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Department of Plant Sciences

Three diagrams. 1st a line graph with six lines decreasing then levelling out. 2nd and 3rd hot point maps of California. 2nd shows high level of disease the 3rd low level.


Supervisor: Dr Nik Cunniffe


Brief summary

This project will test whether and how insights from optimal control theory can be applied to detailed spatio-temporal, stochastic, landscape-scale models as used by plant health policy-makers, to show how to control invasive forest diseases as effectively as possible, even when budgets and epidemiological-knowledge are limited.


Importance of Research 

Increasing rates of global trade and travel, and changing climatic patterns, have led to more frequent outbreaks of plant disease epidemics worldwide. Non-native invasive pathogens in forest environments routinely cause significant population, community, ecosystem and economic impacts. A prominent historical example is Dutch elm disease (caused by Ophiostoma novo-ulmi) which decimated elm populations in the United States and Western Europe in the 1960s/70s. Contemporary examples include Phytophthora ramorum, the causal agent of sudden oak death in the United States and ramorum disease in the United Kingdom, as well as ash dieback (caused by Chalara fraxinea) across almost all of Europe. What disease management has been attempted in all three cases might perhaps be characterised as “too little too late”, driven by small budgets for disease detection & control. But mathematical modelling can predict where and how invading pathogens will spread, as well as providing a rational methodology for comparing the performance of possible control strategies against one another. This project focuses on how modelling can be used to optimise control of forest diseases under limited budgets.


Project Summary

The conventional approach to optimise controls – averaging an ensemble of simulations – is limited by computational power. The complexity of policy-relevant models (e.g. Cunniffe et al (2016)) and the vast array of controls/combinations of controls mean that only a small subset of all strategies can be fully tested. In contrast, the mathematics of optimal control theory can unambiguously select the strategy expected to offer the best mitigation of any given epidemic. However, the complexity of the mathematics means that it can only be applied to very simple models. A recent PhD project in my laboratory has shown how insights from optimal control theory might be practically useful, essentially by optimising via a simpler approximate model. Addressing the various remaining challenges to make these techniques useful for policy makers is the focus of this project.


What the successful applicant will do

The student will build on a recent model of sudden oak death in California (Bussell & Cunniffe (2020)), adding stochasticity, more detailed spatial dynamics and – particularly – tracking spread at larger spatial scales. The initial focus will be continuing to test model predictive control – in which optimal control is applied to a simpler approximation and then the optimal solutions are “lifted” back to the full simulation – in this more detailed setting. There are outstanding questions around the detail required in the approximate model, and which heterogeneities must be accounted for. A potentially very interesting area is how the complex and detailed control strategies that emerge from optimal control can be translated to the simpler strategies (essentially rules-of-thumb) appropriate for policy use. When epidemics are invading, it is also important to account for the unavoidable trade-off that emerges when attempting active control of an epidemic for which estimates of key epidemiological parameters become more precise only as the epidemic spreads and so becomes more difficult to control (Thompson et al (2018)). This important (and generic) tension will be a key focus of the work.


Training Provided 

The student would learn i) mapping a complex biological system to a parsimonious mathematical model; ii) modern methods for simulating epidemiological models; iii) high performance computing, via use of the university’s HPC cluster; iv) experience of applying mathematics to a biological system; v) methods of fitting complex mathematical models to spatio-temporal data; vi) the mathematics of optimal control theory.


Educational History

The project would perhaps be best suited to a student with a background in mathematics, engineering, physics or theoretical ecology, ideally with some prior knowledge of computer programming, who is motivated to work on biological problems. However, students with a background in wet-lab biology have enjoyed and been successful in my laboratory in the past, and any such candidates with a strong interest in making a transition to mathematical modelling are encouraged to get in touch to discuss.



  • Cunniffe, N.J., Cobb, R.C., Meentemeyer, R.K., Rizzo, D.M. and Gilligan, C.A. (2016) Modelling When, Where and How to Manage a Forest Epidemic, Motivated by Sudden Oak Death in California PNAS. 113 (20), 5640-5645. doi:10.1073/pnas.1602153113
  • Bussell, E.H. and Cunniffe, N.J. (2020) Applying Optimal Control Theory to a Spatial Simulation Model of Sudden Oak Death: Ongoing Surveillance Protects Tanoak While Conserving Biodiversity Journal of the Royal Society: Interface. 17 (156). doi:10.1098/rsif.2019.0671
  • Thompson, R.N., Gilligan, C.A. and Cunniffe, N.J. (2018) Control Fast or Control Smart: When Should Invading Pathogens be Controlled PLOS Computational Biology. 14 (2). doi:10.1371/journal.pcbi.1006014