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This paper studies the spatial propagation dynamics in diffusive disease transmission models with infectious stages, which may be nonmonotonic and partially degenerate. Using the solutions of linear heat equations, we transform the system into a new system that contains nonlocal delays and two unknown functions. From this new system, it is easy to obtain an important threshold and the numerical estimation for this threshold is easy. When the initial infection satisfies proper decaying behavior, we find that this threshold is the spreading speed for all infectious subgroups. Then the minimal wave speed of traveling wave solutions is proved to be the threshold, which connects the disease-free state to the endemic case. Moreover, some numerical examples are presented to explore the possible extension. [ABSTRACT FROM AUTHOR]

This paper is concerned with the asymptotic speed of spreading of a nonlocal delayed equation, which does not satisfy the local quasimonotonicity. By constructing auxiliary undelayed equations, the asymptotic speed of spreading is established. In particular, for such a nonmonotonic equation, the asymptotic speed of spreading is the same as that in the corresponding undelayed equation. [ABSTRACT FROM AUTHOR]