- and minimum power, as well as running times at 40, 60, 70, 80, 90, 150 and 300 meters were found to be significantly correlated to performance (r2>0.4; p<0.01). A multiple correlation comparison was used to determine a significant difference between correlations with performance time for the different variables. A stepwise multiple regression determined that 300 meter time-trial time was the strongest predictor of performance, accounting for 79% of the variability in performance, which was a better predictor of performance than a prediction model. The following formula was derived to estimate 800 meter performance from 300 meter time-trial time: 800m time = 37.1062 + 2.17(300m time) [time in seconds] The tests most able to predict 800 meter running performance were sport-specific track tests of high-speed running ability and tests of anaerobic capacity (especially the Wingate cycle ergometer test).

This thesis is concerned with mathematical modelling and optimal control of constrained systems. Each of the systems under consideration is a system that can be controlled by one of the variables, and this control is subject to constraints. First, we consider middle-distance running where a runner's horizontal propulsive force is the control which is constrained to be within a given range. Middle-distance running is typically a strategy-intensive race as slipstreaming effects come into play since speeds are still relatively fast and runners can leave their starting lane. We formulate a two-runner coupled model and determine optimal strategies using optimal control theory. Second, we consider two applications of control systems with delay related to R&D expenditure. The first of these applications relates to the defence industry. The second relates to the pharmaceutical industry. Both applications are characterised by a long delay between initial investment in R&D and seeing the benefits of R&D realised. We formulate models tailored to each application and use optimal control theory to determine the optimal proportion of available funds to invest in R&D over a given time horizon. Third, we consider a mathematical model of urban burglary based on the Short model. We make some modifications to this model including the addition of deterrence due to police officer presence. Police officer density is the control variable, which is constrained due to a finite number of police officers. We look at different control strategies for the police and their effect on burglary hot-spot formation.