Lecture 29: Infectious Disease Modeling Flashcards
What are communicable disease and how do infectious diseases differ?
-Communicable disease: A subset of infectious diseases that can be transmitted from person to person or animal (zoonotic)
-with Infectious diseases also have a risk factor to everyone
-As well as positive feedback= more cases you have, the more cases you will get
-Variety, capacity for change, and continuing emergence
-prevention and control depends on the “herd” or population not just the individuals
What are the main differences b/w epidemics and pandemics?
Epidemics ex foot and mouth disease
-outbreak not felt the same around the country
Pandemic ex covid
-Until we have global spread ie across entire world
-Everyone is susceptible
What is the basic reproductive number (Rnot)?
-R0: average # of secondary infections from a single infectious case introduced into a completely susceptible population
-Describes the “transmissibility” of a disease
-Tells us about epidemic potential:
R0 > 1 : epidemic can occur
R0 = 1 disease in endemic (no increase/decrease stay)
R0< 1 disease will be eradicated
-Relationship with critical fraction to vaccinate to eliminate a disease
How do we calculate R0?
R0 = cpD
c=contact rate (more contact more infectious you can create)
p= probability of transmission given contact (when2 individuals come together, chance that pathogen will be passed)
D= Duration of infectiousness (depending on pathogen can be 1-14d etc)
NOTE: cp= transmission coefficient= beta
What is the critical proportion to vaccinate (Pc)?
-Also called “herd immunity threshold”
-Tells us how many individuals in a population need to be immune to a disease to stop transmission (it can also indicate how easily an infectious agent can be eradicated)
-We need an estimate of R0 to calculate Pc
What is the equation for the critical proportion to vaccinate?
Pc= 1-(1/R0)
Ex rabies: given that we now rabies has a R0 of 2 what proportion of animals should the MNR aim to vaccinate?
Pc= 1- (1/R0)
=1-(1/2)
=0.5 or 50%
This means we need to get 1/2 of the raccoon population in Hamilton to eat the bait to stop raccoon rabies
NOTE* different disease have different Pc values and as R0 increases Pc increases
What is the effective reproductive number (Re)? And what is the equation
-Re: average # of secondary infections generated from a single infectious case when only a proportion of those contacted are susceptible
Re= cpD*proportion susceptible
l——–l = R0
What does the effective repro # (Re) caries depending on what?
- The basic reproduction number (R0)
- The proportion of the population that is “fully” vaccinated (X)
- Te effectiveness of the vaccine (V)
What is mathematical modelling?
-A way to ask questions about disease dynamics in a way contained to a laptop
-Mathematical models are conceptual tools that explain how an object or system of objets will behave
-Models come in a variety of forms (highly complex or simple and in-between) depending on precision required, available data, time frame for getting results
-Even the most complex models make simplifying assumptions
What is the difference between statistical models and mathematical models?
Stat models
-Describe associations b/w variables, and used to derive parameter estimates from empirical data
Math models
-Provides a framework to represent proposed causal pathways
-Describes mechanisms that link exposures, interventions, infections, disease
-Used to make projections/predictions
What is the basic SIR model?
-Transmission of pathogen
-Susceptible (sus individual contacts infected individual)
-Infectious (individual becomes infected and is infectious to others)
-Recovered (individual recovers from disease or dies, might become immune)
CANT BE IN MORE THAN 1 COMPARTMENT, ALL MEMBERS IN THE POP WILL BE IN 1 OF 3
How do we create a model?
- Define host population of interest (ex all ppl in room)
- Define the states that individuals might be in as they go through the disease process –> “compartments” talked about previously
- Define how individuals will transition in and out of the compartments using previous knowledge about the biology of a disease (describes rate of ppl moving from sus – infected – recovered
How can we put that model into a math model?
-We can write a set of equations that describe the flow in/out of these compartments
What are interventions and why are they important?
-We use models to test interventions to understand their impact on disease spread in the population
-Our goal is to prevent to reduce transmission b/w individuals
-Slice of cheese ex how each one represents cup or D and how combining will give additive (or multiple 2 together) effect
-ex vaccinate (beings from sus all way to recovered
-Masks=p and physical distancing=c relates to infectious
-Treatment= recovered
What are the limitations of math models?
-A model is a simplified version of a real situation
-Requires good data
-Might not be an option for time-sensitive issues- long time to build
-All of these properties are population and disease dependant
