Contributions to the mathematical theory of epidemics—I

Kermack, W. O.; McKendrick, A. G.

doi:10.1016/s0092-8240(05)80040-0

Cited by 1,031 publications

(1,343 citation statements)

References 2 publications

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“…Recognizing adaptive behavior means explicitly incorporating behavioral responses to disease risk and other incentives into epidemiological models (2,3). The workhorse of modern epidemiology, the compartmental epidemiological model (4,5), does not explicitly include behavioral responses to disease risk. The transmission factors in these models combine and confound human behavior and biological processes.…”

mentioning

confidence: 99%

Adaptive human behavior in epidemiological models

Fenichel

Castillo‐Chavez

Ceddia

et al. 2011

Proc. Natl. Acad. Sci. U.S.A.

400

397

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The science and management of infectious disease are entering a new stage. Increasingly public policy to manage epidemics focuses on motivating people, through social distancing policies, to alter their behavior to reduce contacts and reduce public disease risk. Person-to-person contacts drive human disease dynamics. People value such contacts and are willing to accept some disease risk to gain contact-related benefits. The cost-benefit trade-offs that shape contact behavior, and hence the course of epidemics, are often only implicitly incorporated in epidemiological models. This approach creates difficulty in parsing out the effects of adaptive behavior. We use an epidemiological-economic model of disease dynamics to explicitly model the trade-offs that drive person-toperson contact decisions. Results indicate that including adaptive human behavior significantly changes the predicted course of epidemics and that this inclusion has implications for parameter estimation and interpretation and for the development of social distancing policies. Acknowledging adaptive behavior requires a shift in thinking about epidemiological processes and parameters.susceptible-infected-recovered model | R 0 | reproductive number | bioeconomics T he science and management of infectious disease is entering a new stage. The increasing focus on incentive structures to motivate people to engage in social distancing-reducing interpersonal contacts and hence public disease risk (1)-changes what health authorities need from epidemiological models. Social distancing is not new-for centuries humans quarantined infected individuals and shunned the obviously ill, but new approaches are being used to deal with modern social interactions. Scientific development of social distancing public policies requires that epidemiological models explicitly address behavioral responses to disease risk and other incentives affecting contact behavior. This paper models the role of adaptive behavior in an epidemiological system. Recognizing adaptive behavior means explicitly incorporating behavioral responses to disease risk and other incentives into epidemiological models (2, 3). The workhorse of modern epidemiology, the compartmental epidemiological model (4, 5), does not explicitly include behavioral responses to disease risk. The transmission factors in these models combine and confound human behavior and biological processes. We develop a simple compartmental model that explicitly incorporates adaptive behavior and show that this modification alters understanding of standard epidemiological metrics. For example, the basic reproductive number, R 0 , is a function of biological processes and human behavior, but R 0 lacks a behavioral interpretation in the existing literature. Biological and behavioral feedbacks muddle R 0 's biological interpretation and confound its estimation.Prior approaches that incorporate behavior into epidemiological models generally fall into three categories: specification of nonlinear contact rate functions, expanded epidemiologi...

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mentioning

confidence: 99%

Adaptive human behavior in epidemiological models

Fenichel

Castillo‐Chavez

Ceddia

et al. 2011

Proc. Natl. Acad. Sci. U.S.A.

400

397

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“…In 1927 doctors Kermack and McKendrick developed a mathematical model to the study the Spanish Influenza pandemic of 1921. 6 This model, with some modifications, was used for forecasts and analysis of the 2009 influenza outbreak in Mexico City. 7 This same model, supplemented with classical diffusion (which in the context of an epidemic is managed as a dispersion of the infection) has been quite useful in studies of the spread of some infections as, for example, rabies.…”

Section: Methodsmentioning

confidence: 99%

Dispersion of a new coronavirus SARS-CoV-2 by airlines in 2020: Temporal estimates of the outbreak in Mexico

Cruz-Pacheco

Bustamante-Castañeda

Caputo

et al. 2020

Preprint

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On January 23, 2020, China imposed a quarantine on the city of Wuhan to contain the SARS-CoV-2 outbreak. Regardless of this measure the new infection has spread to several countries around the world. Here, we developed a method to study the dissemination of this infection by the airline routes and we give estimations of the time of arrival of the outbreaks to the different cities. In this work we show an analysis of the dispersion of this infection to other cities by airlines based on the classic model the Kermack and McKendrick complemented with diffusion on a graph composed of nodes which represent the cities and edges which represent the airline routes. We do several numerical simulations to estimate the date of arrival to different cities starting the infection at Wuhan, China and to show the robustness of the estimation respect to changes in the epidemiological parameters and to changes on the graph. we use Mexico City as an example. In this case, our estimate of the arrival time is between March 20 and March 30, 2020. This analysis is limited to the analysis of dispersion by airlines, so this estimate should be taken as an overestimate since the infection can arrive by other means. This model estimates the arrival of the infectious outbreak to Mexico between March 20 and March 30.This estimation gives a time period to implement and strengthen preventive measures aimed at the general population, as well as to strengthen hospital infrastructure and training of human resources in health.

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“…We adopted a susceptible-exposed-infectiousrecovered (SEIR) model to describe the dynamic system of the infectious disease [15].…”

Section: Mathematical Modelmentioning

confidence: 99%

Estimating the incidence reporting rates of new influenza pandemics at an early stage using travel data from the source country

2013

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SUMMARYDuring the surveillance of influenza pandemics, underreported data are a public health challenge that complicates the understanding of pandemic threats and can undermine mitigation efforts. We propose a method to estimate incidence reporting rates at early stages of new influenza pandemics using 2009 pandemic H1N1 as an example. Routine surveillance data and statistics of travellers arriving from Mexico were used. Our method incorporates changes in reporting rates such as linearly increasing trends due to the enhanced surveillance. From our results, the reporting rate was estimated at 0·46% during early stages of the pandemic in Mexico. We estimated cumulative incidence in the Mexican population to be 0·7% compared to 0·003% reported by officials in Mexico at the end of April. This method could be useful in estimation of actual cases during new influenza pandemics for policy makers to better determine appropriate control measures.

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Contributions to the mathematical theory of epidemics—I

Cited by 1,031 publications

References 2 publications

Adaptive human behavior in epidemiological models

Adaptive human behavior in epidemiological models

Dispersion of a new coronavirus SARS-CoV-2 by airlines in 2020: Temporal estimates of the outbreak in Mexico

Estimating the incidence reporting rates of new influenza pandemics at an early stage using travel data from the source country

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