Edited by: Jimmy Thomas Efird, East Carolina University, USA
Reviewed by: Tony Kuo, Los Angeles County Department of Public Health, USA; Ana M. S. Guimaraes, University of São Paulo, Brazil
Specialty section: This article was submitted to Epidemiology, a section of the journal Frontiers in Public Health
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Disease modeling is increasingly being used to evaluate the effect of health intervention strategies, particularly for infectious diseases. However, the utility and application of such models are hampered by the inconsistent use of infectious disease modeling terms between and within disciplines. We sought to standardize the lexicon of infectious disease modeling terms and develop a glossary of terms commonly used in describing models’ assumptions, parameters, variables, and outcomes. We combined a comprehensive literature review of relevant terms with an online forum discussion in a virtual community of practice, mod4PH (Modeling for Public Health). Using a convergent discussion process and consensus amongst the members of mod4PH, a glossary of terms was developed as an online resource. We anticipate that the glossary will improve inter- and intradisciplinary communication and will result in a greater uptake and understanding of disease modeling outcomes in heath policy decision-making. We highlight the role of the mod4PH community of practice and the methodologies used in this endeavor to link theory, policy, and practice in the public health domain.
Mathematical and computational models are useful tools to provide important information on key aspects of infectious disease epidemiology. Models can assist in quantifying the transmission potential of a pathogen within a population, as well as assessing the effects of various control and prevention strategies. In times of uncertainty, public health responses may be based on expected outcomes obtained from models (
Ambiguities caused by inconsistent use of terms in models can have enormous impact on model design, usefulness for public health, and understanding and comparability of model outcomes. Standardization of the terms used in modeling could improve this process and its applications. In recent years, considerable efforts have been made to develop unity of thought about modeling approaches in health sciences, including the particular case of infectious diseases (
To address this gap, we developed a multidisciplinary dialog between the members of a recently established virtual “Community of Practice,” called mod4PH (Modeling for Public Health) (
A comprehensive literature review of infectious disease terms used in modeling studies was combined with an online discussion in “mod4PH,” a predominately social media platform complemented by a face-to-face annual meeting. Considering the importance of a standard lexicon of terms in understanding modeling outcomes and their comparability, we discussed several key terms that are commonly used in disease models.
Sponsored by the National Collaborating Center for Infectious Diseases (NCCID), Canada, mod4PH represents a virtual community of practice that promotes the best procedures for research activities and collaborations and integrates resources and expertise for knowledge translation to improve the uptake of infectious disease modeling (
The mod4PH forum was initially established with a number of participants from the face-to-face 2014 Pan-InfORM workshop (
The literature review was conducted for specific terms that are used in peer-reviewed published articles in a wide array of journals published in English. The search engines “PubMed,” “Google Scholar,” “Web of Science,” and “Scopus” were used to find terms used in both mathematical epidemiology and public health with an ambiguous and discrepant definition. We also consulted a previous review of terms in modeling influenza infection, which relied on a variety of sources including systematic reviews, peer-reviewed published articles, books, advisory health reports, and websites of public health agencies and organizations (e.g., World Health Organization, U.S. Centers for Disease Prevention and Control, Public Health Agency of Canada, and European Center for Disease Control) (
We considered essential terms that are used often in epidemiological models of infectious diseases with two main criteria: (i) a term was defined differently between articles or (ii) two different terms were used interchangeably, with the threshold that one of the criteria is met in at least two peer-reviewed articles. Terms and definitions identified in the review of relevant studies were classified as “discussion topics” based on their definitions and usage. Each week, a discussion topic and the associated references were posted on the mod4PH forum (
For the purpose of this study, a convergent discussion process was followed (
Models of infectious disease dynamics are developed to reflect: (i) the biology of the infectious agent and (ii) the physiological processes and attributes of the disease at both the individual and population levels. These are defined by: (a) the time course of the stages of disease progression through the infection process, from exposure to recovery or death (which constitutes the area of clinical medicine) and (b) a time course of states of transmission potential from exposure to post infectiousness (which constitutes the area of public health and epidemiology) (
In most disease dynamic models, a compartmental structure is developed that divides the population into several classes of individuals according to their epidemiological statuses. These include: susceptible (S), exposed (E), infectious (I), and recovered (R), and their relationship describes a basic disease transmission dynamic model, referred to as the classical SEIR model (Figure
Susceptible refers to a non-infected individual (or population) who may become infected through contact with individuals or environmental organisms that can transmit the disease. Individuals may show varying degrees of susceptibility based on a number of host factors (e.g., immunity; see “
In disease dynamic models, infected individuals are often considered to be infectious, that is, they are capable of transmitting the disease. When this classification is made, it is important for the model to clearly state that these individuals are both “infected and infectious” since the assumption of infectivity is inconsistent with the epidemiological observation that an infected individual is not necessarily infectious.
For a disease in which the causative pathogen can be eliminated from the infected person or become dormant, the infectious stage is followed by a non-infectious stage. Models of disease transmission dynamics refer to this non-infectious stage as “recovered,” since the individuals in this stage can no longer transmit the disease. However, we note that, in the epidemiological and clinical contexts, a non-infectious individual is not necessarily pathogen-free.
In most disease transmission dynamic models, the term “exposed” is used to refer to individuals who are infected but are not yet capable of transmitting the disease (
The term “latent” describes an infected individual who cannot transmit the pathogen, regardless of the time for exposure to the pathogen. For a number of infectious diseases (e.g., influenza), the individual becomes latent immediately following the exposure to pathogen when transmission occurs (
The latent period refers to the period of time between exposure to a disease with successful transmission and the onset of infectiousness. During the latent period, infected individuals do not transmit the disease. This period has commonly been referred to as the “exposed period” in infectious disease modeling; however, the exposed period may suggest a period of time during which the event of exposure to disease continually occurs, rather than a period of time following exposure. It is therefore suggested that the “latent period” should be used as the standard lexicon in models of disease transmission.
The incubation period is defined as the period of time between exposure to the disease (if transmission occurs) and the onset of clinical symptoms. For diseases in which the onset of infectiousness coincides with the appearance of symptoms, the latent and incubation periods are the same. However, in a number of diseases (e.g., influenza, measles, and varicella), the infected individual may become infectious before the onset of symptoms. For such diseases, the models may account for the incubation period by including the latent and presymptomatic periods (see “
The infectious period is defined as the time interval in which the infected individual is capable of transmitting the disease. Since this period may overlap with the incubation period, it may be difficult to obtain accurate estimates of the infectious period.
Disease incidence is defined by both epidemiologists and modelers as the number of new cases in a population generated within a certain time period. In SEIR models, it is often calculated as the product of the number of susceptible individuals, the number of infected individuals (who are considered infectious and can transmit the disease), and the transmission rate per contact per unit of time. In continuous time models, the incidence of a disease is measured at a single time point and typically represents the rate at which the infected population changes. However, in discrete time models (
Disease prevalence is defined as the number of cases of a disease at a single time point in a population. In compartmental models, the prevalence is represented by the number of infectious individuals at any time.
The basic reproduction number is defined as the average number of secondary cases caused by a single infectious individual in a totally susceptible population (
While there is a broad agreement on the definition of the reproduction number, recent studies show that the methodology and type of model used to calculate
Defining the quantity
The term “presymptomatic” describes a stage of disease in which an infected individual is infectious and can transmit the disease without presenting with symptoms. Individuals in the presymptomatic stage will proceed to become symptomatic at some point of time in the future. In contrast, asymptomatic refers to a disease stage in which individuals are infectious but are not exhibiting disease symptoms.
For example, influenza has various stages, including an asymptomatic stage in which individuals are capable of transmitting the disease but may have no knowledge of being infectious as they are not symptomatic. If these individuals develop a symptomatic infection, then the time period before the onset of symptoms is referred to as presymptomatic. A schematic representation of disease stages is illustrated in Figure
In modeling, the generation interval refers to the period of time between the onset of the infectious period in a primary case to the onset of the infectious period in a secondary case infected by the primary case (
The use of these terms in modeling is disease-specific and depends on the transmission characteristics of the pathogen. For example, in influenza, the onset of infectiousness and symptoms may differ in an infected person, and therefore, the duration of the serial interval and the generation interval may not be the same. Using these measures, as has been done in published studies (
Immunity refers to protection against a disease. It can be acquired naturally in an individual by experiencing the disease and recovering from infection or by other means such as active vaccination or passive transfer of maternal antibody across the placenta (
The attack rate describes the proportion of the population that becomes infected over a specified period of time. For diseases for which not all infected individuals develop symptoms (e.g., influenza), it may be more informative to calculate the “clinical attack rate” (which measures the proportion of the population that develops disease symptoms as a result of an infection).
In epidemiological and clinical studies, vaccine efficacy refers to the percentage reduction in the attack rate of the vaccinated cohort compared to the unvaccinated cohort as observed in a randomized controlled (field) trial. Vaccine effectiveness refers to the ability of a vaccine to prevent infection or related outcomes in the population in real-world conditions.
The inclusion of vaccine-induced immunity in disease dynamic models is generally governed by the reduction of disease transmission to vaccinated individuals. This reduction is often based on a parameter that quantifies vaccine efficacy or effectiveness. While these two terms have different meanings and are measured using distinct methods (
While neither vaccine efficacy nor effectiveness is measured with respect to time, the effect of a vaccine in individuals may change over time. This is reflected in the waning of vaccine-induced immunity at the individual level and, as a result, the decline of herd immunity in the population. While there are various ways of including waning immunity in a model, it is important to note that a decline of immunity at the individual level over time is not equivalent to a decrease in vaccine efficacy or effectiveness.
Infectious disease modeling is an important epidemiological tool to inform strategies for disease control and prevention. Tracing its historical roots from the pioneering work of Daniel Bernoulli on smallpox in the 1760s (
While a number of studies exist that aim to clarify and define modeling terms and methodologies in the context of infectious diseases (
The diversity of the individuals in a community of practice does not come without its limitations. Various disciplines and backgrounds often use terms differently, and the lack of a common jargon-free language makes the process and intragroup discussions especially challenging. Furthermore, technical barriers to online forums (e.g., restrictions on the number of characters per post) may limit the extent of discussion that can take place in the platform. To improve communication between the mod4PH members, we implemented a convergent discussion process, enabling the discussion topics to remain active following their initiation in the online forum. This form of interdisciplinary engagement will ensure that, as our knowledge and understanding of infectious disease mechanisms enhances, discussion topics are improved and definitions of pertinent terms and their use in modeling efforts are adapted and informed.
The resulting glossary of terms from the current initiative of mod4PH is published as an online resource by the NCCID (
While this study serves to bridge the gaps in modeling efforts and forge strong links between theory, policy, and practice, there remain many terms for ongoing discussion toward standardizing terminology, which are integral to the application of modeling outcomes to policy decision-making. We hope to use this study as a starting point to foster bidirectional communication between the involved disciplines, and improve the utility of modeling as an invaluable tool in the fight against persistent and emerging infectious diseases.
The authors write for mod4PH (Modeling for Public Health).
RM and SM conceived the study and wrote the first draft of the manuscript. AS, JA, JH, AH, DS, EG, MH-B, HI-K, and JL contributed to the discussion, materials, and reviewing the paper. All authors contributed to the revisions and final version and accepted.
The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.
The authors would like to thank the reviewers for their insightful comments that have improved the paper.
This work was funded by Mitacs, and by the National Collaborating Centre for Infectious Diseases (NCCID) through a contribution from the Public Health Agency of Canada (PHAC). The views expressed herein do not necessarily represent the views of the PHAC.