What a difference a stochastic process makes: epidemiological-based real options models of optimal treatment of disease

The real options approach has been used within environmental economics to investigate the impact of uncertainty on the optimal timing of control measures to minimise the impacts of disease. Previous studies typically model the growth in infected area using geometric Brownian motion. The advantage of this is that it is simple and allows for closed form solutions. However, such a process is unbounded and so does not respect the natural upper boundary of the system which is determined by the maximum size of the host species. We show how the natural upper boundary can be incorporated endogenously into the decision problem, through the formulation of the stochastic process that describes growth in infected area. We find that ignoring the natural upper boundary of the system overestimates the value of the option to control, leading to delayed application of treatment. Indeed, when uncertainty is high or the disease is fast spreading then ignoring the upper boundary can lead to control never being deployed. Thus the results presented here have important implications for the way in which the real options approach is applied to determine optimal timing of disease control given uncertainty in future disease progression.