This paper concerns the global dynamics and asymptotic spreading speeds for a partially degenerate epidemic model with time delay and free boundaries. Given a suitable compatible condition for initial values, we establish the global well-posedness of solutions and provide some sufficient conditions for spreading and vanishing. When spreading occurs, we prove that the asymptotic spreading speed is uniquely determined by a semi-wave problem with time delay. To investigate the existence of monotone increasing solutions to the semi-wave problem, we give a distribution of solutions to a third degree exponential polynomial equation. The results show that time delay slows down the asymptotic spreading speed of the disease.

本文涉及具有时滞和自由边界的部分退化的流行病模型的全局动力学和渐近传播速度。给定合适的初始值相容条件，我们建立了整体的适定性，并提供了一些足以扩散和消失的条件。当扩展发生时，我们证明渐近扩展速度是由具有时滞的半波问题唯一确定的。为了研究半波问题单调递增解的存在，我们给出了三次指数多项式方程的解的分布。结果表明，时间延迟减慢了疾病的渐近传播速度。