Free‐living amoebae (FLA) serve as hosts for a variety of endosymbionts, which are microorganisms that reside and multiply within the FLA. Some of these endosymbionts pose a pathogenic threat to humans, animals, or both. The symbiotic relationship with FLA not only offers these microorganisms protection but also enhances their survival outside their hosts and assists in their dispersal across diverse habitats, thereby escalating disease transmission. This review is intended to offer an exhaustive overview of the existing mathematical models that have been applied to understand the dynamics of FLA, especially concerning their interactions with bacteria. An extensive literature review was conducted across Google Scholar, PubMed, and Scopus databases to identify mathematical models that describe the dynamics of interactions between FLA and bacteria, as published in peer‐reviewed scientific journals. The literature search revealed several FLA–bacteria model systems, including Pseudomonas aeruginosa, Pasteurella multocida, and Legionella spp. Although the published mathematical models account for significant system dynamics such as predator–prey relationships and non‐linear growth rates, they generally overlook spatial and temporal heterogeneity in environmental conditions, such as temperature, and population diversity. Future mathematical models will need to incorporate these factors to enhance our understanding of FLA–bacteria dynamics and to provide valuable insights for future risk assessment and disease control measures.

中文翻译：

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自由生活的变形虫和细菌之间的动力学建模

自由生活的变形虫（FLA）是多种内共生体的宿主，这些内共生体是在 FLA 内居住和繁殖的微生物。其中一些内共生体对人类、动物或两者构成致病威胁。与 FLA 的共生关系不仅为这些微生物提供了保护，而且还增强了它们在宿主之外的生存能力，并有助于它们在不同的栖息地中传播，从而加剧了疾病传播。本综述旨在对现有的数学模型进行详尽的概述，这些模型已用于理解 FLA 的动力学，特别是它们与细菌的相互作用。我们对 Google Scholar、PubMed 和 Scopus 数据库进行了广泛的文献综述，以确定描述 FLA 和细菌之间相互作用动态的数学模型，这些模型发表在同行评审的科学期刊上。文献检索发现了几个 FLA-细菌模型系统，包括铜绿假单胞菌,多杀性巴氏杆菌， 和军团菌种。尽管已发表的数学模型解释了重要的系统动力学，例如捕食者-猎物关系和非线性增长率，但它们通常忽略了环境条件的空间和时间异质性，例如温度和种群多样性。未来的数学模型将需要纳入这些因素，以增强我们对 FLA-细菌动力学的理解，并为未来的风险评估和疾病控制措施提供有价值的见解。