Department of Mathematics, Virginia Tech, 225 Stanger St, Blacksburg, VA, 24061, USA.
Department of Immunology, University of Pittsburgh Medical School, The Assembly, 5051 Centre Avenue, Pittsburgh, PA, 15213, USA.
J Math Biol. 2024 Apr 10;88(6):60. doi: 10.1007/s00285-024-02074-z.
One-dimensional discrete-time population models, such as those that involve Logistic or Ricker growth, can exhibit periodic and chaotic dynamics. Expanding the system by one dimension to incorporate epidemiological interactions causes an interesting complexity of new behaviors. Here, we examine a discrete-time two-dimensional susceptible-infectious (SI) model with Ricker growth and show that the introduction of infection can not only produce a distinctly different bifurcation structure than that of the underlying disease-free system but also lead to counter-intuitive increases in population size. We use numerical bifurcation analysis to determine the influence of infection on the location and types of bifurcations. In addition, we examine the appearance and extent of a phenomenon known as the 'hydra effect,' i.e., increases in total population size when factors, such as mortality, that act negatively on a population, are increased. Previous work, primarily focused on dynamics at fixed points, showed that the introduction of infection that reduces fecundity to the SI model can lead to a so-called 'infection-induced hydra effect.' Our work shows that even in such a simple two-dimensional SI model, the introduction of infection that alters fecundity or mortality can produce dynamics can lead to the appearance of a hydra effect, particularly when the disease-free population is at a cycle.
一维离散时间种群模型，如涉及 Logistic 或 Ricker 增长的模型，可能表现出周期性和混沌动力学。通过扩展系统到一维以纳入流行病学相互作用，会引起有趣的新行为复杂性。在这里，我们检查了一个具有 Ricker 增长的离散时间二维易感-感染（SI）模型，并表明感染的引入不仅可以产生与基础无病系统明显不同的分岔结构，而且还可以导致人口规模的反直觉增加。我们使用数值分岔分析来确定感染对位置和类型的分岔的影响。此外，我们还研究了一种称为“九头蛇效应”的现象的出现和程度，即当对种群产生负面影响的因素（如死亡率）增加时，总种群规模会增加。以前的工作主要集中在固定点的动态上，表明引入感染会降低 SI 模型的繁殖力，从而导致所谓的“感染诱导的九头蛇效应”。我们的工作表明，即使在这样一个简单的二维 SI 模型中，引入改变繁殖力或死亡率的感染也会产生动态，从而导致九头蛇效应的出现，特别是当无病人口处于循环时。
