Bichara Derdei Mahamat
Department of Mathematics, California State University, Fullerton, CA 92831, USA.
J Math Anal Appl. 2019 Jul 15;475(2):1532-1553. doi: 10.1016/j.jmaa.2019.03.030. Epub 2019 Mar 21.
We formulate a multi-group and multi-vector epidemic model in which hosts' dynamics is captured by staged-progression framework and the dynamics of vectors is captured by an framework. The proposed model describes the evolution of a class of zoonotic infections where the pathogen is shared by host species and transmitted by arthropod vector species. In each host, the infectious period is structured into stages with a corresponding infectiousness parameter to each vector species. We determine the basic reproduction number and investigate the dynamics of the systems when this threshold is less or greater than one. We show that the dynamics of the multi-host, multi-stage, and multi-vector system is completely determined by the basic reproduction number and the structure of the host-vector network configuration. Particularly, we prove that the disease-free equilibrium is globally asymptotically stable (GAS) whenever , and a unique strongly endemic equilibrium exists and is GAS if and the host-vector configuration is irreducible. That is, either the disease dies out or persists in all hosts and all vector species.
我们构建了一个多群体和多向量的流行病模型，其中宿主的动态变化由阶段进展框架来描述，而向量的动态变化由一个框架来描述。所提出的模型描述了一类人畜共患感染病的演变，这类感染病的病原体由宿主物种共享，并通过节肢动物媒介物种传播。在每个宿主中，感染期被划分为多个阶段，每个媒介物种都有相应的感染性参数。我们确定了基本再生数，并研究了该阈值小于或大于1时系统的动态变化。我们表明，多宿主、多阶段和多向量系统的动态变化完全由基本再生数和宿主-向量网络配置的结构决定。特别地，我们证明，当 时，无病平衡点是全局渐近稳定的（GAS），如果 且宿主-向量配置是不可约的，则存在唯一的强地方病平衡点且该平衡点是全局渐近稳定的。也就是说，要么疾病消失，要么在所有宿主和所有媒介物种中持续存在。
