Department of Plant Sciences, University of Cambridge, Downing Street, Cambridge, CB2 3EA, UK.
Bull Math Biol. 2019 Jun;81(6):1731-1759. doi: 10.1007/s11538-019-00584-2. Epub 2019 Feb 26.
The number of pathogenic threats to plant, animal and human health is increasing. Controlling the spread of such threats is costly and often resources are limited. A key challenge facing decision makers is how to allocate resources to control the different threats in order to achieve the least amount of damage from the collective impact. In this paper we consider the allocation of limited resources across n independent target populations to treat pathogens whose spread is modelled using the susceptible-infected-susceptible model. Using mathematical analysis of the systems dynamics, we show that for effective disease control, with a limited budget, treatment should be focused on a subset of populations, rather than attempting to treat all populations less intensively. The choice of populations to treat can be approximated by a knapsack-type problem. We show that the knapsack closely approximates the exact optimum and greatly outperforms a number of simpler strategies. A key advantage of the knapsack approximation is that it provides insight into the way in which the economic and epidemiological dynamics affect the optimal allocation of resources. In particular using the knapsack approximation to apportion control takes into account two important aspects of the dynamics: the indirect interaction between the populations due to the shared pool of limited resources and the dependence on the initial conditions.
植物、动物和人类健康的致病威胁数量正在增加。控制这些威胁的传播代价高昂，而且资源往往有限。决策者面临的一个关键挑战是如何分配资源来控制不同的威胁，以实现对集体影响的最小损害。在本文中，我们考虑在 n 个独立目标群体中分配有限的资源来治疗病原体，这些病原体的传播使用易感染-感染-易感染模型进行建模。通过对系统动力学的数学分析，我们表明，为了进行有效的疾病控制，在有限的预算下，治疗应该集中在一部分人群上，而不是试图对所有人群进行不太密集的治疗。治疗人群的选择可以通过背包问题近似。我们表明，背包问题非常接近最优解，并且比许多简单的策略表现要好得多。背包问题近似的一个关键优势是，它提供了对经济和流行病学动态如何影响资源最优分配的深入了解。特别是，使用背包问题近似来分配控制考虑到了动态的两个重要方面：由于有限资源的共享池而导致的群体之间的间接相互作用，以及对初始条件的依赖。
