Department of Mathematics and Statistics, Masaryk University, Brno, Czech Republic.
Center for Computational and Stochastic Mathematics, Instituto Superior Técnico, Lisbon, Portugal.
J Math Biol. 2023 Aug 28;87(3):48. doi: 10.1007/s00285-023-01977-7.
Understanding the interplay of different traits in a co-infection system with multiple strains has many applications in ecology and epidemiology. Because of high dimensionality and complex feedback between traits manifested in infection and co-infection, the study of such systems remains a challenge. In the case where strains are similar (quasi-neutrality assumption), we can model trait variation as perturbations in parameters, which simplifies analysis. Here, we apply singular perturbation theory to many strain parameters simultaneously and advance analytically to obtain their explicit collective dynamics. We consider and study such a quasi-neutral model of susceptible-infected-susceptible (SIS) dynamics among N strains, which vary in 5 fitness dimensions: transmissibility, clearance rate of single- and co-infection, transmission probability from mixed coinfection, and co-colonization vulnerability factors encompassing cooperation and competition. This quasi-neutral system is analyzed with a singular perturbation method through an appropriate slow-fast decomposition. The fast dynamics correspond to the embedded neutral system, while the slow dynamics are governed by an N-dimensional replicator equation, describing the time evolution of strain frequencies. The coefficients of this replicator system are pairwise invasion fitnesses between strains, which, in our model, are an explicit weighted sum of pairwise asymmetries along all trait dimensions. Remarkably these weights depend only on the parameters of the neutral system. Such model reduction highlights the centrality of the neutral system for dynamics at the edge of neutrality and exposes critical features for the maintenance of diversity.
理解多菌株共感染系统中不同特征之间的相互作用在生态学和流行病学中有许多应用。由于感染和共感染中特征表现出的高维性和复杂反馈，此类系统的研究仍然具有挑战性。在菌株相似的情况下（准中性假设），我们可以将特征变化建模为参数的微扰，从而简化分析。在这里，我们同时对许多菌株参数应用奇异摄动理论，并进行解析推导以获得其明确的集体动力学。我们考虑并研究了 N 个菌株之间易感-感染-易感（SIS）动力学的这种准中性模型，这些菌株在 5 个适应度维度上有所不同：传染性、单感染和共感染的清除率、来自混合混合感染的传播概率，以及包含合作和竞争的共定殖脆弱性因素。通过适当的快慢分解，我们用奇异摄动方法分析了这个准中性系统。快速动力学对应于嵌入式中性系统，而缓慢动力学由 N 维复制者方程控制，描述了菌株频率的时间演化。这个复制者系统的系数是菌株之间的成对入侵适应性，在我们的模型中，它是沿着所有特征维度的成对不对称性的显式加权和。值得注意的是，这些权重仅取决于中性系统的参数。这种模型简化突出了中性系统在中性边缘动力学中的核心地位，并揭示了维持多样性的关键特征。
