Intelligent solution predictive networks for non-linear tumor-immune delayed model

In this article, we analyze the dynamics of the non-linear tumor-immune delayed (TID) model illustrating the interaction among tumor cells and the immune system (cytotoxic T lymphocytes, T helper cells), where the delays portray the times required for molecule formation, cell growth, segregation, and transportation, among other factors by exploiting the knacks of soft computing paradigm utilizing neural networks with back propagation Levenberg Marquardt approach (NNLMA). The governing differential delayed system of non-linear TID, which comprised the densities of the tumor population, cytotoxic T lymphocytes and T helper cells, is represented by non-linear delay ordinary differential equations with three classes. The baseline data is formulated by exploiting the explicit Runge-Kutta method (RKM) by diverting the transmutation rate of T_c to T_h of the T_c population, transmutation rate of T_c to T_h of the T_h population, eradication of tumor cells through T_c cells, eradication of tumor cells through T_h cells, T_c cells' natural mortality rate, T_h cells' natural mortality rate as well as time delay. The approximated solution of the non-linear TID model is determined by randomly subdividing the formulated data samples for training, testing, as well as validation sets in the network formulation and learning procedures. The strength, reliability, and efficacy of the designed NNLMA for solving non-linear TID model are endorsed by small/negligible absolute errors, error histogram studies, mean squared errors based convergence and close to optimal modeling index for regression measurements.