Balancing Detection and Eradication for Control of Epidemics: Sudden Oak Death in Mixed-Species Stands

Gilligan CA (2010) Balancing Detection and Eradication for Control of Epidemics: Sudden Oak Death in Mixed-Species Stands. PLoS ONE 5(9): e12317. doi:10.1371/journal.pone.0012317 Balancing Detection and Eradication for Control of Epidemics: Sudden Oak Death in Mixed-Species Stands Martial L. Ndeffo Mbah 0 Christopher A. Gilligan 0 Wayne M. Getz, University of California, United States of America 0 Department of Plant Sciences, University of Cambridge , Cambridge , United Kingdom Culling of infected individuals is a widely used measure for the control of several plant and animal pathogens but culling first requires detection of often cryptically-infected hosts. In this paper, we address the problem of how to allocate resources between detection and culling when the budget for disease management is limited. The results are generic but we motivate the problem for the control of a botanical epidemic in a natural ecosystem: sudden oak death in mixed evergreen forests in coastal California, in which species composition is generally dominated by a spreader species (bay laurel) and a second host species (coast live oak) that is an epidemiological dead-end in that it does not transmit infection but which is frequently a target for preservation. Using a combination of an epidemiological model for two host species with a common pathogen together with optimal control theory we address the problem of how to balance the allocation of resources for detection and epidemic control in order to preserve both host species in the ecosystem. Contrary to simple expectations our results show that an intermediate level of detection is optimal. Low levels of detection, characteristic of low effort expended on searching and detection of diseased trees, and high detection levels, exemplified by the deployment of large amounts of resources to identify diseased trees, fail to bring the epidemic under control. Importantly, we show that a slight change in the balance between the resources allocated to detection and those allocated to control may lead to drastic inefficiencies in control strategies. The results hold when quarantine is introduced to reduce the ingress of infected material into the region of interest. - Funding: This work was supported by a Gates Cambridge Scholarship (to MLNM) and a Biotechnology and Biological Research Council (BBSRC) Professorial Fellowship (to CAG), which the authors gratefully acknowledge. The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript. Competing Interests: The authors have declared that no competing interests exist. There is increasing interest in coupling epidemiological with economic models in order to identify optimal strategies for disease control [15]. Sethi [6] and others [79] first used optimal control theory to identify optimal strategies for disease control under a range of simplified epidemiological scenarios. More recent work has focused on introducing more realistic scenarios, for example when resources for control are limited [2], when disease occurs in heterogeneous landscapes [1], and when the time-scales for control occur within and across multiple seasons [3]. In this paper, we use these new approaches to address the problem of optimization of disease control in mixed species stands. We focus on a culling strategy, a widely used method for the control of plant and animal diseases in which infected hosts are removed to prevent further transmission of infection so that they are no longer capable of spreading infection [1013]. Our principal objective is to identify optimal culling strategies for disease control and to investigate how limited resources should be balanced between disease detection and eradication in order to maximize the effectiveness of the control policy. Here, we define eradication in the sense frequently used in plant disease epidemiology as reducing the rate of production of inoculum during the course of the epidemic by destroying the sources of inoculum (culling) [14,15]. We motivate our analyses for the control of a particular class of unidirectional epidemics in mixed two-species stands, in which both species are susceptible but one is a spreader and the other is an epidemiological dead-end to the pathogen cycle of infection. Such a scenario has been observed in the dynamics of diseases such as bubonic plague [16] in which rats are the spreader species, with humans being largely infected by the rat population [16]. Another example, which we study here, occurs in sudden oak death (SOD) in which the spreader may be an under-storey species, with the deadend species frequently being a target for preservation [17,18]. When the dead-end species is indeed targeted for preservation, a simple solution to the problem of disease control might be to eradicate the species driving the infection. Such a nave solution is, however, far from optimal. Although it prevents further spread onto the target species, complete removal of the spreader species may have extremely negative impacts on the stability of the ecosystem. An optimal control strategy must seek to preserve both species. How this is done depends upon the growth and infection dynamics of the two host species, and importantly too on the ease with which infected spreader hosts are detected and removed. Specifically, we consider the control of an epidemic of sudden oak death in Californian coastal forests, where the pathogen, an oomycete, (Phytophthora ramorun) mainly affects bay laurel (Umbelluria californica) - coast live oak (Quercus agrifolia) communities [10,19]. The causal agent, P. ramorun, affects bay laurel that, in turn, acts as a source of inoculum for secondary infection. From infected bay laurel, the pathogen produces spores that spread aerially, by wind and rain splash dispersal mechanisms, to susceptible individuals (bay laurel and coast live oak)[10]. Bay laurel is an effective spreader species that seldom dies from infection. Coast live oak is only infected from bay laurel and dies from infection, accounting for millions of tree mortalities in California [10]. There is no transmission of infection from coast live oak but it is also primarily targeted for preservation. Several control methods have been tested to prevent and contain the spread of P. ramorum on bay laurel in Californian forests but culling of infected spreader trees and a quarantine policy to minimize introduction of inoculum are by far the most commonly used methods [18]. We consider a mixed species stand of bay laurel and coast live oak, in which the objective is to deploy a fixed amount of resource to preserve as many healthy trees of both species as possible, subject to placing a greater utility in preserving coast live oak than bay laurel. We show first that when there is a limit on expenditure, it is optimal to cull as many infected bay laurel trees as possible for SOD in twospecies mixed evergreen communities. T (...truncated)