Positivity-based stability analysis in testosterone regulation using distributed feedback control

A model describing testosterone regulation by distributed input feedback control is considered. It is aimed to hold testosterone concentration above a corresponding level. The distributed feedback control with integral term is proposed. This leads us to analysis of an integro-differential system which describes the connection between the concentration of hormone GnRH, the concentration of the hormone LH and the concentration of testosterone Te. We propose controls in the form of integral operators, i.e. distributed feedback controls, which allows us to hold a suitable testosterone level without loss stability of the biological system.