A review of mathematical modeling, artificial intelligence and datasets used in the study, prediction and management of COVID-19

Mohamadou, Youssoufa; Halidou, Aminou; Kapen, Pascalin Tiam

doi:10.1007/s10489-020-01770-9

Cited by 291 publications

(221 citation statements)

References 65 publications

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“…Using the identities 2(1 + e −2Y ) −1 = 1 + tanh Y and 2(1 − e −2Y ) −1 = 1 + coth Y we combine the results (C6) and (C11) to the analytical approximation of the SIR-model equations at all reduced times, stated in Eqs. (10), (11), and (12). A comparison with the exact numerical solution of the SIR model is provide in Fig.…”

Section: Maximum Of Jmentioning

confidence: 99%

“…The SIR system is the simplest and most fundamental of the compartmental models and its variations. [3][4][5][6][7][8][9][10][11][12][13][14][15] The considered population of N 1 persons is assigned to the three compartments s (susceptible), i (infectious), or r (recovered/removed). Persons from the population may progress with time between these compartments with given infection (a(t)) and recovery rates (µ(t)) which in general vary with time due to non-pharmaceutical interventions taken during the pandemic evolution.…”

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confidence: 99%

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Epidemics forecast from SIR-modeling, verification and calculated effects of lockdown and lifting of interventions

Schlickeiser

Kröger

2020

Preprint

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Due to the current COVID-19 epidemic plague hitting the worldwide population it is of utmost medical, economical and societal interest to gain reliable predictions on the temporal evolution of the spreading of the infectious diseases in human populations. Of particular interest are the daily rates and cumulative number of new infections, as they are monitored in infected societies, and the influence of non-pharmaceutical interventions due to different lockdown measures as well as their subsequent lifting on these infections. Estimating quantitatively the influence of a later lifting of the interventions on the resulting increase in the case numbers is important to discriminate this increase from the onset of a second wave. The recently discovered new analytical solutions of Susceptible-Infectious-Recovered (SIR) model allow for such forecast and the testing of lockdown and lifting interventions as they hold for arbitrary time dependence of the infection rate. Here we present simple analytical approximations for the rate and cumulative number of new infections.

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Section: Maximum Of Jmentioning

confidence: 99%

mentioning

confidence: 99%

Epidemics forecast from SIR-modeling, verification and calculated effects of lockdown and lifting of interventions

Schlickeiser

Kröger

2020

Preprint

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“…A practical study has been performed using a COVID-19 database to illustrate the application of cure models. COVID-19 databases are broadly studied in the present time, as reviewed in [37], to develop a variety of mathematical models on the disease features [38]. The data was extracted from the Servicio Galego de Saúde and provided by the Dirección Xeral de Saúde Pública (Galicia, NW Spain).…”

Section: Datasetmentioning

confidence: 99%

Cure models to estimate time until hospitalization due to COVID-19. A case study in Galicia (NW Spain)

Pedrosa-Laza

López-Cheda

Cao

2020

Preprint

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A short introduction to survival analysis and censored data is included in this paper. A thorough literature review in the eld of cure models has been done. An overview on the most important and recent approaches on parametric, semiparametric and nonparametric mixture cure models is also included. The main nonparametric and semiparametric approaches were applied to a real time dataset of COVID-19 patients from the rst weeks of the epidemic in Galicia (NW Spain). The aim is to model the elapsed time from diagnosis to hospital admission. The main conclusions, as well as the limitations of both the cure models and the dataset, are presented, illustrating the usefulness of cure models in this kind of studies, where the influence of age and sex on the time to hospital admission is shown.

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“…The present investigation can be extended to the many variants of the SIR model. [13][14][15][16][17][18][19][20][21]…”

Section: Introductionmentioning

confidence: 99%

Analytical Solution of the SIR-Model for the Temporal Evolution of Epidemics. Part A: Time-Independent Reproduction Factor

Kröger

Schlickeiser

2020

Preprint

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We revisit the Susceptible-Infectious-Recovered/Removed (SIR) model which is one of the simplest compartmental models. Many epidemological models are derivatives of this basic form. While an analytic solution to the SIR model is known in parametric form for the case of a time-independent infection rate, we derive an analytic solution for the more general case of a time-dependent infection rate, that is not limited to a certain range of parameter values. Our approach allows us to derive several exact analytic results characterizing all quantities, and moreover explicit, non-parametric, and accurate analytic approximants for the solution of the SIR model for time-independent infection rates. We relate all parameters of the SIR model to a measurable, usually reported quantity, namely the cumulated number of infected population and its first and second derivatives at an initial time t=0, where data is assumed to be available. We address the question on how well the differential rate of infections is captured by the Gauss model (GM). To this end we calculate the peak height, width, and position of the bell-shaped rate analytically. We find that the SIR is captured by the GM within a range of times, which we discuss in detail. We prove that the SIR model exhibits an asymptotic behavior at large times that is different from the logistic model, while the difference between the two models still decreases with increasing reproduction factor. This part A of our work treats the original SIR model to hold at all times, while this assumption will be released in part B. Releasing this assumption allows to formulate initial conditions incompatible with the original SIR model.

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A review of mathematical modeling, artificial intelligence and datasets used in the study, prediction and management of COVID-19

Cited by 291 publications

References 65 publications

Epidemics forecast from SIR-modeling, verification and calculated effects of lockdown and lifting of interventions

Epidemics forecast from SIR-modeling, verification and calculated effects of lockdown and lifting of interventions

Cure models to estimate time until hospitalization due to COVID-19. A case study in Galicia (NW Spain)

Analytical Solution of the SIR-Model for the Temporal Evolution of Epidemics. Part A: Time-Independent Reproduction Factor

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