A nonstandard finite difference scheme for a basic model of cellular immune response to viral infection

I will present a numerical method designed for the simulation of the basic mathematical model of cellular immune response to viral infection (originally proposed by M.A. Nowak and C.R. Bangham). The proposed numerical method is a nonstandard (semi-implicit) finite difference scheme, which preserves the essential qualitative features of the continuous model independently of the chosen step-size of the simulation. Namely, the non-negativity, boundedness and equilibria of the original model (along with their stability conditions) are preserved. Our numerical scheme does not generate qualitative errors that can easily be obtained using a standard simulation approach.