Class Notes (808,549)
TRN125Y1 (30)
Lecture 5

# HLTC07-Lecture 5 (oct 17).docx

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School
University of Toronto St. George
Department
Trinity College Courses
Course
TRN125Y1
Professor
Semester
Fall

Description
Lecture 5- Disease Modelling HLTC05- Oct 17  Tool for the analysis of policy options 1. Complexity of infectious disease dynamics (they’re different for different diseases); link between agent and environment 2. Not possible to decide by pure reasoning 3. Process requires quantitative estimates (eg. lets increase the vaccination rate of the flu) What is Involved?  Mechanistic description of the transmission-> trying to get a system that tells us how is transmission happening; how are things preceeding and if thigns change, what will it come up to  Connect the individual-level process of transmission with a population-level description (population goes up to 8 bill, arnaught might by 25)  Detail requirements of all the dynamic processes (the dynamic processes are different – symptomatic and asymptomatic) - Focus on essential processes involved in shaping the epidemiology of an infectious disease (death rate matters, birth rates important) - Reveals the parameters that are most influential and amenable for control (you can identity which of those factors in the models can be changed; can be the target for interventions) -> if we can reduce the rate of smoking by 50%, our cancer rates will go down 10-15% What has fuelled the applicability of mathematical disease modelling?  Bernoulli - 18 century  Hamer in 1906 used modelling to argue that an epidemic can come to an end  Kermack and Mckendrick (1927) - basis for SIR modelling and R o  Based on your knowledge, which diseases require or make use of mathematical modelling? SIR Model  Basic assumption: human population is subdivided into 3 groups: - susceptible persons (S) - infected persons (I) -> if they have acquired immunity, they’ll move to the R group - removed persons (R) -> not longer part of the infectious disease  Movements in and out of these groups via: - Birth -> a flow into the susceptible group - Death - Transmission of infection -> movement from the S to the I group - Recovery -> I group to recovery  Birth rate, ν; if p=fraction of vaccinated newborns, then birth rate=(1-p)ν  Death rate, µ  Recovery rate, γ  ϐ , mass action term where Β = κq; κ=contact rate, q=probability of transmission  Force of infection, λ = ϐ I  Where N=total population size, λ = ϐ I / N  I= rate of infection occurring (how many people are getting infected) dS/dt = ν(1-p) - ϐS(I/N) - µS (death rate of those susceptible) dI/dt = ϐS (I/N) – γI (those that are recovering) - µI (die out in the infected group) dR/dt = νp + γI - µR Basic Concepts  If an infectious disease that spreads on a much faster time scale than the demographic process, how do we
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