In this work we propose a variant of a classical SIR epidemiological model where pathogens are characterized by a (phenotypic) mutant trait x . Imposing that the trait x mutates according to a random walk process and that it directly influences the epidemiological components of the pathogen, we studied its evolutionary development by interpreting the tenet of maximizing the basic reproductive number of the pathogen as an optimal control problem. Pontryagin’s maximum principle was used to identify the possible optimal evolutionary strategies of the pathogen. Qualitatively, three types of optimal evolutionary routes were identified and interpreted in the context of virulence evolution. Each optimal solution imposes a different tradeoff relation among the epidemiological parameters. The results predict (mostly) two kinds of infections: short-lasting mild infections and long-lasting acute infections.

中文翻译：

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最佳毒力、扩散和权衡

在这项工作中，我们提出了经典 SIR 流行病学模型的变体，其中病原体的特征在于（表型）突变特征 x 。强加性状 x 根据随机游走过程发生突变并且它直接影响病原体的流行病学成分，我们通过将最大化病原体基本繁殖数的原则解释为最优控制问题来研究其进化发展。庞特里亚金的最大值原理用于确定病原体可能的最佳进化策略。定性地，在毒力进化的背景下确定和解释了三种类型的最佳进化路线。每个最佳解决方案在流行病学参数之间施加不同的权衡关系。结果预测（主要）两种感染：