Stochastic Interpretation for Whack-A-Mole Model

The Whack-A-Mole Model(WAM) by Manabe et al. has been developed as an alternative model to the Liner No-Threshold model(LNT), because of theoretical defects inherent to the LNT design. Although there are other alternatives to LNT, the merit of WAM is its equivalency to "exponential distribution" in probability theory. This reinforces the adequacy of WAM as an alternative theory to LNT, making it possible to verify it from a legitimate stochastic viewpoint. Before WAM for LNT by Manabe et al., Inamura had derived a solution from differential equation analogous to atomic collapse theory. It matches the data of mutated mice under low-dose rate radiation exposure. Afterward, Manabe et al. derived another similar equation and then indicated the scaling function based on the equation matching mutation data of five different species. However, both of them have some stochastic problems.