Mathematical epidemiology: Past, present, and future

Brauer, Fred

doi:10.1016/j.idm.2017.02.001

Cited by 313 publications

(315 citation statements)

References 93 publications

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“…In the long run, such diseases can disappear and recur in the future or become less deadly due to people getting immune. Some notable epidemics in history include the "Spanish" flu (1918)(1919) as well as the Black Deaths (1346-1350) which invaded Europe from Asia and recurred for three decades afterwards before getting eliminated ( Brauer, 2017 ).…”

Section: Introductionmentioning

confidence: 99%

A model for epidemic dynamics in a community with visitor subpopulation

Dansu

Seno

2019

Journal of Theoretical Biology

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a b s t r a c tWith a five dimensional system of ordinary differential equations based on the SIR and SIS models, we consider the dynamics of epidemics in a community which consists of residents and short-stay visitors. Taking different viewpoints to consider public health policies to control the disease, we derive different basic reproduction numbers and clarify their common/different mathematical natures so as to understand their meanings in the dynamics of the epidemic. From our analyses, the short-stay visitor subpopulation could become significant in determining the fate of diseases in the community. Furthermore, our arguments demonstrate that it is necessary to choose one variant of basic reproduction number in order to formulate appropriate public health policies.

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Section: Introductionmentioning

confidence: 99%

A model for epidemic dynamics in a community with visitor subpopulation

Dansu

Seno

2019

Journal of Theoretical Biology

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“…Although possibly unrealistic, some epidemic models that assume random mixing have performed remarkably well at reproducing disease dynamics particularly in large population contexts . Despite the limitations, these models continue to provide useful insight into the transmission dynamics and control of infectious diseases …”

Section: Introductionmentioning

confidence: 99%

“…[5][6][7] Despite the limitations, these models continue to provide useful insight into the transmission dynamics and control of infectious diseases. 8 Departures from standard mass action can be derived by modifying the mathematical form of the infection rate (see, for example, other studies [9][10][11] ). That is, the incidence rate is modified by introducing growth scaling exponents, which aim to capture scenarios where the number of contacts that an individual has is in fact less than that obtained by the standard mass action form.…”

Section: Introductionmentioning

confidence: 99%

Assessing inference of the basic reproduction number in an SIR model incorporating a growth‐scaling parameter

Ganyani

Faes

Chowell

et al. 2018

Statistics in Medicine

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The standard mass action, which assumes that infectious disease transmission occurs in well-mixed populations, is popular for formulating compartmental epidemic models. Compartmental epidemic models often follow standard mass action for simplicity and to gain insight into transmission dynamics as it often performs well at reproducing disease dynamics in large populations. In this work, we formulate discrete time stochastic susceptible-infected-removed models with linear (standard) and nonlinear mass action structures to mimic varying mixing levels. Using simulations and real epidemic data, we demonstrate the sensitivity of the basic reproduction number to these mathematical structures of the force of infection. Our results suggest the need to consider nonlinear mass action in order to generate more accurate estimates of the basic reproduction number although its uncertainty increases due to the addition of one growth scaling parameter.

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“…5 With this paper, we hope to contribute to the ongoing research on this topic and to 6 give a practical instrument for a deeper comprehension of the virus spreading features 7 and behaviour. 8 The modelling of infectious diseases is currently performed by Ordinary Differential 9 Equations (ODEs) deterministic compartmental models [1] or by stochastic 10 procedures [2]. The tuning of the parameters of the equations allows better modelling of 11 environmental features, such as social restrictions or changes of political strategies in beginning, severe lockdown measures were imposed in very restricted areas and only 48 after March 10th uniform restrictions were imposed all over the country.…”

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confidence: 99%

“…Identification of the parameters (α, β, f ) in(1), using a restricted data 141 set: in our examples we considered the data of the first 18 days. Identification of the parameters (α, f ) in SEIRD(rm)(4) model, using all 143 the measures available (times t 0 , t 1 , .…”

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confidence: 99%

Monitoring Italian COVID-19 spread by an adaptive SEIRD model

Piccolomini

Zama

2020

Preprint

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Due to the recent diffusion of COVID-19 outbreak, the scientific community is making efforts in analysing models for understanding the present situation and predicting future scenarios. In this paper, we propose a Susceptible-Infected-Exposed-Recovered-Dead (SEIRD) differential model [Weitz J. S. and Dushoff J., Scientific reports, 2015] for the analysis and forecast of the COVID-19 spread in Italian regions, using the data from the Italian Protezione Civile from February 24th 2020. In this study, we investigate an adaptation of SEIRD that takes into account the actual policies of the Italian government, consisting of modelling the infection rate as a time-dependent function (SEIRD(rm)). Preliminary results on Lombardia and Emilia-Romagna regions confirm that SEIRD(rm) fits the data more accurately than the original SEIRD model with constant rate infection parameter. Moreover, the increased flexibility in the choice of the infection rate function makes it possible to better control the predictions due to the lockdown policy. 12 the outbreak containment. 13 We consider here deterministic compartmental models, based on a system of initial 14 value problems of Ordinary Differential Equations. This theory has been studied since 15 the beginning of the century by W.O. Kermack and A. G. MacKendrick [3] who 16proposed the basic Susceptible-Infected-Removed (SIR) model. The SIR model and its 17 later modifications, such as Susceptible-Exposed-Infected-Removed (SEIR) [4] were later 18 introduced in the study of outbreaks diffusion. These models split the population into 19 : medRxiv preprint groups, compartments, and reproduce their behaviour by formalising their reciprocal 20 interactions. For example, the SIR model groups are Susceptible who can catch the 21 disease, Infected who have the disease and can spread it, and Removed those who have 22 either had the disease or are recovered, immune or isolated until recovery. The SEIR 23 model proposed by Chowell et al. [5] also considers the Exposed group: containing 24 individuals who are in the incubation period. 25The evolution of the Infected group depends on a critical parameter, usually denoted 26 as R0, representing the basic reproductive rate and it measures of how transferable a 27 disease is. This quantity determines whether the infection will spread exponentially, die 28 out, or remain constant. When R 0 > 1 the epidemic is spreading.

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Mathematical epidemiology: Past, present, and future

Abstract: We give a brief outline of some of the important aspects of the development of mathematical epidemiology.

Cited by 313 publications

References 93 publications

A model for epidemic dynamics in a community with visitor subpopulation

A model for epidemic dynamics in a community with visitor subpopulation

Assessing inference of the basic reproduction number in an SIR model incorporating a growth‐scaling parameter

Monitoring Italian COVID-19 spread by an adaptive SEIRD model

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