Stability Analysis of Mathematical Models of Diabetes Type one By Using Pade Approximate

This paper investigates the stability of mathematical model of diabetes type one by using two systems of three differential equations, one of the systems without time delay, the second system contain time delay equation, time delay is important when we study diabetes disease. First step in studying this system is to represent as matrix representation and we calculate the eigen values of the cofactors matrix of the system. Pade approximate is used to deals with time delay system before we test the stability of the system. Pade approximates transform the exponential characteristic equation to algebraic characteristic equation. we make new method of stability; this new method is companied between two methods of stability (Lyapunov Function with Continued Fraction) by using ways of stability and new method we found the systems are unstable.