Reverse Engineering a Model for T-Cell Vaccination

A class of minimal models is constructed that can exhibit several salient phenomena associated with T-cell inoculations that prevent and cure auto-immune disease. The models consist of differential equations for the magnitude of two populations, the effectors $E$ (which cause the disease), and an interacting regulator population $R$. In these models, normality, vaccination, and disease are identified with stable steady states of the differential equations. Thereby accommodated by the models are a variety of findings such as the induction of vaccination or disease, depending on the size of the effector inoculant. Features such as spontaneous acquisition of disease and spontaneous cure require that the models be expanded to permit slow variation of their coefficients and hence slow shifts in the number of steady states. Other extensions of the basic models permit them to be relevant to vaccination by killed cells or by antigen, or to the interaction of a larger number of cell types. The discussion includes an indication of how the highly simplified approach taken here can serve as a first step in a modeling program that takes increasing cognizance of relevant aspects of known immunological physiology. Even at its present stage, the theory leads to several suggestions for experiments.