STOCHASTIC PROCESS - BIRTH AND DEATH PROCESS
BDP: HEALTHCARE MODELLING
• Suppose that a population of employees remain healthy for an
exponential time with mean $1/\lambda$ before becoming sick. Assume that
it takes an exponential time to recover from sick to healthy again,
with mean sick time of $1/\mu$. If an employee starts employment in
the healthy state at time 0, find the probabilities of falling sick and
healthy in future times. We denote the healthy and sick states as
H and S.
• State the Kolmogorov backward equations for both states
• Find the expression for $p_{HH}(t)$, $p_{HS}(t)$, $p_{SH}(t)$ and $p_{SS}(t)$
• Find the stationary probability for each state
