Simulating disease development and economic-impact and the application of mathematical optimization methods for plant-disease management

Mathematical optimization could be a valuable tool for disease management. Optimization techniques include linear programming, which is of limited use for describing biological systems due to restrictions on model structure, and dynamic programming (DP), which is well-suited for solving multi-stage management problems. The four components of any DP model are decision periods, state variables, a transition function, and a criterion function. A disease management decision is made at each decision period. The decision may be binary (i.e. control or no control) or may consist of choosing among different control choices or application rates. State variables describe the state of the system at any point in time and may represent key stages in the life cycle of the pathogen, for example. For computational reasons, the number of state variables should be kept as small as possible (i.e. ¸<10). The transition function describes the change in state variables from one decision period to the next as a function of the state of the system and the management decision and must have a Markovian property. The criterion function describes the actual quantity to be optimized. Because pest management decisions are based ultimately on economic returns, rather than yield or disease level, the criterion function can be stated as a maximization of profit ot minimization of costs. The DP model provides a feedback mechanism, to ensure optimal decisions regardless of the current, state of the system or past decisions. Simple numerical examples of deterministic and stochastic DP are presented to demonstrate the computational efficiency of the technique, the property of optimality, and applicability of the technique to decision-making in disease management.