The challenges of modeling and forecasting the spread of COVID-19

Bertozzi, Andrea L.; Franco, Elisa Marques; Mohler, George; Short, Martin B.; Sledge, Daniel

doi:10.1073/pnas.2006520117

Cited by 531 publications

(505 citation statements)

References 52 publications

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“…SIR epidemiological models and their extensions have been proposed to study the spread of the COVID-19 epidemic at the country or state scale (e.g., [3] in France and [4] in three US states), and at the regional scale ( [5,6] in China, [7] in France and [8] in Italy). In all cases, a different set of parameters has been estimated for each considered region/province.…”

Section: Introductionmentioning

confidence: 99%

A parsimonious model for spatial transmission and heterogeneity in the COVID-19 propagation

Roques

Bonnefon

Baudrot

et al. 2020

Preprint

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Raw data on the cumulative number of deaths at a country level generally indicate a spatially variable distribution of the incidence of COVID-19 disease. An important issue is to determine whether this spatial pattern is a consequence of environmental heterogeneities, such as the climatic conditions, during the course of the outbreak. Another fundamental issue is to understand the spatial spreading of COVID-19. To address these questions, we consider four candidate epidemiological models with varying complexity in terms of initial conditions, contact rates and non-local transmissions, and we fit them to French mortality data with a mixed probabilistic-ODE approach. Using standard statistical criteria, we select the model with non-local transmission corresponding to a diffusion on the graph of counties that depends on the geographic proximity, with time-dependent contact rate and spatially constant parameters. This original spatially parsimonious model suggests that in a geographically middle size centralized country such as France, once the epidemic is established, the effect of global processes such as restriction policies, sanitary measures and social distancing overwhelms the effect of local factors. Additionally, this modeling approach reveals the latent epidemiological dynamics including the local level of immunity, and allows us to evaluate the role of non-local interactions on the future spread of the disease. In view of its theoretical and numerical simplicity and its ability to accurately track the COVID-19 epidemic curves, the framework we develop here, in particular the non-local model and the associated estimation procedure, is of general interest in studying spatial dynamics of epidemics.

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Section: Introductionmentioning

confidence: 99%

A parsimonious model for spatial transmission and heterogeneity in the COVID-19 propagation

Roques

Bonnefon

Baudrot

et al. 2020

Preprint

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“…Classical compartment models such as the susceptible-infected-recovered (SIR) and susceptible-exposedinfected-resistant (SEIR) models has been used (14,15). The SIR modelling, which assumes no births or deaths during the development of an epidemic, is de ned as a nonlinear system of three ordinary differential equations that can be implicitly solved.…”

Section: Sars-cov-2 Is the Etiologic Agent Responsible For Coronavirumentioning

confidence: 99%

Novel spatiotemporal evaluative methodology of COVID-19 pandemic velocity based on differential equations

Rodríguez¹

2020

Preprint

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Abstract Introduction: The trajectory of disease outbreaks has been characterized through second order differential equations.Objective: To develop a universal methodology to predict the velocity of COVID-19 pandemic in the United States, Spain, Belgium, and Austria based on differential equations and ranges of the number infected.Methodology: Seven comparison ranges were established to analyze discrete values of COVID-19 total cases. Then, right-angled triangles where their base represented the number of days elapsed and their height the maximum number infected that was reached for each range were designed to then find the triangles’ areas. Given that there is a change rate between the triangles’ areas with respect to time , their velocity was found through a differential equation. Finally, these results were used to compare the propagation speed of the pandemic in these four countries.Results: The areas obtained for the right-angled triangles for all the countries varied between 2.888 and 1.056.204. The change rate between the triangles areas and the days elapsed for a range change oscillated between 3.079 and 1.264.558, while the variation of the number infected with respect to time presented values between 4.6 and 21549.7.Conclusion: An acausal generalization was developed based on differential equations that allows to simplify and facilitate the spatiotemporal evaluation of COVID-19 pandemic velocity which is useful for public health

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“…The parsimonious, classic Susceptible-Infectious-Removed (SIR) compartmental model (Kermack & McKendrick, 1927;Anderson, 1991) gives insights into the dynamics of epidemics and shows utility for understanding how public health interventions affect the trajectory of an epidemic (Bertozzi et al, 2020).…”

Section: Introductionmentioning

confidence: 99%

The SIR dynamic model of infectious disease transmission and its analogy with chemical kinetics

Simon¹

2020

PeerJ Physical Chemistry

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Mathematical models of the dynamics of infectious disease transmission are used to forecast epidemics and assess mitigation strategies. In this article, we highlight the analogy between the dynamics of disease transmission and chemical reaction kinetics while providing an exposition on the classic Susceptible–Infectious–Removed (SIR) epidemic model. Particularly, the SIR model resembles a dynamic model of a batch reactor carrying out an autocatalytic reaction with catalyst deactivation. This analogy between disease transmission and chemical reaction enables the exchange of ideas between epidemic and chemical kinetic modeling communities.

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The challenges of modeling and forecasting the spread of COVID-19

Cited by 531 publications

References 52 publications

A parsimonious model for spatial transmission and heterogeneity in the COVID-19 propagation

A parsimonious model for spatial transmission and heterogeneity in the COVID-19 propagation

Novel spatiotemporal evaluative methodology of COVID-19 pandemic velocity based on differential equations

The SIR dynamic model of infectious disease transmission and its analogy with chemical kinetics

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