Strategy minimizing potential losses.

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Chapter 14, Problem 3.1P

To determine

Strategy minimizing potential losses.

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- 1. (Maximum length one page) Consider an infectious disease with the following characteristics: Individuals can exist in three states, susceptible, infected, and recovered. Once recovered, an individual cannot be re-infected and remains immune for life. The transmission rate, t, is 1/20. The recovery rate, k, is 1/5. Each person interacts randomly with others in the population and has contacts with 10 people each time period. There is no birth or death in the population. -Initially all people are susceptible. - No one dies from the disease and there is no treatment. a) Draw a compartmental model for this infectious disease.

Consider an obstetrician who can perform two types of deliveries: normal deliveries and cesarean deliveries. Each typeof delivery provides different levels of income for the physician, and the physician has some ability to induce patientsto opt for cesarean deliveries. The model is as follows:The physician’s utility is defined as:U = U(Y, I)where:• Y is the income from performing deliveries.• I is the total disutility from inducementThe income Y from deliveries depends on the type of delivery:Y = Yn · N + YC · Cwhere:• Yn is the income per normal delivery, Yn = 1, 000• YC is the income per cesarean delivery, Yc = 1, 500,• Initial number of births Binitial = 100,• Post-shock number of births Bshock = 90,• a(i) = 0.1 + 0.05i is the fraction of total births that are cesareans, which increases with inducement level i,• the physician sets the inducement level to i = 2.• N = B · (1 − a(i)) is the number of normal deliveries,• C = B · a(i) is the number of cesarean deliveriesDue to a…