Application, Formula Interpretation, and Compare + Contrast

A pathogen has R₀ = 0.7. What happens if it is introduced into a completely susceptible population?

It should fail to establish on average because each infected host produces fewer than one secondary infection.

A pathogen has R₀ = 3. What does that tell you?

Each infected host produces an average of 3 secondary infections under the conditions defining R₀, so the infection can increase when introduced into a susceptible population.

Two pathogens have the same β but different γ values. Which has greater transmission potential?

The pathogen with lower γ because infected hosts remain infectious longer.

Two pathogens have the same γ but different β values. Which has greater transmission potential?

The pathogen with higher β.

If a pathogen's infectious period becomes shorter but its contact rate stays the same, what happens to R₀?

R₀ decreases because infected hosts have less time to transmit.

If host density increases in a density-dependent system, what happens to transmission?

Transmission increases because contact rate increases with density.

If host density increases in a frequency-dependent system, what happens to per-capita contact rate?

It remains approximately constant.

A pathogen persists in a very small host population. What transmission type might this suggest?

Frequency-dependent transmission, because there is no threshold host density in the basic model.

A pathogen disappears whenever host density falls below a particular value. What does this suggest?

Density-dependent transmission with a threshold host density.

A disease has high prevalence but short infectious duration. What could explain this?

High incidence or rapid ongoing transmission may be maintaining the high prevalence despite short infections.

A disease has low incidence but high prevalence. What could explain this?

Long infection duration can maintain a high number of infected individuals even when few new infections occur.

An epidemic occurs in a dense population but not a sparse population. What model concept could explain this?

A threshold host density caused by density-dependent transmission.

A pathogen has R₀ = 4 and 75% of the population becomes immune. What is R′?

R′ = 4(1 − 0.75) = 1. The population is exactly at the transmission threshold.

A pathogen has R₀ = 4 and 80% are immune. What happens?

R′ = 4(0.20) = 0.8, so transmission should decline below the replacement threshold.

If R₀ increases because the pathogen becomes more transmissible, what happens to pc?

pc increases because pc = 1 − 1/R₀.

If β increases, what happens to NT?

NT decreases because NT = γ/β.

If γ increases, what happens to NT?

NT increases because NT = γ/β.

If vaccination decreases S, what happens to transmission?

Transmission decreases because there are fewer susceptible hosts.

If a pathogen is highly aggregated among hosts, should a control program necessarily treat every host equally?

Not necessarily. If heavily infected hosts contribute disproportionately to transmission, targeting them may remove a disproportionate amount of parasite transmission.

Why would removing the most infected hosts be more effective for an aggregated macroparasite than randomly removing hosts?

The most infected hosts carry a disproportionately large fraction of parasites and may contribute disproportionately to transmission.

A vector has a 10-day latent period and an average lifespan of 5 days. What does this imply?

Most vectors will die before becoming capable of transmission, limiting transmission.

A vector's biting rate increases. What happens to vector-borne R₀?

R₀ increases because vectors have more opportunities to acquire or transmit infection.

Vector mortality increases. What happens to vector-borne R₀?

R₀ decreases because vectors have less time to survive and transmit.

A pathogen spends most of its lifecycle outside the host and multiplies in the environment. What type of transmission should you consider?

Environmental transmission because the reservoir can strongly influence transmission dynamics.

A parasite alters a rodent so it is more likely to be eaten by a cat. What transmission mode is this?

Trophic transmission.

A disease can spread both through contaminated water and directly between people. What concept describes this?

Dual transmission modes.

Why could the same environmental event increase disease transmission through two different pathways?

A change such as flooding can simultaneously alter environmental pathogen exposure and human contact patterns.

What does R₀ = βS/γ tell you?

R₀ increases with transmission and susceptible-host availability and decreases as infected hosts leave the infectious class faster.

What does R₀ = βN/γ tell you at the start of an epidemic?

When nearly everyone is susceptible, R₀ depends on transmission, host density, and the rate infected hosts are lost.

What does NT = γ/β tell you?

The host density required for establishment increases with infection loss and decreases with transmission.

What does pc = 1 − 1/R₀ tell you?

The fraction that must be immunized to bring R′ to 1 under the simple homogeneous-mixing model.

What does R′ = R₀(1 − p) tell you?

Vaccination reduces the original reproductive ratio according to the fraction of the population remaining susceptible.

What does c(S/N)δI tell you?

Transmission depends on contact rate, the fraction of contacts with susceptible hosts, transmission success per appropriate contact, and the number of infected hosts.

What does βSI tell you?

Under density-dependent transmission, new infections increase with both susceptible and infected host densities.

What does βSI/N tell you?

Under frequency-dependent transmission, transmission depends on infected-host density and the fraction of hosts that are susceptible.

What does 1/γ mean biologically?

Average duration of infectiousness.

If a variable is in the numerator of a formula, what generally happens when it increases?

The value of the formula increases, assuming all other variables remain constant.

If a variable is in the denominator, what generally happens when it increases?

The value of the formula decreases, assuming all other variables remain constant.

Why should you not just plug numbers into R₀ formulas?

Because exam questions may ask you to predict biological consequences from changing parameters rather than calculate a numerical answer.

Microparasite vs macroparasite

Microparasites multiply within hosts and impact is often related to prevalence. Macroparasites generally accumulate within hosts and impact is often related to intensity or abundance.

Prevalence vs intensity

Prevalence is the proportion of hosts infected. Intensity is the number of parasites in an infected host.

Incidence vs prevalence

Incidence measures new infections over time. Prevalence measures existing infections at a particular time.

R₀ vs R′

R₀ describes transmission under the conditions used to define the basic reproductive ratio. R′ represents reproduction after a change such as vaccination.

Deterministic vs stochastic fadeout

Deterministic fadeout results from conditions that do not support replacement. Stochastic fadeout occurs by chance even when average conditions could support transmission.

Density-dependent vs frequency-dependent transmission

Density-dependent transmission increases with host density and has a threshold host density. Frequency-dependent transmission depends on the frequency of susceptible hosts and lacks a basic host-density threshold.

Acquisition vs inoculation

Acquisition is when a vector gets the pathogen. Inoculation is when the vector transmits it to another host.

Persistent vs nonpersistent transmission

Persistent pathogens remain transmissible in the vector for longer periods, while nonpersistent pathogens are retained only briefly.

Trophic vs environmental transmission

Trophic transmission depends on one host being eaten by another. Environmental transmission involves a pathogen reservoir outside the host.

Intermediate vs definitive host

An intermediate host supports developmental stages. A definitive host supports the adult or sexually reproducing stage.

Individual immunity vs herd immunity

Individual immunity directly protects an immune host. Herd immunity indirectly reduces infection risk for susceptible hosts because immune hosts reduce transmission.

Vaccination vs vector control

Vaccination reduces host susceptibility. Vector control reduces the vector population or vector-host contact.

Host-density threshold vs vaccination threshold

Host-density threshold describes the minimum host density needed for establishment in density-dependent systems. Vaccination threshold describes the immune fraction needed to reduce transmission below replacement.