Transmission dynamics of a reaction–advection–diffusion dengue fever model with seasonal developmental durations and intrinsic incubation periods

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 \( \Re _{0} \) ${\Re }_0$ for this model and show that \( {\Re _0} \) ${\Re }_0$ is a threshold parameter: if \( {\Re _0} <1 \) ${\Re }_0<1$ , then the disease-free periodic solution is globally attractive; if \( {\Re _0}>1 \) ${\Re }_0>1$ , 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 \( \Re _{0}\) ${\Re }_0$ . Our findings indicate that ignoring seasonality may underestimate \(\Re _0\) ${\Re }_0$ . 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.