Epidemiology and Disease Dynamics

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Questions and Answers

What does the fraction rac{S(∞)}{N} represent in the formula for estimating the basic reproductive number post-epidemic?

The fraction of the population remaining susceptible at the end of the epidemic (correct)

The total population size during an epidemic

The overall mortality rate in the population

The portion of the population that has recovered

Which model describes the initial exponential rise in cases during an epidemic?

Static model

Cohort model

SIR model (correct)

Deterministic model

What is a disadvantage of forward tracing in contact tracing?

It can identify superspreaders effectively

It relies solely on technology for tracking

It decreases transmission rates aggressively

It may miss superspreading events (correct)

What is the purpose of implementing cordon sanitaries during an epidemic?

To restrict movement into or out of a geographic area to control disease spread Signup and view all the answers

Which of the following is a novel strategy used in contact tracing?

Wastewater analysis Signup and view all the answers

What is the primary focus of epidemiology?

Study of disease outbreaks using statistics Signup and view all the answers

Which disease is characterized by sudden outbreaks in specific locations or populations?

Epidemic Signup and view all the answers

Which of the following diseases can be described as crowd diseases?

Measles and smallpox Signup and view all the answers

What is the relationship between the susceptible population, S(t), and the infected population, I(t), according to the mass action principle?

S(t) decreases as more people become infected. Signup and view all the answers

What does the term 'critical community size' refer to?

Population size needed for disease sustainability Signup and view all the answers

What is the primary mode of transmission for bubonic plague?

Flea bites Signup and view all the answers

What does a basic reproductive number, R0, greater than 1 indicate?

More infected individuals than recovered. Signup and view all the answers

What describes a long-term consistent presence of a disease within an animal population?

Enzootic Signup and view all the answers

How can the spread of an epidemic be slowed according to the provided information?

By reducing the transmission rate ß. Signup and view all the answers

What does the effective reproductive number, Re, account for in epidemic modeling?

Changes in the susceptible population over time. Signup and view all the answers

Which of the following is an assumption of the SIR model in epidemiology?

All rates of transmission are uniform Signup and view all the answers

According to the SIR model, what happens once individuals are removed from the infected category?

They recover permanently without re-infection. Signup and view all the answers

In the SIR model, what does the symbol ß represent?

Transmission rate from infected to susceptible Signup and view all the answers

What is the formula used to determine the herd immunity threshold?

$rac{R(t)}{N} > 1 - rac{1}{R0}$ Signup and view all the answers

In the context of the SIR model, what does increasing the rate of recovery v imply?

Reduction in the infected population. Signup and view all the answers

What condition indicates an epidemic decline when referring to Re?

Re < 1 Signup and view all the answers

Study Notes

Epidemiology

The study of epidemics using statistics and probability to study disease.
John Snow is considered the father of epidemiology due to his work tracing a cholera outbreak to a contaminated water pump.

Epidemics, Endemics, and Crowd Diseases

Epidemic: A sudden, short-term outbreak in a specific location or population over a short time.
Endemic: A long-term, consistent presence of a disease at a baseline level within a specific region.
Crowd Diseases: Spread rapidly and are sustained in large populations, typically in dense communities. Examples include smallpox and measles.

Disease Transmission and Cycles

Critical Community Size (CCS): The minimum population size needed for a disease to sustain itself without dying out.
Zoonotic: A disease that is transmitted from animals to humans.
Sylvatic Cycle: The transmission cycle of a pathogen that primarily circulates in wild animal populations without immediate human involvement.
Enzootic: A long-term consistent presence of a disease within an animal population in a specific region.
Epizootic: A disease outbreak that briefly affects an animal population in a short period of time.

Plague

Three clinical forms:
- Bubonic: Inflamed lymph nodes, transmitted by fleas. Mortality rate of 30-90%, death occurs within 10 days.
- Pneumonic: Lung infection, transmitted human-to-human via droplets. Mortality rate of 90-100%.
- Septicemic: Flea-human transmission within the blood.

SIR Model

Answers the question: "Will an epidemic occur?"
A compartment model that measures the rate of individuals moving across compartments.
β: Transmission rate or rate of an infected person getting someone sick.
ν: Clearance rate or rate of recovery/death.

SIR Model Assumptions

Population size is constant (N = S(t) + I(t) + R(t)).
No births/deaths.
Well-mixed populations: everyone has an equal chance of coming into contact with one another.
Mass action: The rate of change of new infections (β) is proportional to S x I, assuming well-mixing.
Everyone starts susceptible, except for one infected.
Once removed, individuals cannot become infected again.
Rates are uniform across individuals.

SIR Model Equations

Susceptible Population:
- dS(t)/dt = -β * (I(t) * S(t) / N)
Infected Population:
- dI(t)/dt = β * (I(t) * S(t) / N) - ν * I(t)
Recovered Population:
- dR(t)/dt = ν * I(t)

Reproductive Numbers

Basic Reproductive Number (R0):
- R0 > 1: More infected than recovered, resulting in an epidemic.
- R0 < 1: More recovered than infected.
Effective Reproductive Number (Re):
- Accounts for changes in the susceptible population over time.
- Re = R0 * (S(t) / N)
- Re > 1: Each infected person causes more than one new infection, leading to exponential growth.
- Re < 1: Epidemic decline.

Slowing Epidemic Spread

Increasing ν: Reducing the duration of infection through antibiotics and vaccines.
Reducing β: Public health measures such as masking and quarantine.

Breaking SIR Model Assumptions

N = constant: Assumes a constant population size, which is a reasonable assumption.
Everyone starts susceptible except for one infected:
- This assumption is challenged by herd immunity.
Rates are uniform between individuals:
- Superspreaders can significantly impact transmission.
Mass action:
- Social distancing and quarantine decrease contact frequency, challenging the mass-action principle.
Once removed cannot get sick:
- The reality is more complex, with multiple compartments.

Herd Immunity and R0

Herd Immunity: The protection of a population from a disease when a sufficiently high percentage of individuals are immune.
Herd Immunity Threshold: The percentage of the population that needs to be immune to achieve herd immunity.
- R(t) / N > 1 - (1 / R0)
ν and Infection Time:
- ν = 1 / Infection Time
S(0): At the beginning of an epidemic (t = 0), the entire population is susceptible.
- S(0) = N
Estimating R0 after an Epidemic:
- R0 = ln(S(∞) / N) / [(S(∞) / N) - 1]
  - S(∞)/N represents the fraction of the population that remains susceptible at the end of the epidemic.

SIR Model Limitations

The SIR model is a good model for the initial exponential rise in cases.

Non-Pharmaceutical Interventions (NPI)

NPIs, such as social distancing and quarantine, can "flatten the curve" of an epidemic.
- Examples include:
  - The 1918 flu outbreak in St. Louis (appropriate NPI) versus Philadelphia (inadequate NPI).
  - Early COVID-19 mortality in China decreased due to the availability of resources.

Contact Tracing and Novel Strategies

Stochastic Models: Account for certain levels of unpredictability or randomness.
Backward Tracing: Identifies the source of infection by tracing who infected the patient.
- Pros: Useful for identifying superspreaders.
- Cons: Difficult to keep up.
Forward Tracing: Identifies people who were in contact with an infected person.
- Pros: Effective for stopping future transmissions.
- Cons: May miss superspreading events.
Contact Tracing Impact: Contact tracing reduces transmission rates (β) by decreasing the number of infected people.
Novel Contact Tracing Strategies:
- Wastewater Analysis: 50% of asymptomatic/symptomatic patients shed the virus in feces.
  - Helps identify novel variants.
- Genetic Epidemiology:
  - Everyone with the same strain indicates a hotspot.
  - Two people with different strains suggests they did not infect each other.
  - It can supplement contact tracing.

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Description

Test your knowledge on the principles of epidemiology, including the definitions of epidemics and endemics, as well as disease transmission mechanisms. Explore critical concepts such as John Snow's contributions and the significance of community sizes in disease sustainability.