HLTC07 - Lec 5 - Disease Modelling (near-verbatim)

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Trinity College Courses
Caroline Barakat

C07 5: Disease Modelling Date: Oct 17, 2012 Slide 2: Lecture Outline  Infectious Disease Modelling o SIR Model o Basic reproduction number R0 o 2 states to show why ppl use modelling:  Endemic steady state  Critical vaccination coverage o Advanced models  With continuous age structure  Stochastic models where something happens out of the blue  Network models o Model use  General reasons  Chronic Disease Modelling o Macrosimulation o Microsimulation Slide 3: Intro – Infectious Disease Modelling  Tool for the analysis of policy options- to come up with good policy options, use mathematical modelling – constantly developed  Reasons why mathematical modelling became so popular: o 1) Complexity of infectious disease dynamics  Complexity not simple to understand and they are diff for diff diseases  Transmission of infectious diseases involves contact between individual and someone else, interaction between age, enviro, agents, ease of transmission  a system that is pretty complex and has many diff dimensions/dynamics  Virulence can change, enviro can change, contact can change and it is this complexity that makes modelling so good to use  Using model doesn’t mean you have to address that question all over again – can just change that one factor (ex: population became 10 million) and put that into model and it will spit out new answer  To simplify complexity of diseases o 2) Not possible to decide on different interventions just by pure reasoning  Look @ the effectiveness which is dependent on diff factors  Ex) if you increase vaccination rates for the flu, the incidence rate will go down by X factor  Trying to get the possible interventions which will lead to the best option – based on the model – can decide on the best intervention o 3) Process requires quantitative estimates – gives us indication of what we can do 1 C07 5: Disease Modelling Date: Oct 17, 2012  In order to get sound cost-effective analysis, the impact of diff interventions on the prevalence/incidence is best if it is quantified  Ex) let’s increase vaccination rates for the flu by 95% - what does that mean in terms of incidence/prevalence/admission to hospital wrt flu events?  Put those #s in – and get results li0e R – so modelling gives quantitative estimate that is needed in order to make sound policies and for proper intervention  So, you want to know how changing one input impacts the output; want to make decisions based on sound science; want to look @ various interventions Slide 4: What is involved?  Mechanistic description of the transmission of infection between 2 individuals = modelling o A system to tell us how infection is happening, developing a way to find out how things are proceeding and if things change, what would happen o This description makes it possible to describe the time-evolution of an epidemic in math terms o Ex) if population increases at some point, what does that have to do with the epidemic – how will it increase? Trying to put evolution of disease in mathematical term – can connect the individual level of transmission with the population level description o If you know that R0 for the flu is 20 and you want to bring it down to 10 – what should we do in terms of population? So, connecting individual level process to population level description of incidence and prevalence of an infectious disease  Connect the individual-level process of transmission with a population-level description  Detail requirements of all the dynamic processes that contribute to disease transmission o Every disease = diff and dynamic processes behind each disease is diff  some are symptomatic, some asymptomatic; some are host-related, some enviro-related o So, detailed info can be used in getting that mechanistic description of transmission Slide 5: Why is developing a mathematical model impt?  2 main reasons for importance of developing math model: o Model helps focus thoughts on essential processes involved in shaping the epidemiology of an infectious disease  Based on those dynamic processes and when you have a model in place – can see what is impt (does death rate, birth rate, contact matter?) in the epidemiology of infectious diseases – what variables are most important  It also reveals the parameters that are most influential and amenable for control  Can identify which of the factors in the model can be changed and can be a target for control & intervention  Ex) if we reducing smoking by 50%, can reduce cancer by 15%; can only know this if we manipulate variables in the equation o Reveals the parameters that are most influential and amenable for control 2 C07 5: Disease Modelling Date: Oct 17, 2012 Slide 6: What has fuelled the applicability of mathematical disease modelling? – certain events that fuelled: SARS (incubation periods, travelling patterns, density etc;  can all be inputs to the model), H1N1, smallpox (huge)  Bernoulli – 18 century used disease modelling to estimate impact of smallpox vaccination on life expectancy  Hamer in 1906 used modelling to argue that an epidemic can come to an end without all susceptible ppl having the infection/not exposed to the disease  Kermack and Mckendrick (1927) – basis for SIR modelling and R0  Based on your knowledge, which diseases required or make use of mathematical modelling? o HIV/AIDS in 1980s, SARS, and diff pandemics (infectious diseases) Slide 7: SIR Model – all elements for the transmission of a disease are in this simple model  Basic assumption: human population is subdivided into 3 groups: o Susceptible persons (S) o Infected persons (I) o Removed persons (R)  Maybe because they’ve acquired resistance to an infection or they’re no longer part of this infectious disease  Movements in and out of these groups via: o Birth o Death o Transmission of infection o Recovery  Movements: o So you have people who are susceptible who get the infection – so people from S group move to the I group and assuming that they now have this acquired immunity they’ll move from I group to R group o Movements occur also via birth = flow into the susceptible group; immunity from breastfeeding (antibodies that mom has); nevertheless, everyone who is born is susceptible to certain infections o Death is flow out from all groups:  Ppl who are susceptible may die  Ppl who are infected may die  Ppl who are removed may die o If a transmission of infection occurs  mvt from S to I group o Recovery  mvt from I group to recovery; and if it’s something like the flu, can be back in the S group again (because flu mutates) or can be thought of as new infection altogether Slide 8: 3 C07 5: Disease Modelling Date: Oct 17, 2012  Transmission between compartments is governed by rates  SIR model = interpreted in terms of rates; all transmission between those compartments happen based on rates o So, how many ppl per unit of time go into susceptible group, how many in infected group and how many ppl in recovery group o Anytime looking @ rate of change of some variable with respect to time – this refers to a rate o Rate = looking @ change of a variable y wrt time  R = dy/dt  Birth rate = v, but if a fraction of vaccinated newborns are brought in there, then birth rate = (1-p)v where p = the # of newborns are vaccinated o Ppl who are vaccinated fall out of that equation; (1-p)v is the rate that’ll be going in the equation  Death rate = µ  Recovery rate = ƴ  Key element is the term describing the transmission of infection; how is the transmission of infection happening? And it happens according to a rate known as β  aka mass action term o β = transmission of infection and it is related to two diff factors:  K= contact rate  Q = probability of transmission o Β = Kq  So we have: o Birth rate o Death rate o Recovery rate o The rate of transmission of infection (Beta = Kq)  Things depend on population density or prevalence in a population o Force of infection, λ = βI  Infection can have higher force if the population is pretty dense  It measures the risk of a susceptible person to become infected with certain disease per unit time – depends on the # of ppl that are infected in the population o Where N = total population size, λ = βI / N  Where I is the rate of infection occurring o So, the force of infection is the mass action term times the rate of ppl being infected and then the force of infection will be divided by the total population  gives us indication of how strong is that infection affecting the population  So, this is all wrt to the terms  Now, look at the rate of change of the susceptible individuals, rate of change of infected and rate of change of the recovered individuals o 1) rate of change of susceptible individuals 4 C07 5: Disease Modelling Date: Oct 17, 2012  V(1-P) – have certain birth rate and some individuals are getting vaccinated and
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