$$\begin{pmatrix} D(t) \\ P(t) \\ R(t) \\ 1 \end{pmatrix}= \begin{pmatrix} 1 & \frac{-1}{20} & 0 & 1 \\ \frac{1}{100} & 1 & \frac{-1}{10} & 0 \\ \frac{-1}{100} & 0 & 1 & 1 \\ 0 & 0 & 0 & 1 \end{pmatrix} \begin{pmatrix} D(t-1) \\ P(t-1) \\ R(t-1) \\ 1 \end{pmatrix}$$
when solving this system, the eigenvalues with magnitude part are[1.0162 1.0162 0.9677 1] the system of difference equations is given below. \begin{align*} D(t) &= D(t-1) + \left( 1 - \frac{P(t-1)}{20} \cdot 1 \right) \\ P(t) &= P(t-1) - \left( 1 - \frac{D(t-1)}{10} \cdot 1 \right) + \left( 1 - \frac{R(t-1)}{100} \cdot 1 \right) \\ R(t) &= R(t-1) + \left( 1 - \frac{D(t-1)}{100} \cdot 1 \right) \end{align*} when I try to make system positive, I cant do it even if I try 0.98379 in diagonal of above matrix to make eigenvalues equal to 1. can anybody explain me where I am wrong?