- #1

LogarithmLuke

- 83

- 3

a) Let Y (t) denote the number of infected individuals in the population at time t measured in days. Specify the birth and death rates of this birth and death process.

The total population contains 5.26 million individuals.

b) Assume the stochastic process {Y (t) : t ≥ 0} has reached its stationary distribution. For each infection, there is a probability of 1% that the infection will result in serious compli- cations that requires hospitalization. On average, the hospitals only have capacity to handle 2000 individuals with complications from a cold. Use Little’s law to calculate the average treatment time required to not exceed the capacity.So for a) the birth rates should decrease with an increase in the amount of infected individuals, however the overall population size remains the same in this model, so I am thinking the birth rate is just 𝜆 and the death rate simply 𝜇? Or should the death rate be 𝜇𝑖 and birth rate 𝜆/𝑖 where 𝑖 is the number of infected individuals?

For b) I am not sure what I need to calculate. From what I see we can just plug straight into Little's law 𝐿=𝜆𝑊 and put 𝐿=2000

and use the 𝜆 given to solve for 𝑊, however the answer obtained that way makes no sense.