This website uses publicly available data sources and applies transformations and subject matter expertise in order to transform them into useful information.

Basic Reproduction Number

The basic reproduction numbers (\(R_0\)) is defined as the average number of secondary cases caused by a single infection in a fully susceptible population (Anderson, Anderson, and May 1992). The important point here is that the population must be fully susceptible. We often estimate the \(R_0\) using serology studies and can observe it indirectly when a new disease enters a population that have never seen said disease.


A disease or infection is said to be endemic if a level of infection is constantly maintained or at a steady state. For instance, the common cold could said to be endemic because a constant level of disease in the community.

Force of Infection

The force of infection is the rate at which susceptible people (no previous contact with the infection and can be infected) are infected.

Generation Time

The average time or distribution between two acquired cases. This includes the latent phase when the person may or may not be symptomatic and the period in which the person is infectious (Anderson, Anderson, and May 1992).

Herd Immunity

Herd Immunity is the threshold by which the incidence of new cases will drop and is related to the number of available susceptible hosts and those who have acquired immunity through vaccination or natural infection. The herd immunity threshold is the target for vaccination campaigns which seek to achieve herd immunity through vaccination rather than natural infection. Herd immunity is roughly calculated using the Basic Reproduction Number, \(R_0\).


So for example, the measles, which has an \(R_0\) of about 16 would require that nearly 94% of the population would need immunity through vaccination or natural infection. This is a rough approximation for the herd immunity threshold because there are many factors that contribute to this calculation. For instance is has been shown that spatial heterogeneous can have an influence on the herd immunity threshold (Champagne et al. 2016; Kissler et al. 2020). Additionally, not all persons are candidates for vaccination (especially the very young and very old).

Non-Pharmaceutical Interventions

Non-Pharmaceutical Interventions (NPIs) are interventions to slow or stop the spread of disease that do not include the use of drugs (most commonly vaccination). NPIs can include social and economic lockdown, restricting travel, physical distancing, wearing of personal protective equipment, and other social policies that reduce contact between persons (Ferguson et al. 2020; Thompson et al. 2020). The primary purpose of these interventions is to slow the spread of disease by reducing the contact rate between persons (Jarvis et al. 2020).1 The aim of these policies is to reduce the spread of the disease such that the infection does not overwhelm the health care system and other interventions such as testing, tracing, isolating and supporting can be more effective (Fraser et al. 2004, @fateh_moghadam_contact_2020; Hellewell et al. 2020; Kucharski et al. 2020; Eames 2007, @montazeri_shahtori_quantifying_2018; Firth et al. 2020).

Reproduction Number

The reproduction number, \(R\) or \(R(t)\), is the average number of secondary cases caused a single infection. The important distinguishing factor between \(R_0\) and \(R(t)\) is that the population is not full susceptible and that there can be a time and behavioral impact. For instance, by practicing physical distancing or good hygiene we can lower the reproduction number, \(R\), but the basic reproduction will remain unchanged.

Serial Interval

The average time between two reported cases. This measure is what is more likely observed and reported than generation time. The Serial Interval is subject to testing delay and in the case of high asymptomatic transmission can actually be negative (e.g. a secondary case can test positive before the identified index case who may have communicated the disease without having symptoms).


Serology or antibody tests look for the presence of specific proteins called antibodies in the blood. The presence of SARS-CoV-2 IgM and IgG in a person’s blood indicate that they had a previous SARS-CoV-2 infection regardless of if they had symptoms. Serology tests cannot tell us when someone had an infection only if they had an infection at some point. Serology tests are useful for understand the Basic Reproduction Number, \(R_0\) of a virus as well as the force of infection. This is because serology tests capture the portion of the population who may have been asymptomatic or had mild symptoms and were not tested for SARS-CoV-2.


Super-spreaders are index cases (infected individuals) who go on to transmit to a higher expected number of people than would be expected. There is not a precise numerical value but a simple example would be one in which the basic reproduction number is 2 meaning that in a fully susceptible population we would expect the first infection to be based to two others. A super-spreader may instead go on to infect 8 people rather than 2. There is evidence to suggest that SARS-CoV-2 is transmitted by super-spreaders and super-spreading events. It is important to note that people might be super-spreader through no fault of their own (Park et al. n.d.; Ghinai 2020; Lu et al. n.d.; Adam et al. 2020; Liu, Eggo, and Kucharski 2020; Endo et al. 2020). Our behavior, environment, and luck play a strong role in super-spreading. Someone who is asymptomatic and goes to a church choir practice could be deemed a super-spreader (Hamner 2020).

Adam, Dillon, Peng Wu, Jessica Wong, Eric Lau, Tim Tsang, Simon Cauchemez, Gabriel Leung, and Benjamin Cowling. 2020. “Clustering and Superspreading Potential of Severe Acute Respiratory Syndrome Coronavirus 2 (SARS-CoV-2) Infections in Hong Kong.” Preprint. In Review.

Anderson, R. M., B. Anderson, and R. M. May. 1992. Infectious Diseases of Humans: Dynamics and Control. Dynamics and Control. OUP Oxford.–xXBguQC.

Champagne, Clara, David Georges Salthouse, Richard Paul, Van-Mai Cao-Lormeau, Benjamin Roche, and Bernard Cazelles. 2016. “Structure in the Variability of the Basic Reproductive Number (R0) for Zika Epidemics in the Pacific Islands.” eLife 5 (November): e19874.

Eames, K. T. D. 2007. “Contact Tracing Strategies in Heterogeneous Populations.” Epidemiology & Infection 135 (3): 443–54.

Endo, Akira, Centre for the Mathematical Modelling of Infectious Diseases COVID-19 Working Group, Sam Abbott, Adam J. Kucharski, and Sebastian Funk. 2020. “Estimating the Overdispersion in COVID-19 Transmission Using Outbreak Sizes Outside China.” Wellcome Open Research 5 (April): 67.

Fateh-Moghadam, Pirous, Laura Battisti, Silvia Molinaro, Steno Fontanari, Gabriele Dallago, Nancy Binkin, and Mariagrazia Zuccali. 2020. “Contact Tracing During Phase I of the COVID-19 Pandemic in the Province of Trento, Italy: Key Findings and Recommendations.” Preprint. Epidemiology.

Ferguson, Neil, Daniel Laydon, Gemma Nedjati-Gilani, Natsuko Imai, K Ainslie, Marc Baguelin, Sangeeta Bhatia, and Adhiratha Boonyasiri. 2020. “Impact of Non-Pharmaceutical Interventions (NPIs) to Reduce COVID-19 Mortality and Healthcare Demand.” Imperial College London.

Firth, Josh A., Joel Hellewell, Petra Klepac, Stephen Kissler, Adam J. Kucharski, and Lewis G. Spurgin. 2020. “Using a Real-World Network to Model Localized COVID-19 Control Strategies.” Nature Medicine, August, 1–7.

Fraser, Christophe, Steven Riley, Roy M. Anderson, and Neil M. Ferguson. 2004. “Factors That Make an Infectious Disease Outbreak Controllable.” Proceedings of the National Academy of Sciences 101 (16): 6146–51.

Ghinai, Isaac. 2020. “Community Transmission of SARS-CoV-2 at Two Family Gatherings — Chicago, Illinois, February–March 2020.” MMWR. Morbidity and Mortality Weekly Report 69.

Hamner, Lea. 2020. “High SARS-CoV-2 Attack Rate Following Exposure at a Choir Practice — Skagit County, Washington, March 2020.” MMWR. Morbidity and Mortality Weekly Report 69.

Hellewell, Joel, Sam Abbott, Amy Gimma, Nikos I. Bosse, Christopher I. Jarvis, Timothy W. Russell, James D. Munday, et al. 2020. “Feasibility of Controlling COVID-19 Outbreaks by Isolation of Cases and Contacts.” The Lancet Global Health 8 (4): e488–e496.

Jarvis, Christopher I., Kevin Van Zandvoort, Amy Gimma, Kiesha Prem, Megan Auzenbergs, Kathleen O’Reilly, Graham Medley, et al. 2020. “Quantifying the Impact of Physical Distance Measures on the Transmission of COVID-19 in the UK.” BMC Medicine 18 (1): 124.

Kissler, Stephen M., Christine Tedijanto, Edward Goldstein, Yonatan H. Grad, and Marc Lipsitch. 2020. “Projecting the Transmission Dynamics of SARS-CoV-2 Through the Postpandemic Period.” Science, April.

Kucharski, Adam J., Petra Klepac, Andrew Conlan, Stephen M. Kissler, Maria Tang, Hannah Fry, Julia Gog, John Edmunds, and CMMID COVID-19 Working Group. 2020. “Effectiveness of Isolation, Testing, Contact Tracing and Physical Distancing on Reducing Transmission of SARS-CoV-2 in Different Settings.” medRxiv, April, 2020.04.23.20077024.

Liu, Yang, Rosalind M. Eggo, and Adam J. Kucharski. 2020. “Secondary Attack Rate and Superspreading Events for SARS-CoV-2.” The Lancet 395 (10227): e47.

Lu, Jianyun, Jieni Gu, Kuibiao Li, Conghui Xu, Wenzhe Su, Zhisheng Lai, Deqian Zhou, Chao Yu, Bin Xu, and Zhicong Yang. n.d. “COVID-19 Outbreak Associated with Air Conditioning in Restaurant, Guangzhou, China, 2020 - Volume 26, Number 7—July 2020 - Emerging Infectious Diseases Journal - CDC.” Accessed June 19, 2020.

Montazeri Shahtori, Narges, Tanvir Ferdousi, Caterina Scoglio, Faryad Darabi Sahneh, and,Department of Electrical and Computer Engineering, Kansas State University, Manhattan, KS 66506, USA. 2018. “Quantifying the Impact of Early-Stage Contact Tracing on Controlling Ebola Diffusion.” Mathematical Biosciences & Engineering 15 (5): 1165–80.

Mossong, Joël, Niel Hens, Mark Jit, Philippe Beutels, Kari Auranen, Rafael Mikolajczyk, Marco Massari, et al. 2008. “Social Contacts and Mixing Patterns Relevant to the Spread of Infectious Diseases.” PLOS Medicine 5 (3): e74.

Park, Shin Young, Young-Man Kim, Seonju Yi, Sangeun Lee, Baeg-Ju Na, Chang Bo Kim, Jung-il Kim, et al. n.d. “Early Release - Coronavirus Disease Outbreak in Call Center, South Korea - Volume 26, Number 8—August 2020 - Emerging Infectious Diseases Journal - CDC.” Accessed June 19, 2020.

Thompson, Robin N., T. Déirdre Hollingsworth, Valerie Isham, Daniel Arribas-Bel, Ben Ashby, Tom Britton, Peter Challenor, et al. 2020. “Key Questions for Modelling COVID-19 Exit Strategies.” Proceedings of the Royal Society B: Biological Sciences 287 (1932): 20201405.

  1. See Mossong et al. (2008) for more details on the POLYMOD survey which explored contact patterns in different groups and ages. These data are vitally important in understanding how disease is communicated↩︎



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