IGEPP, INRAE, Institut Agro, Univ Rennes, 35000, Rennes, France.
Department of Mathematics, Oregon State University, Corvallis, OR, 97331, USA.
Bull Math Biol. 2021 Mar 21;83(5):46. doi: 10.1007/s11538-021-00872-w.
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.
无病种植材料（“清洁种子”）的分配和使用是发展中国家控制植物病害的一种很有前途的方法。我们通过清洁种子的最优使用来解决使植物疾病发生率最小化的问题。我们考虑了最简单的 S-I 模型，以及一个最大化的简单经济标准。静态优化问题显示了根据经济和流行病学参数，存在多种可能的结果。我们推导出一个简单的条件，表明相对于疾病的流行病学特征，补贴清洁种子在多大程度上可以帮助消灭或控制疾病。然后，我们考虑了动态最优控制和庞特里亚金极大值原理，以研究清洁种子的最佳使用来控制疾病。动态结果与静态结果相当，在某些方面甚至更简单。特别是，使清洁种子使用在经济上可行的临界补贴率的条件与静态优化情况相同。我们讨论了这些结果如何应用于东非玉米致死性坏死的控制。
