Department of Mathematics, Center for Computational and Applied Mathematics, California State University, Fullerton, CA, 92831, USA.
IECL (UMR 7502), Inria, Université de Lorraine, CNRS, Metz, France.
Bull Math Biol. 2018 Jul;80(7):1810-1848. doi: 10.1007/s11538-018-0435-1. Epub 2018 Apr 25.
A class of models that describes the interactions between multiple host species and an arthropod vector is formulated and its dynamics investigated. A host-vector disease model where the host's infection is structured into n stages is formulated and a complete global dynamics analysis is provided. The basic reproduction number acts as a sharp threshold, that is, the disease-free equilibrium is globally asymptotically stable (GAS) whenever [Formula: see text] and that a unique interior endemic equilibrium exists and is GAS if [Formula: see text]. We proceed to extend this model with m host species, capturing a class of zoonoses where the cross-species bridge is an arthropod vector. The basic reproduction number of the multi-host-vector, [Formula: see text], is derived and shown to be the sum of basic reproduction numbers of the model when each host is isolated with an arthropod vector. It is shown that the disease will persist in all hosts as long as it persists in one host. Moreover, the overall basic reproduction number increases with respect to the host and that bringing the basic reproduction number of each isolated host below unity in each host is not sufficient to eradicate the disease in all hosts. This is a type of "amplification effect," that is, for the considered vector-borne zoonoses, the increase in host diversity increases the basic reproduction number and therefore the disease burden.
本文构建了一个能够描述多种宿主物种与节肢动物媒介之间相互作用的模型，并对其动力学行为进行了研究。该模型将宿主的感染过程分为 n 个阶段，对其进行了完整的全局动力学分析。基本再生数充当了一个尖锐的阈值，即当 [Formula: see text] 时，无病平衡点全局渐近稳定（GAS），且当 [Formula: see text] 时存在唯一的内部地方病平衡点，且该平衡点 GAS。然后，我们将这个模型扩展到了 m 个宿主物种，用于捕捉一类以节肢动物媒介为交叉物种桥梁的人畜共患病。多宿主-媒介模型的基本再生数 [Formula: see text]，其被证明是每个宿主与节肢动物媒介隔离时模型的基本再生数之和。结果表明，只要疾病在一个宿主中持续存在，它就会在所有宿主中持续存在。此外，随着宿主数量的增加，整体基本再生数也会增加，而且降低每个孤立宿主的基本再生数并不能在所有宿主中消除疾病。这是一种“放大效应”，即对于所考虑的虫媒传染病，宿主多样性的增加会增加基本再生数，从而增加疾病负担。
