A deterministic model for transmission of Echinococcus multilocularis (EM), a parasitic disease responsible for human alveolar echinococcosis, is formulated and analyzed rigorously. The model consists of two hosts, with three compartments each, and concentration of the parasites from environment as sources of infection. The model takes into account a predator‐prey relationship between the major hosts and obtained a threshold value for their existence. Systematic derivation of basic reproduction number, ${\mathcal{R}}_0$, is provided. Thorough qualitative analysis of the model reveals that it has a local and global asymptotic stable disease‐free equilibrium when ${\mathcal{R}}_0<1$; thus, (EM) will die out in the populations. However, when ${\mathcal{R}}_0$ exceeds unity, the model exhibits a unique endemic equilibrium, which is globally asymptotic stable; hence, disease will persist. The elasticity indices and partial rank correlation coefficients of the basic reproduction number and cumulative new cases of the two hosts with respect to parameter values are computed. Sensitivity analyses identified key parameters that are the most sensitive and can be used for control strategies in reducing ${\mathcal{R}}_0$ below unity. Numerical simulations are used to verify theoretical results and quantify prevalence of the disease in host populations.

中文翻译：

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啮齿动物和赤狐中棘球E虫数学模型的全局动力学

严谨地建立并分析了确定性传播多球棘球transmission虫（EM）的确定性模型，该棘球human虫是导致人的肺泡棘球菌病的寄生虫病。该模型由两个宿主组成，每个宿主具有三个隔室，并且来自环境的寄生虫集中作为感染源。该模型考虑了主要宿主之间的天敌关系，并获得了它们存在的阈值。基本繁殖数的系统推导，${\mathcal{[R}}_0$提供。对该模型进行彻底的定性分析表明，当该模型具有局部和全局渐近稳定的无病平衡时，${\mathcal{[R}}_0<\mathrm{1个}$; 因此，（EM）将在人群中消失。但是，当${\mathcal{[R}}_0$超过1，模型表现出独特的地方均衡，全局渐近稳定；因此，疾病将持续存在。计算基本再现次数的弹性指数和部分等级相关系数以及两个主机相对于参数值的累积新情况。敏感性分析确定了最敏感的关键参数，可用于控制策略中降低${\mathcal{[R}}_0$低于统一。数值模拟用于验证理论结果并量化宿主人群中该病的患病率。