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Disease Epidemiology > Epidemiological Models > Flashcards

Epidemiological Models Flashcards

1
Q

Purpose of epidemiological models

A
  • Tools that help scientists understand whether and how infectious disease will spread through the host population
  • Used to identify what features or aspects of the infectious disease we need to know more about
  • Allow for the comparison of the outcomes of different control strategies
  • Used to make predictions that help policy makers make decisions
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2
Q

Deterministic Compartment models

A
  • Use compartments to symbolize host individuals in different states
    o Susceptible
    o Infectious
    o Recovered
    o Pre-infectious
  • Use arrows to show transitions between compartments
  • Many different models may be used
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3
Q

Examples of deterministic compartment models

A

Ex. SIRS
- Susceptibles becomes Infectious, Infectious becomes Recovered, Recovered becomes Susceptibles again

Ex. SEIR
- Susceptible –> pre-infectious (latent) stage (where individuals have been exposed but are not yet infectious) –> infectious –> recovered/immune

Ex. SIR
- Susceptibles becomes Infected and Infected becomes Recovered/immune

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4
Q

Simple SIR model

A
  • Individuals can belong to 3 different groups: susceptible, infected, recovered
  • S becomes I, I becomes R
    Susceptible individuals can acquire the infection from infected individuals. Infected individuals can become recovered individuals that are resistant to future infection
  • Closed population (no births, no deaths)
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5
Q

Why is transmission a function of the product of S and I?

A
  • The susceptible and infected individuals are in relationship with each other and impact the rate of transmission
  • If high numbers of infected or susceptible, then there is an increased rate of transmission
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6
Q

Modal parameters and notation

A

S= susceptible individuals
I= infected individuals
R= resistant individuals
N= total population (N= S + I + R)
Beta= proportionality constant for infection (transmission coefficient)
Nu (v)= rate of recovery of infected hosts

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7
Q

Under what conditions will the disease invade the host population?

A

R0 must be bigger than 1 for disease to invade a population

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8
Q

Closed system, SIR model, movement of numbers

A

Individuals change position within the model over time. There is no way to get more susceptible so a loss of susceptible will mean a gain in infected. Infected number will decrease when number of recovered individuals increases.

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9
Q

Basic Reproduction Number of the disease and the factors contributing to it

A
  • R0- basic reproductive number of disease= the avg number of new infections caused by a single infection over its duration
  • betaS= rate at which a single infected host causes new infections
  • 1/nu= the average duration of an infection (based on rate of recovery)
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10
Q

How do beta, S, and nu influence disease invasion?

A
  • Beta (transmission coefficient) increases, probability of disease invasion increases
  • S (susceptibles) increases, probability of disease invasion increases
  • Nu (rate of recovery) increases, probability of disease invasion decreases therefore the average duration of an infection decreases
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11
Q

Dynamics of SIR model on a graph

A
  • Number of susceptibles decreases over time (starts as the highest number)
  • Number of infected originally increases and then will reach plateau and decrease
  • At point of equilibrium, the disease has died out and there are no infected individuals in the population. Therefore at this point, the host population consists of susceptibles and recovered individuals
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12
Q

Epidemic of influenza B Model

A
  • Real data fit almost perfectly into the SIR predicted model
  • This means that these models can be used to estimate parameters that are difficult to measure AND can be used to determine public health strategies
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13
Q

SIR model with births and deaths

A
  • Open population means we have two more parameters (b= birth rate, mu = death rate)
  • Natural births increase the susceptible population
  • Deaths can decrease all categories- susceptible, infected, and recovered individuals
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14
Q

How does mortality rate influence R0 in open population SIR model?

A

R0 and disease transmission decrease with an increase in deaths and an increase in recovery rates THEREFORE high turnover decrease disease invasion

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15
Q

Importance of host population in disease invasion

A

Mathematical proof that disease invasion and persistence depends on the size of the host population (N)
- Host population affected by births and deaths

Often infectious diseases can only persist if a population passes a critical threshold

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16
Q

Measles and SIR models

A
  • Measles needs a population size greater than 200,000 to persist within a population
  • Measles did not exist in human populations before agricultural revolution which brought large groups of people together
  • Proven through measles island experiment. Measles persisted 100% of the time when the island had a certain population size. For smaller islands, measles goes extinct and has to be reintroduced from the outside world.
17
Q

Critical vaccination threshold (qcrit)

A

Disease invasion and persistence depend on susceptibles but vaccinations converts susceptibles into recovered individuals which can prevent disease invasion.

18
Q

Effective reproductive number (Reff)

A
  • Looks at R when less than 100% of population are susceptible which would occur when a disease has already invaded a population and the susceptible individuals is only a portion of the population.
  • Reff must be greater than 1 to invade. Once at 1, the disease will begin to die out.
19
Q

Susceptible and vaccinated individuals

A
  • Host population (N)= susceptibles (S) + vaccinated (Q)
  • s= proportion of susceptible individuals (S/N)
  • q= proportion of vaccinated individuals (Q/N)
  • s+q= 1

Allows us to determine a fraction of individuals in a population that need to be vaccinated to prevent disease transmission

20
Q

Proportion of vaccinated individuals needed to prevent disease

A
  • Critical vaccination threshold (qcrit> 1- (1/R0))
  • Provides us with the fraction of individuals that need to be vaccinated to prevent disease transmission

Ex. R0=2, then qcrit= 1-(1/2)= 0.50 therefore 50% of population would need to be vaccinated

21
Q

Herd immunity

A
  • Same as qcrit but natural immunity instead of vaccinations

-Herd immunity threshold (HIT) is a percentage of individuals that must become infected to prevent the infection from spreading.

  • Natural immunity reduces S and disease transmission
  • Higher chance of mortality and morbidity (suffering) with natural immunity compared to vaccination
  • Can be used to determine what public health measures need to be put in place. Ex. COVID would need a high level of immunity with many individuals becoming infected to gain herd immunity which was risky/dangerous to the population

Disease Epidemiology (9 decks)

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