SEIR Model for COVID-19 Epidemic Using Delay Differential Equation

Devipriya, R.; Dhamodharavadhani, S.; Selvi, S.

doi:10.1088/1742-6596/1767/1/012005

Cited by 17 publications

(6 citation statements)

References 2 publications

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“…Combination of these advantages makes the model more reliable with real properties of the pandemic and eliminates most of the abstract parameters usually used in SEIR-like models. It is worth to note there are other studies addressing these issues using Erlang distribution (Arino and Portet, 2020) and delayed equations (Devipriya et al, 2021; Yang et al, 2021). However, to our best knowledge, there are no publications demonstrating DDE-based approach with weighted components of delayed arguments and instant transitions.…”

Section: Discussionmentioning

confidence: 99%

A Delay Differential Equation approach to model the COVID-19 pandemic

Kiselev

Akberdin

Kolpakov

2021

Preprint

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SEIR (Susceptible - Exposed - Infected - Recovered) approach is a classic modeling method that has frequently been applied to the study of infectious disease epidemiology. However, in the vast majority of SEIR models and models derived from them transitions from one population group to another are described using the mass-action law which assumes population homogeneity. That causes some methodological limitations or even drawbacks, particularly inability to reproduce observable dynamics of key characteristics of infection such as, for example, the incubation period and progression of the disease's symptoms which require considering different time scales as well as probabilities of different disease trajectories. In this paper, we propose an alternative approach to simulate the epidemic dynamics that is based on a system of differential equations with time delays to precisely reproduce a duration of infectious processes (e.g. incubation period of the virus) and competing processes like transition from infected state to the hospitalization or recovery. The suggested modeling approach is fundamental and can be applied to the study of many infectious disease epidemiology. However, due to the urgency of the COVID-19 pandemic we have developed and calibrated the delay-based model of the epidemic in Germany and France using the BioUML platform. Additionally, the stringency index was used as a generalized characteristic of the non-pharmaceutical government interventions implemented in corresponding countries to contain the virus spread. The numerical analysis of the calibrated model demonstrates that adequate simulation of each new wave of the SARS-CoV-2 virus spread requires dynamic changes in the parameter values during the epidemic like reduction of the population adherence to non-pharmaceutical interventions or enhancement of the infectivity parameter caused by an emergence of novel virus strains with higher contagiousness than original one. Both models may be accessed and simulated at https://gitlab.sirius-web.org/covid-19/dde-epidemiology-model utilizing visual representation as well as Jupyter Notebook.

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Section: Discussionmentioning

confidence: 99%

A Delay Differential Equation approach to model the COVID-19 pandemic

Kiselev

Akberdin

Kolpakov

2021

Preprint

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“…By introducing lag factors into the system of differential equations, some models have considered including delay factors. Further details can be found in references such as [26][27][28][29][30][31].…”

Section: Introductionmentioning

confidence: 99%

A Novel Hybrid Crossover Dynamics of Monkeypox Disease Mathematical Model with Time Delay: Numerical Treatments

Sweilam,

Al-Mekhlafi,

Hassan

et al. 2024

Fractal Fract

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In this paper, we improved a mathematical model of monkeypox disease with a time delay to a crossover model by incorporating variable-order and fractional differential equations, along with stochastic fractional derivatives, in three different time intervals. The stability and positivity of the solutions for the proposed model are discussed. Two numerical methods are constructed to study the behavior of the proposed models. These methods are the nonstandard modified Euler Maruyama technique and the nonstandard Caputo proportional constant Adams-Bashfourth fifth step method. Many numerical experiments were conducted to verify the efficiency of the methods and support the theoretical results. This study’s originality is the use of fresh data simulation techniques and different solution methodologies.

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“…The ordinary differential equation (ODE) models only simulate the rate of change of the compartment sizes. Historically, the delay differential equation (DDE) compartment models [56, 57] are an alternative to the exposed (E) compartment of the SEIR ODE model [58–60]. Both the delay term and the E compartment incorporate an incubation period into the SIR prototype.…”

Section: Introductionmentioning

confidence: 99%

Basic reproduction number projection for novel pandemics and variants. Ancestral SARS-CoV2 R0 projection

Benjamin¹

2022

Preprint

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The recently derived Hybrid-Incidence Susceptible-Transmissible-Removed (HI-STR) prototype is a deterministic epidemic compartment model and an alternative to the Susceptible-Infected-Removed (SIR) model prototype. The HI-STR predicts that pathogen transmission depends on host population characteristics including population size, population density and some common host behavioural characteristics. The HI-STR prototype is applied to the ancestral Severe Acute Respiratory Syndrome Coronavirus 2 (SARS-CoV2) to show that the original estimates of the Coronavirus Disease 2019 (COVID-19) basic reproduction number ($\mathcal{R}_0$) for the United Kingdom (UK) could have been projected on the individual states of the United States of America (USA) prior to being detected in the USA. The Imperial College London (ICL) R0 estimate for the UK is projected onto each USA state. The difference between these projections and ICL estimates for USA states is either not statistically significant on the paired student t-test or epidemiologically insignificant. Projection provides a baseline for evaluating the real-time impact of an intervention. Sensitivity analysis was conducted because of considerable variance in parameter estimates across studies. Although the HI-STR predicts that increasing symptomatic ratio and inherently immune ratio reduce R0, relative to the uncertainty in the estimates of R0 for the ancestral SARS-CoV2, the projection is insensitive to the inherently immune ratio and the symptomatic ratio.

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SEIR Model for COVID-19 Epidemic Using Delay Differential Equation

Cited by 17 publications

References 2 publications

A Delay Differential Equation approach to model the COVID-19 pandemic

A Delay Differential Equation approach to model the COVID-19 pandemic

A Novel Hybrid Crossover Dynamics of Monkeypox Disease Mathematical Model with Time Delay: Numerical Treatments

Basic reproduction number projection for novel pandemics and variants. Ancestral SARS-CoV2 R0 projection

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