A model of workplace safety incorporating worker interactions and simple interventions

Although there was substantial research into the occupational health and safety sector over the past forty years, this generally focused on statistical analyses of data related to costs and/or fatalities and injuries. There is a lack of mathematical modelling of the interactions between workers and the resulting safety dynamics of the workplace. There is also little work investigating the potential impact of different safety intervention programs prior to their implementation. In this article, we present a fundamental, differential equation-based model of workplace safety that treats worker safety habits similarly to an infectious disease in an epidemic model. Analytical results for the model, derived via phase plane and stability analysis, are discussed. The model is coupled with a model of a generic safety strategy aimed at minimising unsafe work habits, to produce an optimal control problem. The optimal control model is solved using the forward-backward sweep numerical scheme implemented in Matlab. References Australian Bureau of Statistics. Forms of employment. Commonwealth of Australia, 2010. http://www.abs.gov.au/AUSSTATS/[email protected]/DetailsPage/6359.0November%202010?OpenDocument Bahn, S. Power and Influence: Examining the Communication Pathways that Impact on Safety in the Workplace. J. Occup. Health Safety–-Aust. N.Z., 25(3):213–222, 2009. Bird, P. Reducing Manual Handling Workers Compensation Claims in a Public Health Facility. J. Occup. Health Safety–-Aust. N.Z., 25(6):451–459, 2009. Breslin, P. Improving ohs Standards in the Building and Construction Industry through safe design. J. Occup. Health Safety–-Aust. N.Z., 23(4):89–99, 2007. Breslin, P. National Harmonisation: Designers' Duties of Care in the Australian Building and Construction Industry. J. Occup. Health Safety–-Aust. N.Z., 25(6):495–504, 2009 . Driscoll, T., Mitchell, T., Mandryk, J., Healey, S., Hendrie, L. and Hull, B. Trends in Work-Related Fatalities in Australia, 1982 to 1992. J. Occup. Health Safety–-Aust. N.Z., 18(1):21–33, 2002. Driscoll, T. Fatal Injury of young workers in Australia. J. Occup. Health Safety–-Aust. N.Z., 22(2):151–161, 2006. Foley, G., Gale, J. and Gavenlock, L. The Cost of Work-Related Injury and Disease. J. Occup. Health Safety–-Aust. N.Z., 11(2):171–194, 1995. Glendon, I. and Waring, A. Risk management as a framework for occupational health and safety. J. Occup. Health Safety–-Aust. N.Z., 13(6):525–532, 1997. Gunningham, N. and Healy, P. Agricultural ohs Policy: Towards Systemic Reform. J. Occup. Health Safety–-Aust. N.Z., 20(4):311–318, 2004. Hawkins, A., Eather, J. and Fragar, L. Improving Health and Safety in the Farm Workshop. J. Occup. Health Safety–-Aust. N.Z., 24(2):155–160, 2008. Heads of Workers' Compensation Authorities. 2008/09 Australia and New Zealand Return to Work Monitor. http://www.hwca.org.au/documents/Australia%20and%20New%20Zealand%20Return%20to%20Work%20Monitor%202008-2009.pdf Kermack, W. O. and McKendrick, A. G. A Contribution to the Mathematical Theory of Epidemics. Proc. R. Soc. Lond. A., 115(772):700–721, 1927. doi:10.1098/rspa.1927.0118 Lenhart, S. and Workman, J. T. Optimal control applied to biological models. Chapman and Hall CRC Mathematical and Computational Biology Series, 2007. Mallet, D. G., Bagher-Oskouei, M., Farr, A. C., Simpson, D. P. and Sutton, K-J. A mathematical model of Chlamydial infection incorporating movement of Chlamydial particles. B. Math. Biol., 75(11):2257–2270, 2013. doi:10.1007/s11538-013-9891-9 Murray, J. D. Mathematical Biology, I: An Introduction. Springer, 2002. Raggett, G. F. Modelling the Eyam plague. B. I. Math. Appl., 18:221–226, 1982. Safe Work Australia. The cost of work-related injury and illness for australian employers, workers and the community:2008-2009. Commonwealth of Australia, 2012. http://www.safeworkaustralia.gov.au/sites/SWA/about/Publications/Documents/660/Cost%20of%20Work-related%20injury%20and%20disease.pdf Shulgin, B., Stone, L. and Agur, Z. Pulse vaccination strategy in the sir Epidemic Model. B. Math. Biol., 60(6):1123–1148, 1998. doi:10.1006/S0092-8240(98)90005-2 Vanderkruk, R. Workplace health and safety officers: a Queensland success story. J. Occup. Health Safety–-Aust. N.Z., 15(6):557–563, 1999. Winder, C. The development of ohs legislation in Australia. J. Occup. Health Safety–-Aust. N.Z., 25(4):277–287, 2009

Mathematical modelling of worker interactions and the impact on workplace safety

This research involves applying mathematical modelling techniques coupled with data on work and safety practices to investigate workplace safety programs and improvement strategies. The thesis investigated the potential impact of different safety intervention programs prior to their implementation within the workplace. As there was a lack of mathematical modelling of the interactions between workers and workplace safety intervention programs and how these interactions and programs impacted the safety of the worker while at work, this research presents mathematical models that may be used as a basis for further investigation regarding Occupational Health and Safety