Optimal Control of Plant Disease Epidemics with Clean Seed Usage
Optimal Control of Plant Disease Epidemics with Clean Seed Usage
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DOI：
10.1007/s11538-021-00872-w
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发表时间：
2021-03-21
影响因子：
3.5
通讯作者：
Bokil, V. A.
中科院分区：
文献类型：
--
作者：
Hamelin, F. M.;Bowen, B.;Bokil, V. A.
在发展中国家，分发和使用无病原体种植材料（“清洁种子”）是一种很有前途的控制植物病害的方法。我们解决的问题，最大限度地减少病害流行的植物通过清洁种子的最佳利用。我们考虑最简单的可能S-I模型和一个简单的经济准则来最大化。静态优化问题显示了经济和流行病学参数不同的可能结果。我们得出了一个简单的条件，表明相对于疾病的流行病学特征，在多大程度上补贴干净的种子可能有助于根除或控制疾病。在此基础上，结合动态最优控制和庞特里亚金极大值原理，研究了清洁种子的最优利用对病害的控制。动态结果与静态结果相当，在某种意义上甚至更简单。特别是，与静态优化情况相比，使清洁种子使用具有经济可行性的临界补贴率条件没有变化。我们讨论了这些结果如何应用于东非玉米致命坏死的控制。
The distribution and use of pathogen-free planting material ("clean seeds") is a promising method to control plant diseases in developing countries. We address the question of minimizing disease prevalence in plants through the optimal usage of clean seeds. We consider the simplest possible S-I model together with a simple economic criterion to be maximized. The static optimization problem shows a diversity of possible outcomes depending on economical and epidemiological parameters. We derive a simple condition showing to what extent subsidizing clean seeds relative to the epidemiological features of the disease may help eradicate or control the disease. Then we consider dynamic optimal control and Pontryagin's maximum principle to study the optimal usage of clean seeds to control the disease. The dynamical results are comparable to the static ones and are even simpler in some sense. In particular, the condition on the critical subsidy rate that makes clean seed usage economically viable is unchanged from the static optimization case. We discuss how these results may apply to the control of maize lethal necrosis in East-Africa.