Definition:
The basic reproductive ratio, R0 (also called the basic reproductive “rate” or “number”), is the average
number of persons directly infected by an infectious case during their entire infectious period when the
infectious case enters a totally susceptible population.
Notice: In your reference book, Nelson et al. use “R” to refer to R0. For most other authors, R is a slightly
different concept (see below).
Question 1:
In a sense, R0 is an abstraction though it can in fact be estimated from simple observations. Calculate R0
based on the following schematic spread of an infectious disease.
Question 2:
Severe Acute Respiratory Syndrome (SARS) is a recently described viral respiratory illness caused by a
coronavirus, called SARS-associated coronavirus (SARS-CoV). The main way that SARS seems to spread is
by close person- to-person contact (droplets). At present, there is no direct evidence of SARS
transmission from asymptomatic persons. Epidemics of SARS were reported in 29 countries between
November 2002 and July 2003. A total of 8,098 probable SARS cases were reported to the World Health
Organization (WHO), including 29 cases from the United States; 774 SARS-related deaths (case-fatality
rate: 9.6 percent) were reported (none of which occurred in the United States).
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In Singapore, 205 probable cases of SARS were reported in a population of 4.6 million inhabitants. The
mean time from the onset of SARS symptoms in an index case to the onset of SARS symptoms in a
subsequent case infected by the index case in this Asian country was 8.4 days. What term would you use
to describe this parameter?
Question 3:
The number of secondary SARS cases per index case fell from a mean of 7 for index
cases with symptom outset in the first week of the Singapore outbreak to a mean of 1.6 in the second
week, and to a mean of below 1 in most weeks thereafter. Based on these data, what is the best
estimate of the basic reproductive ratio, R0, for the SARS epidemic in Singapore?
Information for question 4: Note that R0 refers to the situation that prevails early during the course of an
outbreak in an entirely susceptible population. R is generally used to refer to the actual (or effective)
reproductive ratio– the reproductive rate actually observed at any specific time during the course of an
epidemic in a population that may include any proportion of non- susceptible individuals. R0 can be
estimated from the value of R at a given time during the epidemic and the proportion of susceptibles in
the population at that time.
Where Rt = value of R at time t and St = number of susceptible in population of size N at time t.
Equivalently,
Question 4:
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Based on the above formula and data from question 3, calculate estimates of the proportion of persons
susceptible to SARS in Singapore during the second week and the following weeks of the outbreak.
Question 5:
Based on the data from question 3 and the calculations from question 4, is the decline with time in
number of secondary cases per index case (R) likely to be explained by the simple depletion of the
number of susceptibles over the natural course of the epidemic? (Provide a rationale for your answer.)
Question 6:
As a continuation from question 5, besides the simple depletion of the number of susceptibles over
time, can you think of another reason why the value of R dropped so markedly during the course of the
epidemic?
Question 7:
Using information from the table below, how would you characterize the epidemic potential of SARS
compared to that of measles and smallpox?
Disease
Latent Period
Incubation Period
TG
R0
(days)
(days)
(days)
SARS
~7
~5
~10
~3
Measles
~7
~12
~11
~17
Smallpox
~15
~12
~21
~6
Question 8:
Since neither effective antiviral therapy nor vaccine was available, control of SARS outbreaks was
achieved by implementing aggressive measures of isolation, segregation, and quarantine. Considering
that the best estimate of R0 for SARS is ? 3 and that control measures were successful, what minimal
reduction in overall SARS infectiousness was achieved with these methods?
Question 9:
Fortunately, extensive contact tracing in Hong Kong identified a known symptomatic
SARS contact for 91.4% of reported cases. Would your conclusion regarding potential for success in SARS
control be changed if new evidence were shown that infected persons who never become symptomatic
contributed substantially to transmission? (Provide a rationale for your answer.)
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Question 10:
Early studies of viral titers in nasopharyngeal aspirates suggest that viral shedding increases over the
first 10 days after the onset of SARS symptoms and then drop abruptly. What is the implication of this
finding with regard to the potential efficacy of isolation as a measure of outbreak control?
Question 11:
In practice, what factors may limit the effectiveness or feasibility of quarantine? (Propose
at least three factors.)
Question 12:
In practice, what factors may limit the effectiveness or feasibility of isolation? (Propose at least three
factors.)
The figure below show trends in measles rate in New York between 1944 and 1964 (i.e., before measles
vaccine became available). Use this figure as a basis for answering questions 13-15.
Question 13:
Describe the variations in incidence over time for the disease.
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Question 14:
How do you explain these variations?
Question 15:
What do these variations tell you about average age of measles in New York during this period?
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