Ordinary Differential Equations (ODEs) Based Modeling

Ordinary differential equations (ODEs) are a system of equations used to describe changes of quantity or concentration of different species with respect to time. The mathematical formalism has been used successfully in an array of different fields, from social to natural sciences and biochemistry. Mathematical models build on the basis of ODEs are frequently used to describe dynamical phenomena as well as evolution. There are different tools (such as Matlab or Mathematica) that can be used to analytically solve a system of differential equation; however, in cases where an analytical solution cannot be found due to the complexity of the system, a numerical solution can be estimated. We have developed a user-friendly tool for ODE modeling called COmplex PAthway SImulator (COPASI) and MIEP adapted its use to ODE-based immune modeling.