Whack-A-Mole (WAM) Model Simulator

The simulator solves a following differential equation: $$\frac{F(t)}{dt} = A(t) - B(t) F(t)$$ where, $$A(t) = a_0 + a_1 d(t)$$ $$B(t) = b_0 + b_1 d(t)$$

Notation Description
\(t\) Time (hour)
\(F(t)\) Mutation frequency at \(t\)
\(A(t)\) Increasing rate of mutation frequency \(t\)
\(B(t)\) Decreasing rate of mutation frequency \(t\)
\(a_0\) Increasing rate of mutation occurred in natural environment (1/hour)
\(a_1\) Increasing rate of mutation correspnding to radiation dose (1/Gy)
\(b_0\) Decreasing rate occurred in natural environment (1/hour)
\(b_1\) Decreasing rate caused by radiation (1/Gy)
\(d(t)\) Dose rate at \(t\) (Gy/hour)

See http://radi.rirc.kyoto-u.ac.jp/wam/en/index.html for more details.


  • Manabe, Y., Ichikawa, K., & Bando, M. (2012). A mathematical model for estimating biological damage caused by radiation. Journal of the Physical Society of Japan, 81(10), 104004.
  • Manabe, Y., & Bando, M. (2013). Comparison of data on mutation frequencies of mice caused by radiation with low dose model. Journal of the Physical Society of Japan, 82(9), 94004.
  • Nakamura, I., Manabe, Y., & Bando, M. (2014). Reaction rate theory of radiation exposure and scaling hypothesis in mutation frequency. Journal of the Physical Society of Japan, 83(11), 114003.
  • Manabe, Y., Wada, T., Tsunoyama, Y., Nakajima, H., Nakamura, I., & Bando, M. (2015). Whack-a-mole model: towards a unified description of biological effects caused by radiation exposure. Journal of the Physical Society of Japan, 84(4), 44002.
  • Wada, T., Manabe, Y., Nakamura, I., Tsunoyama, Y., Nakajima, H., & Bando, M. (2016). Dose and dose-rate dependence of mutation frequency under long-term exposure–a new look at DDREF from WAM model. Journal of Nuclear Science and Technology, 53(11), 1824–1830.
  • Bando, M., Wada, T., & Manabe, Y. (2017). From DDREF to EDR - what the history of LNT indicates. In 4th International Symposium on the System of Radiological Protection, 2nd European Radiological Protection Research Week (p. 57).
  • Tsunoyama, Y., Suzuki, K., Masugi-Tokita, M., Nakajima, H., Manabe, Y., Wada, T., & Bando, M. (2019). Verification of a dose rate-responsive dynamic equilibrium model on radiation-induced mutation frequencies in mice. International Journal of Radiation Biology, (just-accepted), 1–19.