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AIDS and the S-I-R Model A study of three groups of people most susceptible to the AIDS virus A Presentation by Tiana Towns and Tanya Milki Objective Create an SIR model that realistically predicts AIDS movement throughout the given populations The key issues and themes The main issue in this project was determining the transmission coefficient that would give us realistic, feasible results Finding statistical data to help us create realistic models The General SIR Model S’(t)=-aS(t)I(t) I’(t)=aS(t)I(t)-bI R’(t)=bI Our tweaked model… S’(t)=-aS(t)I(t) I’(t)=aS(t)I(t)-bI D’(t)=bI General assumptions Everyone who has the virus eventually dies We are only working with fixed populations No natural disasters will compromise our model No cure will be found Male-to-male homosexual contact 7000000 6000000 5000000 Series1 4000000 Series2 3000000 Series3 2000000 1000000 0 0 10 20 30 40 50 60 Injected drug users 2000000 1800000 1600000 1400000 1200000 Series1 1000000 Series2 800000 Series3 600000 400000 200000 0 0 10 20 30 40 50 60 Heterosexual contact 140000000 120000000 100000000 Series1 80000000 Series2 60000000 Series3 40000000 20000000 0 0 10 20 30 40 Conclusions We are only able to make speculations as to how the AIDS epidemic will spread in the coming years because of the uncertainties in information, such as population sizes, those not taken into account for, those belonging to more than one susceptible population, etc.