Comments on abstract, title, references

The authors investigate the numerical determination of space and time-dependent for heat equation form some overdetermination conditions in additive form of function.

the abstract reflect the new findings and achievements. The tittle is clear and explain the topic of the research . The references are new and relevant to the research.

Comments on introduction/background

The introduction start with the significant of the current research in biology and they clearly addressed the problem under investigation. However , the paper need more illustrations for why we need to solve this inverse problem (the authors gives two references only ) I think is not enough.

Comments on methodology

The authors used finite difference method for solving direct problem which consists the solution of parabolic in details. While the inverse problem solved iteratively using lsqnonlin routine from matlab optimisation toolbox.

Comments on data and results

The results are true and clear with very good display within three test examples that show the efficiency of the adapted method. Also, various noise level and various regularisation parameters applied in order to obtain accurate results.

Comments on discussion and conclusions

the conclusions addressed very well the finding of the paper and explain the vision of the authors for the research. Also, the authors express their future work.