Ndeffo Mbah Martial L, Gilligan Christopher A
Epidemiology and Public Health, Yale School of Medicine, 135 College Street, New Haven, CT 06520, USA and Department of Plant Sciences, University of Cambridge, Downing Street, Cambridge CB2 3EA, UK.
Math Med Biol. 2014 Mar;31(1):87-97. doi: 10.1093/imammb/dqt012. Epub 2013 Jul 18.
The design of durable and sustainable strategies for the control of plant diseases is not possible without due consideration of landscape structure and economic factors. However, many studies on control strategies of plant infestation have overlooked these considerations. In this paper, we address the problem of how best to deploy resources for the control of disease outbreaks during a single agricultural season. We consider a spatial model for the spread of a plant pathogen over an agricultural region, and model the effect of control on disease dynamics. We associate with a control strategy a 'costs function' that balances amount invested for treatment to the cost incurred by disease infestation. Our objective is to minimize the level of disease infestation and the effort of control. We prove the existence of a solution to the optimal control problem, and devise a numerical algorithm to compute it. We present results of our numerical studies, and show that the solution depends on the interplay between economic and epidemiological factors, as well as the nature of the control agent.
若不充分考虑景观结构和经济因素，就无法设计出持久且可持续的植物病害控制策略。然而，许多关于植物病虫害控制策略的研究都忽略了这些因素。在本文中，我们探讨了在单个农业季节中如何以最佳方式调配资源来控制病害爆发的问题。我们考虑一种植物病原体在农业区域传播的空间模型，并对控制措施对病害动态的影响进行建模。我们将一种“成本函数”与控制策略相关联，该函数平衡了用于治疗的投入量与病害侵袭所产生的成本。我们的目标是将病害侵袭水平和控制力度降至最低。我们证明了最优控制问题存在解，并设计了一种数值算法来计算该解。我们展示了数值研究的结果，并表明该解取决于经济和流行病学因素之间的相互作用以及控制媒介的性质。
