Characteristics of an epidemic outbreak with a large initial infection size

A deterministic model proposed in previous literatures to approximate the well-known Richards model is investigated. However, the model assumption of small initial value for infection size is released in the current manuscript. Taking the advantage of the closed form of solutions, we establish the epidemic characteristics of disease transmission: the outbreak size, the peak size and the turning point for the cumulative infected cases. It is shown that the usual disease outbreak threshold condition (the basic reproduction number R0is greater than unity) fails to fully guarantee the existence of peaking time and turning point when the initial infection size is not relatively small. The epidemic characteristics not only depend on R0but also on another index, the net reproduction number R0*.