Based on the classical Ross-Macdonald model, in this paper we propose a periodic malaria model to incorporate the effects of temporal and spatial heterogeneity on disease transmission. The temporal heterogeneity is described by assuming that some model coefficients are time-periodic, while the spatial heterogeneity is modeled by using a multi-patch structure and assuming that individuals travel among patches. We calculate the basic reproduction number [Formula: see text] and show that either the disease-free periodic solution is globally asymptotically stable if [Formula: see text] or the positive periodic solution is globally asymptotically stable if [Formula: see text]. Numerical simulations are conducted to confirm the analytical results and explore the effect of travel control on the disease prevalence.

中文翻译：

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不完整环境中的周期性罗斯-麦克唐纳模型。

基于经典的罗斯-麦克唐纳模型，在本文中，我们提出了一种周期性疟疾模型，以纳入时间和空间异质性对疾病传播的影响。时间异质性是通过假设某些模型系数是时间周期来描述的，而空间异质性是通过使用多斑块结构并假设个体在斑块之间移动来建模的。我们计算基本再生数[公式：参见文本]，并表明如果[公式：参见文本]，则无病周期解是全局渐近稳定的；如果[公式：参见文本]，则正周期解是全局渐近稳定的。进行数值模拟以证实分析结果并探讨旅行控制对疾病流行的影响。