Nik Cunniffe When, where and how to manage a forest disease epidemic? Modelling control of sudden oak death in California 1

Exotic invader in NW Europe, UK & USA Generalist; infects many tree/shrub species Epidemic very well established in California Killed millions of oaks since ~1990 In UK since ~2002 (on larch since ~2009) Sudden “oak” death (Phytophthora ramorum)

Developing a mathematical model - host - environment - pathogen Modelling management - can we control starting now? - when could we have controlled? - how to optimise local deployment? - how to select sites to treat? - what is effect of a changing budget? Outline

Developing a mathematical model - host - environment - pathogen Modelling management - can we control starting now? - when could we have controlled? - how to optimise local deployment? - how to select sites to treat? - what is effect of a changing budget? Developing a mathematical model

Host. Capture host density via a spatial host index ~1.5 million 250m x 250m cells containing susceptible host GIS mapping h=10h=50h=90

Stochastic compartmental model (with cryptic class) Difficult part is capturing the rate and spatial scale of new infection

Environment. Moisture and temperature drive spread Use historic weather to drive infection rates for dates in past Project into future using state-wide sample of entire years

Pathogen. Dispersal kernel/infection rate fitted to data Short Long MCMC Fitting - (power law) dispersal - rate of infection 99.4% 0.6%

Prediction. Spread accelerates once reach North West

Developing a mathematical model - host - environment - pathogen Modelling management - can we control starting now? - when could we have controlled? - how to optimise local deployment? - how to select sites to treat? - what is effect of a changing budget? Modelling management

Can the epidemic be managed starting now? Up to 200km 2 /yr (approx. cost 100 Million USD/yr!), starting 2014 Even v. extensive control starting “now” has almost no effect

When could the epidemic have been controlled? Why focus on 2002? -Pathogen identified -Epidemiology “known” -Control in Oregon -EU emergency measures -Pragmatic: gives a response to optimize! Consider control of up to 50 km 2 /yr starting in 2002

How can local deployment of control be optimised? Last result contingent on fixed local control strategy (375m radius) Test varying radius of removal around detected infected locations

How can local deployment of control be optimised? Can optimise, but significant variability in the outcome Optimal radius depends on tolerable level of risk

How can local deployment of control be optimised? Optimal radius goes up as budget increased Optimal radius goes down with level of risk aversion

How can set of sites to treat around be selected? Preferentially treating on and ahead of the wave front is best Dynamic version of barrier strategy (cf. van Duzen in Humboldt and also Xylella in Italy)

How can set of sites to treat around be selected? For this epidemic, robust to budget and year of starting control

What if expenditure can change over time? Unsurprising, but almost certainly the opposite of what happens in practice Normalise to fixed total spend from Optimal to treat as hard as possible as early as poss.

Using these ideas in practice - This talk takes a retrospective view -But surely it’s sensible to use a well-understood case study to understand how to manage outbreaks of tree disease? -Models like these now used fairly routinely often in “real-time” - P. ramorum in U.K. - Chalara ash dieback -And even for established epidemics, when “all is lost”, one use is to optimise protection of high-value/disease-free areas

21 Spread of P. Ramorum in the UKDutch elm in East Sussex Ash diebackOriental chestnut gall wasp 21 Practical use of models in “real-time” DEFRA’s Tree Health Management Plan

Co-authors and funders Richard Cobb, University of California, Davis Ross Meentemeyer North Carolina State University Dave Rizzo University of California, Davis Chris Gilligan University of Cambridge