Please solve & show steps... Daniel Bernoulli's work in 1760 had the goal of appraising theeffectiveness of a controversial inoculation program against smallpox,which at that time was a major threat to public hecalth. His modelapplies equally well to any other disease that, once contracted andsurvived, confers a lifetime immunity. Consider the cohort ofindividuals born in a given year (t = 0), and let n(t) be the number ofthese individuals surviving t years later. Let x(t) be the number ofmembers of this cohort who have not had smallpox by year t and whoare therefore still susceptible. Let 3 be the rate at which susceptiblescontract smallpox, and let v be the rate at which people who contractsmallpox die from the disease. Finally, let u(t) be the death rate fromall causes other than smallpox. Then dr/dt, the rate at which thenumber of susceptibles declines, is given by = -(B+ µ(t))x. The%3Ddifirst term on the right-hand side of this equation is the rate at whichsusceptibles contract smallpox, and the second term is the rate atwhich they die from all other causes. Also = -vßx – u(t)n, wheredtdn/dt is the death rate of the entire cohort, and the two termson the right-hand side are the death rates due to smallpox and to allother causes, respectively.a) Let z = x/n, and show that z satisfies the initial value problemdz= -Bz(1 – vz). Observe that this initial value problem does notdepend on u(t).b) Find z(t) by solving equation (a).z(t) = |Choose onec) Bernoulli estimated that v = ß = 1/8. Using these values, determinethe proportion of 50-year-olds who have not had smallpox.NOTE: Enter an exact answer.Proportion:

Name: Please solve & show steps... Daniel Bernoulli's work in 1760 had the g
Uploaded: 2024-03-20T06:38:44.000Z
Channel: Bartleby
Description: Please solve & show steps... Daniel Bernoulli's work in 1760 had the goal of appraising theeffectiveness of a controversial inoculation program against smallpox,which at that time was a major threat to public hecalth. His modelapplies equally well to