In this session, we will discuss different measures for transmissibility of communicable diseases. One of the most important epidemiologic characteristics of a communicable disease is the transmissibility of the pathogen. Several measures are commonly used to quantify the transmissibility of a pathogen. Attack rate is defined as the proportion of a given exposed population that has been infected by the pathogen, which is simply the cumulative number of infections divided by the population size. Over the course of an epidemic, the attack rate increases as more and more people become infected. Although attack rate provides a measure for the level of spread of the pathogen in a population, it does not directly describe how transmissible the pathogen is from person to person. Secondary attack rate and reproductive number are the two most commonly used measures for person-to-person transmissibility. Secondary attack rate is the attack rate of the exposed susceptible population in a semi-closed setting, such as in a household, a school, or an airplane, after the introduction of an infected individual into this setting. For example, during the 2009 influenza H1N1 pandemic in Hong Kong, a household study of influenza transmission found that the within-household secondary attack rate of pandemic H1N1 and seasonal influenza were similar, which suggested that pandemic H1N1 and seasonal influenza had similar transmissibility. However, secondary attack rate is not necessarily an accurate proxy for person-to-person transmissibility. To see this, consider this example of a household with 4 members where A is the primary case with B and C becoming infected in this household outbreak. Suppose we can rule out the possibility that B and C are infected by someone outside the household, for example, when disease prevalence in the community is known to be very low. The underlying chain of transmission for this household outbreak has three possibilities. The first is that B and C are both infected by A. The second is that A infects B, who then infects C. The third is that A infects C, who then infects B. The probability of these possibilities depend on the person-to-person transmissibility of the pathogen, and knowing only the secondary attack rate is not enough to help us distinguish among these possibilities. Person-to-person transmissibility of a pathogen is most accurately described by the reproductive number, which is defined as the expected number of secondary cases generated by one infected case and usually denoted by R. When a pathogen invades a population that is completely susceptible, for example, SARS in 2003, the reproductive number at that stage is known as the basic reproductive number, which is universally denoted by R0. R0 indicates whether the invasion of the pathogen can give rise to an exponentially growing epidemic. If R0 is not greater than 1, which means that on average every infected individual cannot infect more than one person, then the chain of transmission will die out without exponential growth and the final attack rate will be close to zero. Otherwise, if R0 is greater than 1, then the invasion of the pathogen can lead to an exponentially growing epidemic, the probability of which increases as R0 increases. Let us now look at the change in reproductive number over the course of an epidemic. Suppose infected individuals become immune to reinfection after they have recovered and there are no interventions to mitigate the epidemic. As the epidemic unfolds in the exponential growth phase, the reproductive number and the epidemic growth rate decrease because of depletion of susceptibles. When the reproductive number drops to 1, incidence growth stalls and the epidemic reaches its peak. Incidence then begins to drop monotonically and the epidemic will eventually die out if replenishment of susceptibles, for example, via newborns, is not sufficiently large to maintain disease transmission. The final attack rate refers to the proportion of population that has been infected by the end of the epidemic. In general, the final attack rate does not reach 100%, which means that some proportion of the population will escape infection. Instead, the final attack rate becomes closer and closer to 100% as R0 increases. This is because if R0 is not extremely large, the reproductive number becomes smaller than 1 when a substantial proportion of the population is still susceptible. As the epidemic subsides after the peak, only some of these remaining susceptibles will be infected. This table shows the estimates of R0 for some pathogens. R0 was around 1.5-3 for 1918 pandemic influenza, 2-3 for SARS in Hong Kong and Beijing, and 12-19 for measles. The high R0 of measles explains why measles epidemics occurred every 2 years or so in England and Wales before childhood measles vaccination was implemented. Because R0 for measles is high, the proportion of population susceptible to measles was very small after each epidemic but was continuously replenished by newborns. It took around 2 years for the susceptible population to be large enough again for the reproductive number to rise above 1, hence the biennial cycle of measles epidemics in the pre-vaccination era. The One Health model is built upon a fundamental concept in epidemiology called the epidemiologic triangle, which states that epidemic of a communicable disease is an interplay among the pathogen, the host, as well as the environment. As such, transmissibility of a communicable disease depends not only on the pathogen, but also on the characteristics of the host population such as contact patterns and immunity among individuals, as well as environmental factors such as climate conditions and animal reservoirs. For example, this is the epi curve of SARS in Beijing in 2003 and the corresponding estimates of the reproductive number over the course of the epidemic. The reproductive number dropped sharply in mid-April 2003, not because of depletion of susceptibles. Instead, transmissibility was suppressed because of aggressive public health interventions that aim to reduce contact between susceptible and infected people, including case isolation, contact tracing and quarantine of contacts, as well as population-wide social distancing. In summary, in this session, we have discussed different measures for transmissibility of communicable diseases.
