Based on a susceptible-infected-susceptible patch model, we study the influence of dispersal on the disease prevalence of an individual patch and all patches at the endemic equilibrium. Specifically, we estimate the disease prevalence of each patch and obtain a weak order-preserving result that correlated the patch reproduction number with the patch disease prevalence. Then we assume that dispersal rates of the susceptible and infected populations are proportional and derive the overall disease prevalence, or equivalently, the total infection size at no dispersal or infinite dispersal as well as the right derivative of the total infection size at no dispersal. Furthermore, for the two-patch submodel, two complete classifications of the model parameter space are given: one addressing when dispersal leads to higher or lower overall disease prevalence than no dispersal, and the other concerning how the overall disease prevalence varies with dispersal rate. Numerical simulations are performed to further investigate the effect of movement on disease prevalence.

基于易感-感染-易感斑块模型，我们研究了在地方性平衡时扩散对单个斑块和所有斑块疾病流行的影响。具体来说，我们估计了每个斑块的疾病流行率，并获得了一个弱的保序结果，该结果将斑块繁殖数与斑块疾病流行率相关联。然后我们假设易感人群和受感染人群的传播率成正比，并得出总体疾病流行率，或等效地，未扩散或无限扩散时的总感染规模以及未扩散时总感染规模的右导数。此外，对于双补丁子模型，给出了模型参数空间的两个完整分类：一个是解决扩散导致总体疾病流行率高于或低于没有扩散的情况，另一个是关于总体疾病流行率如何随扩散率变化的问题。进行数值模拟以进一步研究运动对疾病流行的影响。