Question 1Consider a population (or more precisely a population density) of size N in a small city in the formerSoviet Union, which is completely susceptible to a rare disease known as Suriv-Sugob-A, named after aRussian admiral who was the first to contract the disease after an encounter with indigenous people in theSiberian rain forest. The disease is transmitted by droplets through the air or direct contact. It has atransmission coefficient of ?, which is the probability of successful transmission once a susceptibleindividual is exposed. The corresponding recovery period is 1/? days.Suppose you are in charge of managing an immunization campaign to protect against an outbreak of SurivSugob-A. Assume the following disease characteristics:? = 1 10-6, ? = .25, and a population of N = 750,000.(b) How would you determine the number of units of vaccine to be requested from the national strategicstockpile to achieve herd immunity, assuming that it takes one unit of vaccine to inoculate one person?Hint: Herd Immunity is reached when R0 < 1 and no new infections occur in the population.(c) How many units of vaccine would you have to dispense if the vaccine had an efficacy of 75%?(d) How long would the outbreak last if you vaccinated 20% more individuals than required to achieveherd immunity?MathStatistics and Probability MATH 3020

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