Lecture 3 - R0, Thresholds, and Epidemic Dynamics

What is R₀?

The basic reproductive ratio: the expected number of secondary infections produced by one infected host in a susceptible population under specified conditions.

What does R₀ > 1 mean?

On average, each infection produces more than one new infection, so the pathogen can increase when introduced.

What does R₀ < 1 mean?

Each infection produces fewer than one new infection on average, so the infection cannot sustain itself.

What does R₀ = 1 mean?

The pathogen is at the replacement threshold: each infected host produces one new infection on average.

What is the most important way to interpret R₀ on an exam?

Ask whether one infected host replaces itself with more than, fewer than, or exactly one new infection.

What is the relationship between R₀ and host density in a density-dependent model?

R₀ increases as host density increases.

Why does higher host density often increase R₀?

Dense populations create more opportunities for transmission between susceptible and infected hosts.

What is the basic R₀ equation from the Kermack-McKendrick model?

R₀ = βS/γ.

At the beginning of an epidemic, what can S usually be approximated as?

S ≈ N because most of the population is initially susceptible.

What does R₀ become when S ≈ N?

R₀ = βN/γ.

What is the threshold host density NT?

The minimum host density required for a pathogen to establish and produce an epidemic under the model.

What is the threshold host density equation in the basic model?

NT = γ/β.

Why does NT increase when γ increases?

Hosts leave the infectious class more quickly, so a higher host density is needed to sustain transmission.

Why does NT decrease when β increases?

Transmission is more efficient, so fewer hosts are needed to sustain the pathogen.

What is the general idea behind NT = gain rate/loss rate?

Establishment occurs when the rate of generating new infections exceeds the rate at which infections are lost.

If β doubles, what happens to NT = γ/β?

NT is cut in half.

If γ doubles, what happens to NT?

NT doubles.

A population is below NT. What should happen after introducing a pathogen?

The infection should fail to establish because transmission cannot replace infections that are lost.

A population is above NT. What can happen?

The pathogen can establish and an epidemic can occur if other assumptions of the model are met.

What is deterministic fadeout?

Fadeout predicted because the average conditions do not allow the infection to increase, such as R₀ < 1.

What is stochastic fadeout?

Fadeout caused by random chance even when conditions allow an epidemic, such as when an early chain of transmission happens to die out.

Why can an epidemic fade out even when R₀ > 1?

R₀ is an average. Random events can cause the actual early transmission chain to fail.

What is the difference between deterministic and stochastic fadeout?

Deterministic fadeout occurs because transmission conditions prevent growth on average. Stochastic fadeout occurs because chance events terminate transmission.

Why can a pathogen disappear after a large epidemic even when R₀ initially exceeded 1?

The epidemic can reduce the susceptible population enough that transmission can no longer replace infections.

What is critical community size?

The minimum population size needed to maintain transmission over time.

Why can a disease disappear from a small population but persist in a large population?

Small populations are more vulnerable to stochastic fadeout because transmission chains are more likely to terminate by chance.

If two populations have the same R₀ but one is much smaller, which is more vulnerable to stochastic fadeout?

The smaller population.

What does it mean if a pathogen has a high R₀?

It can generate many secondary infections under the conditions used to define R₀, but R₀ alone does not tell you exactly how large an outbreak will be.

What happens to the epidemic curve when susceptible density increases in a density-dependent system?

The epidemic can grow faster and reach a larger peak because more transmission opportunities exist.