Question

Suppose there is an epidemic in which every month half of those who are well become sick, half of those who are sick get well, and a quarter of those who are sick die. Find the steady state for the corresponding Markov process
\[
\left(\begin{array}{l}
w_{n+1} \\
s_{n+1} \\
d_{n+1}
\end{array}\right)=\left(\begin{array}{ccc}
\frac{1}{2} & \frac{1}{2} & 0 \\
\frac{1}{2} & \frac{1}{4} & 0 \\
0 & \frac{1}{4} & 1
\end{array}\right)\left(\begin{array}{l}
w_{n} \\
s_{n} \\
d_{n}
\end{array}\right)
\]