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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

          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

stochastic process birth and death process bdp healthcare modelling suppose that a population of employees remain healthy for an exponential time with mean 1lambda before becoming sick assum 23504

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