On the Continuous-time and Discrete-Time Versions of an Alternative Epidemic Model of the SIR Class

Costa, Jorge Alberto Vieira; Martinez, Amanda Costa; Geromel, J.C.

doi:10.1007/s40313-021-00757-2

Cited by 2 publications

(3 citation statements)

References 11 publications

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“…Based on these, various time-discrete analogues of the differential models have been introduced (see [18][19][20][21][22][23][24]). The time-discrete models with step size h = 1 day provide two interpretations [25]. First, each quantity in the model z k = z(t k ) is expressed in days −1 or alternatively, z k = z(t k )h is dimensionless, where t k is a fixed day of the time frame under consideration.…”

Section: Introductionmentioning

confidence: 99%

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Differential and Time-Discrete SEIRS Models with Vaccination: Local Stability, Validation and Sensitivity Analysis Using Bulgarian COVID-19 Data

et al. 2023

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Bulgaria has the lowest COVID-19 vaccination rate in the European Union and the second-highest COVID-19 mortality rate in the world. That is why we think it is important better to understand the reason for this situation and to analyse the development of the disease over time. In this paper, an extended time-dependent SEIRS model SEIRS-VB is used to investigate the long-term behaviour of the COVID-19 epidemic. This model includes vaccination and vital dynamics. To apply the SEIRS-VB model some numerical simulation tools have been developed and for this reason a family of time-discrete variants are introduced. Suitable inverse problems for the identification of parameters in discrete models are solved. A methodology is proposed for selecting a discrete model from the constructed family, which has the closest parameter values to these in the differential SEIRS-VB model. To validate the studied models, Bulgarian COVID-19 data are used. To obtain all these results for the discrete models a mathematical analysis is carried out to illustrate some biological properties of the differential model SEIRS-VB, such as the non-negativity, boundedness, existence, and uniqueness. Using the next-generation method, the basic reproduction number associated with the model in the autonomous case is defined. The local stability of the disease-free equilibrium point is studied. Finally, a sensitivity analysis of the basic reproduction number is performed.

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Section: Introductionmentioning

confidence: 99%

“…Currently, integer-order explicit or implicit timediscrete models have been used to the model COVID-19 epidemics. For example, timecontinuous and time-discrete versions of the classical SIR model are discussed in [25]. Stability analysis, parameter identification and validation with Brazilian and UK COVID-19 data have been conducted.…”

Section: Introductionmentioning

confidence: 99%

Differential and Time-Discrete SEIRS Models with Vaccination: Local Stability, Validation and Sensitivity Analysis Using Bulgarian COVID-19 Data

et al. 2023

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“…( 2022 ) analyze the epidemic situation through a computational tool that fits logistic curves of growth to the observed data. The paper by Costa et al ( 2022 ) presents a probabilistic dynamic model of the SIR class that describes the temporal behavior of epidemics in discrete time.…”

Section: Introductionmentioning

confidence: 99%

A Multi-Agent-Based Simulation Model for the Spreading of Diseases Through Social Interactions During Pandemics

Salem

Moreno

2022

J Control Autom Electr Syst

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Epidemiological models have a vital and consolidated role in aiding decision-making during crises such as the Coronavirus Disease 2019 (COVID-19) pandemic. However, the influence of social interactions in the spreading of communicable diseases is left aside from the main models in the literature. The main contribution of this work is the introduction of a probabilistic simulation model based on a multi-agent approach that is capable of predicting the spreading of diseases. Our proposal has a simple model for the main source of infections in pandemics of respiratory viruses: social interactions. This simplicity is key for incorporating complex networks topology into the model, which is a more accurate representation for real-world interactions. This flexibility in network structure allows the evaluation of specific phenomena, such as the presence of super-spreaders. We provide the modeling for the dynamical network topology in two different simulation scenarios. Another contribution is the generic microscopic model for infection evolution that enables the evaluation of impact from more specific behaviors and interventions on the overall spreading of the disease. It also enables a more intuitive process for going from data to model parameters. This ease of changing the infection evolution model is key for performing more complete analyses than would be possible in other models from the literature. Further, we give specific parameters for a controlled scenario with quick testing and tracing. We present computational results that illustrate the model utilization for predicting the spreading of COVID-19 in a city. Also, we show the results of applying the model for assessing the risk of resuming on-site activities at a collective use facility.

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On the Continuous-time and Discrete-Time Versions of an Alternative Epidemic Model of the SIR Class

Cited by 2 publications

References 11 publications

Differential and Time-Discrete SEIRS Models with Vaccination: Local Stability, Validation and Sensitivity Analysis Using Bulgarian COVID-19 Data

Differential and Time-Discrete SEIRS Models with Vaccination: Local Stability, Validation and Sensitivity Analysis Using Bulgarian COVID-19 Data

A Multi-Agent-Based Simulation Model for the Spreading of Diseases Through Social Interactions During Pandemics

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