Mathematical and Computational Methods against the COVID-19 Pandemics

A special issue of Mathematics (ISSN 2227-7390). This special issue belongs to the section "Engineering Mathematics".

Deadline for manuscript submissions: closed (31 January 2021) | Viewed by 17880

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Instituto Universitario de Matemática Pura y Aplicada (IUMPA-UPV), Universitat Politècnica de València, E-46022 Valencia, Spain
Interests: applied mathematics; graph theory; data science; interdisciplinary applications of mathematics to computer science; engineering and biology
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Special Issue Information

Dear Colleagues,

At the beginning of 2020, the world was shocked by the scale of the SARS-CoV-2 (severe acute respiratory syndrome coronavirus 2) crisis, causing social and economic collapse throughout the world, as no vaccine or treatment was available at the time. Moreover, in most countries, the existing number of ICU units could not cope with the vast number of people infected by the virus that leads to CoVID-19 (coronavirus disease).

The vast number of asymptomatic cases makes it harder to control the spread of the epidemics. In many cases, the limited amount of data, make it even harder to set precise models to predict the evolution of the disease. The well-known SIR type models have been useful in modeling the evolution of the pandemics. Although they were already very well-known for nearly one hundred years, a new interest in them has attracted researchers to continue working on them. 

Efforts in monitoring infected people from the presumed moment in which they were infected have shown to be effective in controlling the virus expansion. In this line, mathematics can contribute to the data management and development of app tools for monitoring human mobility.

Mathematics can also contribute to the modeling of side problems to the pandemics. We point out some of them, such as data quality analysis, network medicine, healthcare services management, the physical spreading of the virus in the environment, the subsequent impact on the economy, and the social response to confinement government measures.

In any case, all the contributions and developments will be beneficial in many ways aside from coping with pandemics. Some potential topics that this Special Issue will cover, but is not limited to, are as follows:

  • Epidemiological dynamics
  • Diffusion modeling 
  • Compartmental and SIR type models 
  • Human dynamics
  • Agent modeling of structured populations
  • Network medicine
  • Data quality
  • Artificial intelligence and deep learning models 
  • Data analysis of social media

Prof. Dr. J. Conejero
Guest Editor

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Keywords

  • SIR model
  • Epidemiological modelling
  • Network medicine
  • Human dynamics
  • Data quality
  • COVID-19
  • SARS-CoV-2

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Published Papers (2 papers)

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16 pages, 1448 KiB  
Article
An Extended SEIR Model with Vaccination for Forecasting the COVID-19 Pandemic in Saudi Arabia Using an Ensemble Kalman Filter
by Rabih Ghostine, Mohamad Gharamti, Sally Hassrouny and Ibrahim Hoteit
Mathematics 2021, 9(6), 636; https://doi.org/10.3390/math9060636 - 17 Mar 2021
Cited by 115 | Viewed by 12287
Abstract
In this paper, an extended SEIR model with a vaccination compartment is proposed to simulate the novel coronavirus disease (COVID-19) spread in Saudi Arabia. The model considers seven stages of infection: susceptible (S), exposed (E), infectious (I), quarantined (Q), recovered (R), deaths (D), [...] Read more.
In this paper, an extended SEIR model with a vaccination compartment is proposed to simulate the novel coronavirus disease (COVID-19) spread in Saudi Arabia. The model considers seven stages of infection: susceptible (S), exposed (E), infectious (I), quarantined (Q), recovered (R), deaths (D), and vaccinated (V). Initially, a mathematical analysis is carried out to illustrate the non-negativity, boundedness, epidemic equilibrium, existence, and uniqueness of the endemic equilibrium, and the basic reproduction number of the proposed model. Such numerical models can be, however, subject to various sources of uncertainties, due to an imperfect description of the biological processes governing the disease spread, which may strongly limit their forecasting skills. A data assimilation method, mainly, the ensemble Kalman filter (EnKF), is then used to constrain the model outputs and its parameters with available data. We conduct joint state-parameters estimation experiments assimilating daily data into the proposed model using the EnKF in order to enhance the model’s forecasting skills. Starting from the estimated set of model parameters, we then conduct short-term predictions in order to assess the predicability range of the model. We apply the proposed assimilation system on real data sets from Saudi Arabia. The numerical results demonstrate the capability of the proposed model in achieving accurate prediction of the epidemic development up to two-week time scales. Finally, we investigate the effect of vaccination on the spread of the pandemic. Full article
(This article belongs to the Special Issue Mathematical and Computational Methods against the COVID-19 Pandemics)
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18 pages, 10905 KiB  
Article
Numerical Modeling of the Spread of Cough Saliva Droplets in a Calm Confined Space
by Sergio A. Chillón, Ainara Ugarte-Anero, Iñigo Aramendia, Unai Fernandez-Gamiz and Ekaitz Zulueta
Mathematics 2021, 9(5), 574; https://doi.org/10.3390/math9050574 - 8 Mar 2021
Cited by 25 | Viewed by 3505
Abstract
The coronavirus disease 2019 (COVID-19) outbreak has altered the lives of everyone on a global scale due to its high transmission rate. In the current work, the droplet dispersion and evaporation originated by a cough at different velocities is studied. A multiphase computational [...] Read more.
The coronavirus disease 2019 (COVID-19) outbreak has altered the lives of everyone on a global scale due to its high transmission rate. In the current work, the droplet dispersion and evaporation originated by a cough at different velocities is studied. A multiphase computational fluid dynamic model based on fully coupled Eulerian–Lagrangian techniques was used. The evaporation, breakup, mass transfer, phase change, and turbulent dispersion forces of droplets were taken into account. A computational domain imitating an elevator that with two individuals inside was modeled. The results showed that all droplets smaller than 150 μm evaporate before 10 s at different heights. Smaller droplets of <30 µm evaporate quickly, and their trajectories are governed by Brownian movements. Instead, the trajectories of medium-sized droplets (30–80 µm) are under the influence of inertial forces, while bigger droplets move according to inertial and gravitational forces. Smaller droplets are located in the top positions, while larger (i.e., heaviest) droplets are located at the bottom. Full article
(This article belongs to the Special Issue Mathematical and Computational Methods against the COVID-19 Pandemics)
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