Computer simulations of individual-based models are frequently used to compare strategies for the control of epidemics spreading through spatially distributed populations. However, computer simulations can be slow to implement for newly emerging epidemics, delaying rapid exploration of different intervention scenarios, and do not immediately give general insights, for example, to identify the control strategy with a minimal socio-economic cost. Here, we resolve this problem by applying an analytical approximation to a general epidemiological, stochastic, spatially explicit SIR(S) model where the infection is dispersed according to a finite-ranged dispersal kernel. We derive analytical conditions for a pathogen to invade a spatially explicit host population and to become endemic. To derive general insights about the likely impact of optimal control strategies on invasion and persistence: first, we distinguish between ‘spatial' and ‘non-spatial' control measures, based on their impact on the dispersal kernel; second, we quantify the relative impact of control interventions on the epidemic; third, we consider the relative socio-economic cost of control interventions. Overall, our study shows a trade-off between the two types of control interventions and a vaccination strategy. We identify the optimal strategy to control invading and endemic diseases with minimal socio-economic cost across all possible parameter combinations. We also demonstrate the necessary characteristics of exit strategies from control interventions. The modelling framework presented here can be applied to a wide class of diseases in populations of humans, animals and plants.

基于个体的模型的计算机模拟经常用于比较控制通过空间分布的人群传播的流行病的策略。然而，对于新出现的流行病，计算机模拟的实施速度可能很慢，从而延迟了对不同干预方案的快速探索，并且不能立即提供一般见解，例如确定社会经济成本最小的控制策略。在这里，我们通过将解析近似应用于一般流行病学、随机、空间显式 SIR(S) 模型来解决这个问题，其中感染根据有限范围的扩散核进行扩散。我们得出了病原体侵入空间明确的宿主群体并成为地方性流行的分析条件。为了得出关于最优控制策略对入侵和持久性可能产生的影响的一般见解：首先，我们根据对扩散核心的影响来区分“空间”和“非空间”控制措施；其次，我们量化控制干预措施对疫情的相对影响；第三，我们考虑控制干预措施的相对社会经济成本。总体而言，我们的研究显示了两种类型的控制干预措施和疫苗接种策略之间的权衡。我们在所有可能的参数组合中确定了以最小的社会经济成本控制入侵性疾病和地方性疾病的最佳策略。我们还论证了控制干预退出策略的必要特征。这里提出的模型框架可以应用于人类、动物和植物群体中的多种疾病。