AI 中文总结
该研究在三菌株免疫史模型中发现，相同常驻菌株可存在两种局部吸引子，稀有第三菌株的增长受常驻吸引子类型影响，不同吸引子下增长情况相反。
AI 中文摘要
大多数模型通过在稳定地方病背景下测试新引入的病原体菌株，以评估其在稀有状态下是否能够增长。然而，常驻菌株在相同参数下可能具有不止一种长期行为，它们可能达到稳定状态或继续周期性暴发，留下不同比例的具有不同感染史的宿主。我们在一个简化的免疫史模型中研究这种可能性。对于两个常驻菌株，我们确定了一个参数点，其中稳定地方病平衡点和稳定暴发周期均为局部吸引子。数值延拓绘制了一个霍普夫分支和一个周期轨道折叠分支，它们界定了候选双稳区域，该区域在局部由广义霍普夫（鲍廷）点组织。随后，我们将常驻模型精确嵌入一个20状态的三菌株系统中。当菌株3的传染性和总清除率在四类宿主史中相同时，稀有增长由相应未感染宿主比例的加权和决定。平衡点和周期产生不同的加权和，因此某一固定菌株3参数集在一个常驻吸引子附近增长，但在另一个附近下降。第二个参数集给出相反的排序，且两种模式在入侵者参数空间的开放区域内持续存在。60次接种量逐渐减小的全模型模拟在周期阶段和数值求解器中均重现了这些线性预测。因此，仅知道存在哪些常驻菌株可能不足以预测初始入侵；已实现的常驻吸引子也可能产生影响。这些结果涉及稀有状态下的局部增长，而非最终建立、长期共存或入侵后动态。
英文摘要
Most models assess whether a newly introduced pathogen strain can grow when rare by testing it against a steady endemic background. Resident strains, however, can have more than one long-term behavior under the same parameters. They may settle to a steady state or continue through recurring outbreaks, leaving different fractions of hosts with different infection histories. We study this possibility in a stylized immune-history model. For two resident strains, we identify a parameter point where a stable endemic equilibrium and a stable outbreak cycle are both locally attracting. Numerical continuation maps a Hopf branch and a branch of folds of periodic orbits that bound a candidate bistability region, organized locally by a generalized Hopf (Bautin) point. We then embed the resident model exactly in a 20-state, three-strain system. When strain 3 infectiousness and total removal are common across four host-history classes, rare growth is determined by a weighted sum of the corresponding uninfected host fractions. The equilibrium and cycle yield different weighted sums, so one fixed strain 3 parameter set grows near one resident attractor but declines near the other. A second parameter set gives the reverse ordering, and both patterns persist over open regions of invader parameter space. Sixty full-model simulations with progressively smaller inocula reproduce these linear predictions across cycle phases and numerical solvers. Thus, knowing which resident strains are present may not suffice to predict initial invasion; the realized resident attractor can also matter. These results concern local growth from rarity, not eventual establishment, long-term coexistence, or post-invasion dynamics.
