Lewis-Sigler Institute for Integrative Genomics, Princeton University, Princeton, NJ 08544;
Lewis-Sigler Institute for Integrative Genomics, Princeton University, Princeton, NJ 08544.
Proc Natl Acad Sci U S A. 2020 May 26;117(21):11541-11550. doi: 10.1073/pnas.1920761117. Epub 2020 May 8.
Pathogens exhibit a rich variety of life history strategies, shaped by natural selection. An important pathogen life history characteristic is the propensity to induce an asymptomatic yet productive (transmissive) stage at the beginning of an infection. This characteristic is subject to complex trade-offs, ranging from immunological considerations to population-level social processes. We aim to classify the evolutionary dynamics of such asymptomatic behavior of pathogens (hereafter "latency") in order to unify epidemiology and evolution for this life history strategy. We focus on a simple epidemiological model with two infectious stages, where hosts in the first stage can be partially or fully asymptomatic. Immunologically, there is a trade-off between transmission and progression in this first stage. For arbitrary trade-offs, we derive different conditions that guarantee either at least one evolutionarily stable strategy (ESS) at zero, some, or maximal latency of the first stage or, perhaps surprisingly, at least one unstable evolutionarily singular strategy. In this latter case, there is bistability between zero and nonzero (possibly maximal) latency. We then prove the uniqueness of interior evolutionarily singular strategies for power-law and exponential trade-offs: Thus, bistability is always between zero and maximal latency. Overall, previous multistage infection models can be summarized with a single model that includes evolutionary processes acting on latency. Since small changes in parameter values can lead to abrupt transitions in evolutionary dynamics, appropriate disease control strategies could have a substantial impact on the evolution of first-stage latency.
病原体表现出丰富多样的生活史策略，这些策略是由自然选择塑造的。病原体生活史的一个重要特征是，在感染的早期就有诱导无症状但具有生产力（传染性）阶段的倾向。这一特征受到复杂的权衡影响，范围从免疫考虑到群体层面的社会过程。我们旨在对病原体这种无症状行为（以下简称“潜伏期”）的进化动态进行分类，以便为这种生活史策略统一流行病学和进化观点。我们专注于一个具有两个感染阶段的简单流行病学模型，其中第一阶段的宿主可能部分或完全无症状。在免疫学方面，第一阶段的传播和进展之间存在权衡。对于任意的权衡，我们推导出了不同的条件，这些条件保证了在潜伏期为零、某些或最大潜伏期时，至少存在一个进化稳定策略（ESS），或者可能令人惊讶的是，至少存在一个不稳定的进化奇异策略。在后一种情况下，潜伏期为零和非零（可能是最大）之间存在双稳态。然后，我们证明了幂律和指数权衡的内部进化奇异策略的唯一性：因此，双稳态总是存在于潜伏期为零和最大潜伏期之间。总体而言，以前的多阶段感染模型可以用一个包括对潜伏期起作用的进化过程的单一模型来概括。由于参数值的微小变化可能导致进化动力学的突然转变，因此适当的疾病控制策略可能会对第一阶段潜伏期的进化产生重大影响。
