Gao Daozhou, Lou Yuan
Department of Mathematics and Statistics, Cleveland State University, Cleveland, OH, 44115, USA.
School of Mathematical Sciences, CMA-Shanghai and MOE-LSC, Shanghai Jiao Tong University, Shanghai, 200240, China.
J Math Biol. 2025 Sep 5;91(3):33. doi: 10.1007/s00285-025-02254-5.
Human movement plays a key role in spreading vector-borne diseases globally. Various spatial models of vector-borne diseases have been proposed and analyzed, mainly focusing on disease dynamics. In this paper, based on a multi-patch Ross-Macdonald model, we study the impact of host migration on the local and global host disease prevalences. Specifically, we find that the local disease prevalence of any patch is bounded by the minimum and maximum disease prevalences of all disconnected patches and establish a weak order-preserving property. For global disease prevalence, we derive its formula at both zero and infinite dispersal rates and compare them under certain conditions, and calculate the right derivative at no dispersal. In the case of two patches, we give two complete classifications of the model parameter space: one is to compare the host disease prevalences with and without host dispersal, and the other is to determine the monotonicity of host disease prevalence with respect to host dispersal rate. Numerical simulations confirm inconsistence between disease persistence and host disease prevalence, as well as between host prevalence and vector prevalence in response to host movement. In general, a more uneven distribution of hosts and vectors in a homogeneous environment leads to lower host prevalence but higher vector prevalence and stronger disease persistence.
人类活动在全球范围内传播媒介传播疾病方面起着关键作用。人们已经提出并分析了各种媒介传播疾病的空间模型，主要侧重于疾病动态。在本文中，基于多斑块罗斯 - 麦克唐纳模型，我们研究宿主迁移对局部和全球宿主疾病流行率的影响。具体而言，我们发现任何斑块的局部疾病流行率受所有不相连斑块的最小和最大疾病流行率限制，并建立了弱保序性质。对于全球疾病流行率，我们推导了其在零和无限扩散率下的公式，并在某些条件下进行比较，还计算了无扩散时的右导数。在两个斑块的情况下，我们给出了模型参数空间的两种完整分类：一种是比较有无宿主扩散时的宿主疾病流行率，另一种是确定宿主疾病流行率相对于宿主扩散率的单调性。数值模拟证实了疾病持续性与宿主疾病流行率之间以及宿主流行率与媒介流行率之间在宿主移动响应方面的不一致性。一般来说，在均匀环境中宿主和媒介分布越不均匀，宿主流行率越低，但媒介流行率越高，疾病持续性越强。
