COVID-19 Outbreak: Breaking down the Reproduction Number, R
The spread of the pandemic is mathematically determined by the Effective Reproduction Number, R — the average number of secondary infections produced by a case of infection in both susceptible and non-susceptible hosts.
I understand that # reported confirmed cases are used to examine the extent of the spread but it paints an incomplete picture. The aforementioned point is an important one since subsequent data analyses heavily depend on the number of reported confirmed cases, and by the nature of global COVID-19 outbreaks unfolding as we speak, this metric is insufficient to completely scale the extent of the spread (making it quite necessary to put that as a disclaimer here).
The aforementioned point is an important one since subsequent data analyses heavily depend on the # of reported confirmed cases, and by the nature of events unfolding as we speak, it is an insufficient metric to completely understand the extent of the spread, thus making it quite necessary to put that as a disclaimer.
Acknowledging this fact, I focused my attention to better understanding epidemiological modeling, which consists of two noteworthy numbers that measure the pathogen’s transmission:
Basic Reproduction Number, Ro
Effective Reproduction Number, R
where X is the fraction of host population that is susceptible to infection
I understand that it looks complicated and believe me that is the simplest representation that I came across while browsing through numerous research papers. The focus of the article is on R since it encompasses Ro within itself, thus providing a more comprehensive representation of the pandemic than the basic reproduction number.
So, breaking down R into simpler (easy-to-digest) components:
1. The contact rate of an individual, C
2. The probability of transmitting infection during contact, T
3. The duration of infectiousness/ recovery rate, D
4. Fraction of susceptible population, X
After segmenting R into components that decide the actual transmission of the pathogen, let’s shift our focus toward examining factors that impact each component separately. It is important to note that these factors may not be mutually exclusive to the category of components that they have been put under; I have done so by collating them in a manner that puts them in the most representative category.
Contact Rate, C
C depends on the # people in the host population that the infected case comes in close contact with.
International connectivity is one of the most important determinants of pathogen transmission in today’s world. Travel and Tourism is a huge industry and an increase in air-travel providers has brought even the remotest places on Earth extremely close to each other.
The first outbreak in Quebec, Canada happened when families returned home from Europe during spring break. Spring breaks in other provinces of Canada would have happened on later dates but were cancelled as a containment measure, providing them with valuable time and resources to prepare for mitigation efforts.
National economic systems depend on different countries for international trade and that has increased business travel, which makes a whopping global economic contribution of ~1 trillion US dollars every year. Outbreak in Iran began when a merchant from Wuhan travelled to Qom, a religious city in Iran.
Domestic mobility contributes substantially toward an increase in C. Interconnected roadways and railways have made domestic travel convenient, increasing the possibilities of transmission. Urban regions boast of an extensive public transport system, which for pathogen carriers is an excellent opportunity to spread.
Social capital is quite a subtle determinant of transmission, but significant nonetheless.
According to Robert Putnam, social capital refers to “connections among individuals — social networks and the norms of reciprocity and trustworthiness that arise from them.”
Social capital has accumulated in urban households, making them more vulnerable to transmission than rural ones. Tight social bonds and civic capital, make people more susceptible to transmission. Urban cities offer more opportunities for contact through consumerism. Shoppers flooding malls, dining at restaurants, and attending concerts have only accentuated the rate of contact.
Probability of transmission, T
T depends on the type of contact between infected case and host population.
Culture could be an important determinant as well. For instance, people in most European countries greet each other through gestures such as hugs, kisses, and handshakes, which unknowingly offer an opportunity to infect a close-knit community.
Wearing masks has become mandatory in some European countries — Czech Republic, Slovakia, Bosnia, Herzegovina, Austria, Turkey, Poland, and Germany — within the last one month. In Asian nations such as China, Taiwan, and Hong Kong, wearing masks has been relatively common even before the COVID-19 outbreak.
Prior exposure to such epidemics as SARS provided the Asian countries with a better preparedness plan, leveraging from a proactive approach toward containment measures such as increasing public access to masks.
Even though it is not scientifically proven that non-surgical masks are effective in preventing the wearer from contracting infection, it is widely supported that they help to prevent the spread to others if they happen to be carrying the virus. Conclusively, not wearing masks can increase T.
Religiosity could promote close contact such as that witnessed in certain religious gatherings in Daegu (South Korea), Qom (Iran), and Delhi (India) could increase T.
Occupation risk associated with certain professionals are more than others that do not involve either extensive human interaction or close contact with potential virus carriers. Some that are particularly vulnerable to transmission are family and general practitioners, and registered nurses.
Duration of infectiousness, D
D depends on how quickly an individual recovers from an infection, and that in turn depends on the immune system and prior vaccination. A number of governments across the globe have issued directives for people, who experience COVID-19 like symptoms to remain in self-isolation for at least 14 days — helping decrease D. Even though recovery rate varies with age and underlying health conditions, all individuals, irrespective, are capable of containing and spreading the virus.
The time between when one contracts the virus and when the symptoms start is known as incubation period, and that is worth mentioning since during this time the infected case remains asymptomatic but continues to spread.
The average incubation period is 5 days, based on reported data so far.
It is relevant to point out that in this context the statement refers to recovery rate without medical intervention i.e. self-recovery, which happens without a ventilator and due to a stronger body immune system.
Fraction of susceptible population, X
X depends on the how fast infected cases are removed from the host population. One can think of X as the amount of wood on a fire; once the wood burns up, the fire goes out. Measures such as widespread testing and contact tracing help determine the possible infected cases and remove them from the population through self-isolation, 14 day quarantine, and city lockdown measures.
Public health measures a.k.a. non-pharmaceutical interventions (NPIs) decide the extent of decrease in X. Two main containment strategies effective currently in different countries are:
- Mitigation, which focuses on slowing but not necessarily stopping the spread (such as that in USA).
- Suppression, which aims to reverse epidemic growth by reducing the case numbers to really low levels (partially exercised in China).
Five different measures can be considered in combination (or separately) depending on the prescribed containment strategy:
- Case isolation at home
- Voluntary home quarantine
- Social distancing (old population)
- Social distancing (entire population)
- Closure of schools, universities, and non-essential businesses
Cognizant to the fact that the factors mentioned in the article are neither completely exhaustive not mutually exclusive, I have tried to compartmentalize them into four categories based completely on my personal understanding of the pandemic and the reported data available to public sources. Please let me know what you think about the effective reproduction number and the factors that govern this very important epidemiological metric.
Your feedback is valuable.
Thank you for reading the article!
Stay healthy. Stay sane.
