Simulating the spread of COVID-19 via a spatially-resolved susceptible–exposed–infected–recovered–deceased (SEIRD) model with heterogeneous diffusion

Viguerie, Alex; Lorenzo, Guillermo; Auricchio, Ferdinando; Baroli, Davide; Hughes, Thomas J.R.; Patton, Alessia; Reali, Alessandro; Yankeelov, Thomas E.; Veneziani, Alessandro

doi:10.1016/j.aml.2020.106617

Cited by 211 publications

(314 citation statements)

References 15 publications

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“…infection fatality rate. Alex et al reached a similar conclusion when simulating COVID19 by using the SEIRD model with heterogeneous diffusion [26]. When we compared the data recorded during the beginning of the epidemic in Serbia with the results obtained during the simulation, such as the initial doubling time, the two data series matched well.…”

Section: Model Sensitivity Analysis and Calibrationsupporting

confidence: 72%

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Simulation and prediction of spread of COVID-19 in The Republic of Serbia by SEIRDS model of disease transmission

Stanojevic¹,

Ponjavić

Stanojević³

et al. 2020

Preprint

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As a response to the pandemic caused by SARSCov-2 virus, on 15 March, 2020, the Republic of Serbia introduced comprehensive anti-epidemic measures to curb COVID 19. After a slowdown in the epidemic, on 6 May, 2020, the regulatory authorities decided to relax the implemented measures. However, the epidemiological situation soon worsened again. As of 15 October, 2020, a total of 35,454 cases of SARSCov-2 infection have been reported in Serbia, including 770 deaths caused by COVID19. In order to better understand the epidemic dynamics and predict possible outcomes, we have developed a mathematical model SEIRDS (S-susceptible, E-exposed, I-infected, R-recovered, D-dead due to COVID19 infection, S-susceptible). When developing the model, we took into account the differences between different population strata, which can impact the disease dynamics and outcome. The model can be used to simulate various scenarios of the implemented intervention measures and calculate possible epidemic outcomes, including the necessary hospital capacities. Considering promising results regarding the development of a vaccine against COVID19, the model is enabled to simulate vaccination among different population strata. The findings from various simulation scenarios have shown that, with implementation of strict measures of contact reduction, it is possible to control COVID19 and reduce number of deaths. The findings also show that limiting effective contacts within the most susceptible population strata merits a special attention. However, the findings also show that the disease has a potential to remain in the population for a long time, likely with a seasonal pattern. If a vaccine, with efficacy equal or higher than 65%, becomes available it could help to significantly slow down or completely stop circulation of the virus in human population. The effects of vaccination depend primarily on: 1. Efficacy of available vaccine(s), 2. Prioritization of the population categories for vaccination, and 3. Overall vaccination coverage of the population, assuming that the vaccine(s) develop solid immunity in vaccinated individuals. With expected basic reproduction number of Ro=2.46 and vaccine efficacy of 68%, an 87%- coverage would be sufficient to stop the virus circulation.

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Section: Model Sensitivity Analysis and Calibrationsupporting

confidence: 72%

“…This is especially due to the facts that a significant percentage of the infected individuals do not exhibit any symptoms. The other issue is small percentage of tested population [26].…”

Section: Model Sensitivity Analysis and Calibrationmentioning

confidence: 99%

Simulation and prediction of spread of COVID-19 in The Republic of Serbia by SEIRDS model of disease transmission

Stanojevic¹,

Ponjavić

Stanojević³

et al. 2020

Preprint

View full text Add to dashboard Cite

show abstract

“…namics. For the special case in which both subgroups display identical contact rates β, latent rates α, and infectious rates γ [79], our study shows that the overall outbreak dynamics can be represented by the classical SEIR model [28] 11 . CC-BY 4.0 International license It is made available under a perpetuity.…”

Section: For Comparable Dynamics the Size Of The Asymptomatic Populamentioning

confidence: 80%

Visualizing the invisible: The effect of asymptomatic transmission on the outbreak dynamics of COVID-19

Peirlinck¹,

Linka²,

Costabal

et al. 2020

Preprint

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Understanding the outbreak dynamics of the COVID-19 pandemic has important implications for successful containment and mitigation strategies. Recent studies suggest that the population prevalence of SARS-CoV-2 antibodies, a proxy for the number of asymptomatic cases, could be an order of magnitude larger than expected from the number of reported symptomatic cases. Knowing the precise prevalence and contagiousness of asymptomatic transmission is critical to estimate the overall dimension and pandemic potential of COVID-19. However, at this stage, the effect of the asymptomatic population, its size, and its outbreak dynamics remain largely unknown. Here we use reported symptomatic case data in conjunction with antibody seroprevalence studies, a mathematical epidemiology model, and a Bayesian framework to infer the epidemiological characteristics of COVID-19. Our model computes, in real time, the time-varying contact rate of the outbreak, and projects the temporal evolution and credible intervals of the effective reproduction number and the symptomatic, asymptomatic, and recovered populations. Our study quantifies the sensitivity of the outbreak dynamics of COVID-19 to three parameters: the effective reproduction number, the ratio between the symptomatic and asymptomatic populations, and the infectious periods of both groups For nine distinct locations, our model estimates the fraction of the population that has been infected and recovered by Jun 15, 2020 to 24.15% (95% CI: 20.48%-28.14%) for Heinsberg (NRW, Germany), 2.40% (95% CI: 2.09%-2.76%) for Ada County (ID, USA), 46.19% (95% CI: 45.81%-46.60%) for New York City (NY, USA), 11.26% (95% CI: 7.21%-16.03%) for Santa Clara County (CA, USA), 3.09% (95% CI: 2.27%-4.03%) for Denmark, 12.35% (95% CI: 10.03%-15.18%) for Geneva Canton (Switzerland), 5.24% (95% CI: 4.84%-5.70%) for the Netherlands, 1.53% (95% CI: 0.76%-2.62%) for Rio Grande do Sul (Brazil), and 5.32% (95% CI: 4.77%-5.93%) for Belgium. Our method traces the initial outbreak date in Santa Clara County back to January 20, 2020 (95% CI: December 29, 2019 - February 13, 2020). Our results could significantly change our understanding and management of the COVID-19 pandemic: A large asymptomatic population will make isolation, containment, and tracing of individual cases challenging. Instead, managing community transmission through increasing population awareness, promoting physical distancing, and encouraging behavioral changes could become more relevant.

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“…We believe that such a framework may be useful to researchers seeking to better understand general compartmental models, and may ultimately help facilitate interdisciplinary collaboration. Our second goal is to improve our understanding of a specific compartmental PDE model, which describes the spatiotemporal spread of COVID-19, and has demonstrated good agreement with the measured data [22], from the physical, mathematical, and numerical points of view. As the reinterpretation of the COVID-19 model within the continuum mechanics framework plays a significant role in this study, the stated goals are complementary.…”

mentioning

confidence: 99%

“…In Sect. 3 we turn our attention to the COVID-19 model discussed in [22], beginning with its derivation within the newlyintroduced notational system from continuum mechanics. We analyze the model mathematically and establish its formal sensitivity to diffusivity and its stability in the L 1 norm.…”

mentioning

confidence: 99%

Diffusion–reaction compartmental models formulated in a continuum mechanics framework: application to COVID-19, mathematical analysis, and numerical study

et al. 2020

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The outbreak of COVID-19 in 2020 has led to a surge in interest in the research of the mathematical modeling of epidemics. Many of the introduced models are so-called compartmental models, in which the total quantities characterizing a certain system may be decomposed into two (or more) species that are distributed into two (or more) homogeneous units called compartments. We propose herein a formulation of compartmental models based on partial differential equations (PDEs) based on concepts familiar to continuum mechanics, interpreting such models in terms of fundamental equations of balance and compatibility, joined by a constitutive relation. We believe that such an interpretation may be useful to aid understanding and interdisciplinary collaboration. We then proceed to focus on a compartmental PDE model of COVID-19 within the newly-introduced framework, beginning with a detailed derivation and explanation. We then analyze the model mathematically, presenting several results concerning its stability and sensitivity to different parameters. We conclude with a series of numerical simulations to support our findings.

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Simulating the spread of COVID-19 via a spatially-resolved susceptible–exposed–infected–recovered–deceased (SEIRD) model with heterogeneous diffusion

Cited by 211 publications

References 15 publications

Simulation and prediction of spread of COVID-19 in The Republic of Serbia by SEIRDS model of disease transmission

Simulation and prediction of spread of COVID-19 in The Republic of Serbia by SEIRDS model of disease transmission

Visualizing the invisible: The effect of asymptomatic transmission on the outbreak dynamics of COVID-19

Diffusion–reaction compartmental models formulated in a continuum mechanics framework: application to COVID-19, mathematical analysis, and numerical study

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