  The concentration of radiation-induced point defects in general materials
under irradiation is commonly described by the point defect kinetics equations
based on rate theory. However, the parametric uncertainty in describing the
rate constants of competing physical processes such as recombination and loss
to sinks can lead to a large uncertainty in predicting the time-evolving point
defect concentrations. Here, based on the perturbation theory, we derived up to
the third order correction to the solution of point defect kinetics equations.
This new set of equations enable a full description of continuously changing
rate constants, and can accurately predict the solution up to $50\%$ deviation
in these rate constants. These analyses can also be applied to reveal the
sensitivity of solution to input parameters and aggregated uncertainty from
multiple rate constants.
