Parameter estimation and sensitivity analysis for a model of tumor–immune interaction in the presence of immunotherapy and chemotherapy

Abstract

A mathematical model has been utilized to examine the interaction between tumor cells and immune cells. In this model, the immune cells include natural killer cells, circulating lymphocytes, CD8+T cells, CD4+T cells, and cytokines. The model not only represents the traditional role of CD4+T cells in activating CD8+T cells but also illustrates its role in killing the tumor via the secretion of cytokines. Besides, treatments with both chemotherapy and immunotherapy are considered. However, since this model was not fitted to experimental data before, parameter estimation is performed to fit the model with experimental data, first. The estimation is validated to verify the correctness of the model using the experimental data for the tumor growth. Second, numerical experiments are performed using a set of human data. Results show the mutual relations between tumor cells, and body immune cells in the absence and in the presence of therapy. Results also show that CD4+T cells could play a crucial role in immunotherapy. Third, sensitivity analysis is performed by calculating the normalized sensitivity coefficients to identify the relative influence of body parameters on the tumor cell population. The obtained results provide a tool to identify which parameters should be increased or decreased before treatment to get the optimal immune response.

Analysis of HBV and COVID‐19 Coinfection Model with Intervention Strategies

“…Definition: the variable y normalized forward sensitivity index which depends on a differentiable parameter ξ is defined by SI( ϑ ) = ( ∂y / ∂ϑ )∗( ϑ / y ) [ 35 , 36 , 41 , 55 ].…”

Mathematical model for dynamic interaction between tumor, immune system, and combined radiotherapy and chemotherapy based on experimental data

“…The obtained mathematical model is extended to include the body immune system. This extension is accomplished, by incorporating the obtained model with a published model that considers the body immune cells and uses human parameters [6,23,36,37]. The obtained model is in the form of a system of nonlinear ordinary differential equations that forecasts the interaction between tumor cells, immune cells, radiotherapy, and/or chemotherapy.…”

Analytical Models of Intra- and Extratumoral Cell Interactions at Avascular Stage of Growth in the Presence of Targeted Chemotherapy

“…These types of models are typically represented by a small set of ordinary differential equations (ODEs). More sophisticated studies, still being general as regards the tumor dynamics, have also included the effect of the host immune system response and/or a treatment, leading to more realistic results, which fit well with experimental data [ 4 , 5 ]. Gupta et al show how certain species of the immune system facilitate tumor destruction, using fractional order derivatives [ 4 ].…”

“…Gupta et al show how certain species of the immune system facilitate tumor destruction, using fractional order derivatives [ 4 ]. Elkaranshawy et al includes the immune response and the effect of immunotherapy to make the realistic model [ 5 ]. These models extend the ODE set of equations by adding additional interaction terms.…”

“…As can be seen from Table 1 , different models have been developed for the prediction of tumor growth, considering the effects of different factors employing a range of assumptions. For example, many studies consider a single type of generic tumor cells [ 3 , 4 , 5 , 8 , 10 , 11 , 12 , 13 , 14 , 15 ], while others consider separate proliferating, quiescent and necrotic cells within the tumor [ 6 , 7 , 9 , 16 , 17 , 18 ]. The benefit of considering these separate types of cells is a full understanding of intra-tumoral interactions, which prove to be more realistic than a generalized approach.…”