A Spatial-Dynamic Model for Controlling Pine Wilt Disease

Abstract

Pine Wilt Disease (PWD) is an infectious disease that kills most of infected pine trees. Ever since PWD was identified for the first time in 1988, the infected area has increased from 70 ha in 1988 to 8 000 ha in 2005. PWD becomes the most urgent agenda for forest protection in South Korea. However, managers in charge of dealing with PWD confront a shortage of budget for controlling PWD and thus not all of the infected pine trees left uncontrolled. This situation can make more pine forests under the risk of becoming susceptible to PWD in the future. In this research, the objective is to identify optimal control strategies under economic constraints.

This research develops a spatial-dynamic model to effectively manage an outbreak of PWD. The model is composed of hexagonal patches that carry binary information on dispersal, removal, and prevention of PWD in discrete time dimension. The infection is assumed to disperse deterministically from a patch to other patches rather than stochastically to pursue the simplicity of the model. The model determines where, when, and how much removal or prevention measures are to be applied to each patch of pine stand to minimize the net present value of damage and costs of removal and prevention subject to the economic constraints comprised of the amount of budget, the type of budget, and the value of a forest. In this research, the model parameters are estimated, based on the information from literatures or field data. Seven scenarios are developed and used for simulation analysis: no-control scenario, optimal control scenario, optimal control scenario with eradication plan, optimal control scenario with eradication plan using only a removal control procedure, optimal control scenario with eradication plan under the limited amount of budget, optimal control scenario with eradication plan under the different type of budget, optimal control scenario with eradication plan under the different value of a forest.

The result of analysis suggests five important points for PWD control. First, measures for PWD should be applied only when the marginal benefit of applying the control exceeds the opportunity cost of applying the control. This explains why control efforts are concentrated on the edge of the infection. Second, setting a goal of management of the disease determines which method is to be applied. Without eradication plan, the optimal solution uses only nematocide injection. Under eradication plan, however, it seems to be the most effective to two control methods, silvicultural control and nematocide injection, together at the same site and time. Third, when the budget is limited, it is optimal for the infected area to be divided into smaller ones and be removed in earlier stages. Fourth, it is better to make the budgeting for PWD control be more flexible so that the manager can react to the detection of the infection fast. Under the fixed annual budget, if the budget for a given period is smaller than optimal budget, halting infection and removing small area of infection cannot be done up to the optimal level, thus resulting in more costs of removal and prevention of PWD. Lastly, the manager should take the values of forests into account in deciding the timing of the PWD control. As the value of a forest decreases, the timing of any controls becomes close to the first stage.