Apply and reverse a state recurrence with external change
A weekly service model records patients assigned to two health centres
Use the state order central centre then district centre. State matrices are columns. In T, columns are current states and rows are next states. One application represents one week
The transition occurs first. The signed external-change column is applied afterwards. Positive entries of B add to a state and negative entries remove from a state
\[T=\begin{bmatrix} 0.75 & 0.3 \\ 0.25 & 0.7 \end{bmatrix}\]
\[S_{n+1}=T S_n+B\]
After each transition, an external intake adds 2 patients to district centre
\[B=\begin{bmatrix} 0 \\ 2 \end{bmatrix}\]
\[S_{2}=\begin{bmatrix} 160 \\ 180 \end{bmatrix}\]