Using Padé Approximant Method to Solve the Mathematical Model of Tumor-Immune Interactions

A mathematical model, in the form of a system of nonlinear ordinary differential equations, that describes the interaction between tumor cells and effective immune cells is proposed. An exact solution cannot be found to this system like many other nonlinear systems. Yet, approximate analytical solution is explored. This solution should have a large interval of convergence to be acceptable because the interaction can take many days to reach its steady state. Power series method is used to obtain a series solution. In this process, some auxiliary variables are used to transform the system of equations to polynomial form. However, this solution has a small radius of convergence, therefore, Padé approximant method is used to extend the domain of convergence. Hence, the obtained approximate analytical solution is valid over a large interval and has a remarkable accuracy when compared with numerical solution.