Application of scaling and sensitivity analysis for tumor–immune model reduction

Mathematical modeling plays a facilitating role in comprehending tumor growth and its interaction with the immune system. However, there are some hindrances in modeling these phenomena. Firstly, the complexity of the tumor–immune model increases with the inclusion of dynamics of different types of immune cells. In this work, complexity is considered in terms of number of parameters and differences in the order of magnitude of their values. We have assumed that the model structure accurately represents the actual tumor–immune interactions. This may result in non-identifiability, imprecise measurement/estimation of the parameters. Secondly, very few parameters in the model will significantly influence the evolution of state variables and it is important for us to know these sensitive parameters.In this work, a recent and elaborate tumor–immune model is considered and its reduced parametric representation is obtained through a systematic scaling approach without any loss in its predictive ability. The advantage of scaling approach is quantified using theoretical identifiability analysis and by evaluating the condition number of the Fisher information matrix. Then, global sensitivity analysis is applied on the reduced model to identify the key parameters affecting the tumor progression. Such model reduction and parameter analysis may be necessary in order to increase the possibility of bringing model based approaches to standard medical practice and patient care.