A mathematical model for radiation hormesis below 100 mSv has previously been reported, but the origins of the formula used in the previous report were not provided. In the present paper, we first considered a sequential reaction model with identical rate constants. We showed that the function of components produced in the second step of this model agreed well with the previously reported function. Furthermore, in a general sequential reaction model with different rate constants, it was mathematically proved that the function representing the component produced in the second step is always mountain-shaped: the graph has a peak with one inflection point on either side, and such a component may induce radiation hormesis.
Keywords: Bateman equation; LNT; cancer incidence probability; mathematic proof; mountain shape; radiation adaptive response; radiation hormesis; sequential reaction.