2020
DOI: 10.1186/s13662-020-02995-1
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Time-continuous and time-discrete SIR models revisited: theory and applications

Abstract: Since Kermack and McKendrick have introduced their famous epidemiological SIR model in 1927, mathematical epidemiology has grown as an interdisciplinary research discipline including knowledge from biology, computer science, or mathematics. Due to current threatening epidemics such as COVID-19, this interest is continuously rising. As our main goal, we establish an implicit time-discrete SIR (susceptible people–infectious people–recovered people) model. For this purpose, we first introduce its continuous varia… Show more

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Cited by 28 publications
(40 citation statements)
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“…Various studies [3,8,9,[17][18][19][20][21] have mainly investigated continuous or explicit time-discrete schemes. In contrast, Wacker and Schlüter [22] have analysed the properties of the implicit timediscrete SIR model, including nonnegativity and boundedness of solution, global existence and uniqueness in time, monotonicity properties and error analysis. We employed the implicit timediscrete SIR model [22] for short-time prediction and to keep modelling as interpretable as possible.…”
Section: Methodsmentioning
confidence: 99%
See 1 more Smart Citation
“…Various studies [3,8,9,[17][18][19][20][21] have mainly investigated continuous or explicit time-discrete schemes. In contrast, Wacker and Schlüter [22] have analysed the properties of the implicit timediscrete SIR model, including nonnegativity and boundedness of solution, global existence and uniqueness in time, monotonicity properties and error analysis. We employed the implicit timediscrete SIR model [22] for short-time prediction and to keep modelling as interpretable as possible.…”
Section: Methodsmentioning
confidence: 99%
“…The data includes the cumulative number of infected cases ( Î), the cumulative number of recovered cases ( R) and the cumulative number of death cases ( D) in Fiji. Following [22], we define R i = R i + D i and I i = I i − R i . We considered the COVID-19 data of Fiji for the second wave of the pandemic from 4 May 2021 (t = 1) to 9 December 2021 (t = 220) of which the data corresponding to time {t i } 160 i=1 is used for estimating the parameters of the discrete-time SIR model and the data for time {t i } 220…”
Section: Selection and Pre-treatment Of Covid-19 Datamentioning
confidence: 99%
“…where α(t) and β(t) are defined as transmission (α(t)) and removing (i.e., death or recovery, β(t)) rates [33]. This system should be accompanied by suitable initial conditions S(0) > 0, I(0) > 0 and R(0) ≥ 0 [32].…”
Section: The Gaussian Growth Rate Modelmentioning
confidence: 99%
“…This model is used for predicting the number of reported and unreported cases for the COVID-19 epidemics in several countries. There is a number of recent publications on COVID-19 aiming to provide insight and understanding the trends of the disease ( Ajbar, Alqahtani, & Boumaza, 2021 ; Griette, Magal, & Seydi, 2020 ; Griette & Magal, 2021 ; Kucharski, Russell, & Diamond, 2020 ; Li et al., 2020 ; Lin et al., 2020 ; Lobo et al., 2020 ; Nishiura, Linton, & Akhmetzhanov, 2020 ; Pereira, Schimit, & Bezerra, 2021 ; Roosa et al., 2020 ; Shereen, Khan, Kazmi, Bashir, & Siddique, 2020 ; Wacker & Schlüter, 2020 ).…”
Section: Introductionmentioning
confidence: 99%