This paper aims to provide the complete analysis on the threshold dynamics of an age-space structured malaria epidemic model. We formulate the model in a spatially bounded domain by assuming that: (i) the density of susceptible humans at space x stabilizes at H(x); (ii) the force of infection between human population and mosquitoes is given by the mass action incidence. By appealing to the theory of fixed point problem and Picard sequences and iteration, the well-posedness of the model is shown by verifying that the solution exists globally and the model admits a global attractor. In the spatially homogeneous case, we establish the explicit formula for the basic reproduction number, which governs the malaria extinction and persistence. The local and global stability of equilibria is achieved by studying the distribution of characteristic roots of characteristic equation and constructing the suitable Lyapunov functions, respectively.

本文旨在为时空结构性疟疾流行模型的阈值动态提供完整的分析。我们通过假设以下条件在空间有界域中公式化模型：（i）在空间x处的易感人的密度稳定在H（x）; （ii）人口与蚊子之间的感染力是由大规模行动发生率决定的。通过吸引定点问题和Picard序列及迭代的理论，通过验证解是否全局存在并且模型允许全局吸引子来显示模型的适定性。在空间均匀的情况下，我们为基本繁殖数建立了明确的公式，该公式控制着疟疾的灭绝和持久性。通过研究特征方程的特征根的分布并构造合适的Lyapunov函数，可以实现局部和全局平衡的稳定性。