Question 1

In the SIR model for infectious disease spread, which of the following best describes the role of the parameter $$\beta$$?

Accepted Answer

It is the per-capita transmission parameter, representing how often susceptible-infectious encounters lead to new infections.

Question 2

Given the SIR model equations, which of the following correctly expresses the rate of change of the susceptible population $$S$$?

Accepted Answer

$$\frac{dS}{dt} = -\beta \frac{S I}{N}$$

Question 3

If the average recovery time for an infection is $$t$$ days, what is the correct expression for the recovery rate $$\gamma$$?

Accepted Answer

$$\gamma = \frac{1}{t}$$

Question 4

Which of the following best describes the basic reproduction number $$R_0 in $$the SIR model?

Accepted Answer

$$R_0$$ = \frac{\beta}{\gamma}$$

Question 5

Suppose a disease has $$\beta = 0.3$$ days$$^{-1}$$ and $$\gamma = 0.1$$ days$$^{-1}. $$What is the basic reproduction number $$R_0$$?

Accepted Answer

$$R_0 = 3$

Question 6

In the SIR model, which differential equation describes the rate of change of the removed (recovered) population $$R$$?

Accepted Answer

$$\frac{dR}{dt} = \gamma I$$

Question 7

If $$N = 1000$$, $$S = 1000$$, $$I = 1$$, $$R = 0$$, $$R_0 = 3.0$, and t = 8$ days, what is the value of $$\gamma$$ (in days$$^{-1}$$)?

Accepted Answer

$$\gamma = 0.125$$\ days$$^{-1}$$

Question 8

Using the same values as above ($$R_0 = 3.0$, $$\gamma = 0.125$$ days$$^{-1}$$), what is the value of $$\beta$$ (in days$$^{-1}$$)?

Accepted Answer

$$\beta = 0.375$$\ days$$^{-1}$$

Question 9

In the SIR model, what is the effect of increasing $$\gamma$$ while keeping $$\beta$$ constant?

Accepted Answer

The epidemic will last for a shorter time and the peak number of infected individuals will be lower.

Question 10

Which of the following best describes the analogy between the SIR model and chemical kinetics?

Accepted Answer

The transmission event is like a bimolecular reaction, and recovery is like a first-order decay.

Question 11

If a vaccination program instantly moves a fraction $$v of $$the susceptible population to the removed class, which modified differential equation for $$S is $$most appropriate?

Accepted Answer

$$\frac{dS}{dt} = -\beta \frac{S I}{N} - v S$$

Question 12

A disease with $$R_0$$ \u003c 1$$ will:

Accepted Answer

Die out without causing an epidemic.

Question 13

If the initial number of infected individuals is increased while all other parameters remain constant, what is the most likely effect on the epidemic curve?

Accepted Answer

The epidemic will peak earlier but the total number of infections may not change significantly.

Question 14

Which of the following is NOT an assumption of the basic SIR model?

Accepted Answer

The population is open, with births and deaths occurring.

Question 15

In the SIR model, what does the term $$\beta \frac{S I}{N}$$ represent?

Accepted Answer

The rate at which susceptible individuals become infected.

Question 16

If the recovery rate $$\gamma is $$doubled, but $$\beta$$ remains the same, what happens to $$R_0$$?

Accepted Answer

$$R_0 is $$halved.

Question 17

Which of the following would be the best real-world application of the SIR model?

Accepted Answer

Predicting the spread of influenza in a closed community.

Question 18

If $$\beta is $$decreased by half due to social distancing, what is the effect on the basic reproduction number $$R_0$$?

Accepted Answer

$$R_0 is $$decreased by half.

Question 19

Which parameter in the SIR model most directly controls how long the epidemic lasts?

Accepted Answer

The recovery rate $$\gamma$$

Question 20

In the SIR model, which of the following would be the best way to simulate the effect of a new vaccine that instantly immunizes a fraction of the population at $$t=0$$?

Accepted Answer

Decrease the initial value of $$S$$ and increase the initial value of $$R by $$the same amount.

Kinetics of Infectious Disease Spread: The SIR Model and Chemical Kinetics Analogy

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