School of Mathematics, Harbin Institute of Technology, Harbin, 150001, Heilongjiang, People's Republic of China.
J Math Biol. 2024 Apr 29;88(6):74. doi: 10.1007/s00285-024-02089-6.
In this paper, we propose a reaction-advection-diffusion dengue fever model with seasonal developmental durations and intrinsic incubation periods. Firstly, we establish the well-posedness of the model. Secondly, we define the basic reproduction number for this model and show that is a threshold parameter: if , then the disease-free periodic solution is globally attractive; if , the system is uniformly persistent. Thirdly, we study the global attractivity of the positive steady state when the spatial environment is homogeneous and the advection of mosquitoes is ignored. As an example, we use the model to investigate the dengue fever transmission case in Guangdong Province, China, and explore the impact of model parameters on . Our findings indicate that ignoring seasonality may underestimate . Additionally, the spatial heterogeneity of transmission may increase the risk of disease transmission, while the increase of seasonal developmental durations, intrinsic incubation periods and advection rates can all reduce the risk of disease transmission.
在本文中，我们提出了一个具有季节发育持续时间和内在潜伏期的反应-扩散登革热模型。首先，我们建立了模型的适定性。其次，我们定义了这个模型的基本再生数，并表明是一个阈值参数：如果，那么无病周期解是全局吸引的；如果，系统是一致持久的。第三，我们研究了空间环境均匀且忽略蚊子平流时正稳态的全局吸引性。作为一个例子，我们使用该模型研究了中国广东省的登革热传播情况，并探讨了模型参数对的影响。我们的研究结果表明，忽略季节性可能会低估。此外，传播的空间异质性可能会增加疾病传播的风险，而季节发育持续时间、内在潜伏期和平流率的增加都可以降低疾病传播的风险。
