Immunotherapy plays a vital role in strengthening the immune system and enhancing its ability to fight cancer during the tumor-immune interaction. This interaction is a complex process and biological studies are still ongoing to explore the tumor microenvironment with the action of the immune system. The limitations associated with ethical consideration and the costs associated with the biological experiments on human samples, motivate researchers to use other available means, including mathematical modelling to find possible solutions to the problems. In this study, we use a fractional model for tumor-immune interaction incorporating the treatment of cytokine interleukin-2 (IL-2) to boost the immune system to fight cancer. The basic properties of the model such as positivity of the solutions and local stability analysis of the tumor free equilibrium are studied and the conditions for tumor removal highlighted. Furthermore, the existence and uniqueness of solution of the model is proved using the fixed point theory. Given the uncertainty in the selection of model parameters, sensitivity analysis was performed using the Latin Hypercube Sampling scheme to determine model parameters which describe the processes that significantly influence the changes in the model state variables. The model was numerically solved for different orders of the fractional derivative using the Adams–Bashforth–Moulton Method. Our results suggest that, satisfactory stable tumor control can be achieved by adoptive cellular immunotherapy (ACI) alone, or through a combination of ACI and IL-2. We further observed that, the processes affecting the tumor-immune system interaction influence the dynamics variably at different stages of the disease. This observation is vital in informing researchers about the essential processes of emphasis when implementing drug targeting intervention measures aimed at curtailing the progression of cancer.
All Science Journal Classification (ASJC) codes
- Statistical and Nonlinear Physics
- Physics and Astronomy(all)
- Applied Mathematics