An epidemic model for non-first-order transmission kinetics

Mun, Eun Young; Geng, Feng

doi:10.1371/journal.pone.0247512

Cited by 5 publications

(7 citation statements)

References 29 publications

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“…3 Sparse Jacobian representation was used (a Catalyst option only). 4 Automatic differentiation (as a mean of Jacobian calculation) was turned off (a Catalyst option only). 5 An incomplete LU precondition was supplied to the GMRES linear solver (a Catalyst option only).…”

Section: Benchmarksmentioning

confidence: 99%

Catalyst: Fast and flexible modeling of reaction networks

Loman

Ma²,

Ilin

et al. 2022

Preprint

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We introduce Catalyst.jl, a flexible and feature-filled Julia library for modeling and high performance simulation of chemical reaction networks (CRNs). Catalyst acts as both a domain specific language and an intermediate representation for symbolically encoding CRN models as Julia-native objects. This enables a pipeline of symbolically specifying, analyzing, and modifying reaction networks; converting Catalyst models to symbolic representations of concrete mathematical models; and generating compiled code for use in numerical solvers. Currently Catalyst supports conversion to symbolic discrete stochastic chemical kinetics (jump process), chemical Langevin (stochastic differential equation), and mass-action reaction rate equation (ordinary differential equation) models. Leveraging ModelingToolkit.jl and Symbolics.jl, Catalyst models can be analyzed, simplified, and compiled into optimized representations for use in a broad variety of numerical solvers. The performance of the numerical solvers Catalyst targets is illustrated across a variety of reaction networks by benchmarking stochastic simulation algorithm and ODE solver performance. We demonstrate the extendability and composability of Catalyst by highlighting both how it can compose with a variety of Julia libraries, and how existing open source projects have extended the intermediate representation. These benchmarks demonstrate significant performance improvements compared to several popular reaction network simulators.

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Section: Benchmarksmentioning

confidence: 99%

Catalyst: Fast and flexible modeling of reaction networks

Loman

Ma²,

Ilin

et al. 2022

Preprint

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“…Since the outbreak of COVID-19, researchers worldwide have been carrying out a lot of research works on it. These researches can be mainly divided into the following six categories: (1) to study the impact of COVID-19 on human physical and mental health from a biomedical perspective ( Tsamakis et al, 2020 , Xiong et al, 2020 , Pascoal et al, 2021 ); (2) to study the impact of COVID-19 on human production, life, and social and economic development from a sociological perspective ( Takyi and Bentum-Ennin, 2020 , Qian et al, 2021 , Shang et al, 2021 , Beiderbeck et al, 2021 , Jiang et al, 2021 ); (3) to creatively propose new mathematical models or revise some existing models based on relevant data for predicting and analyzing the development of the epidemic in a specific area ( Vianello et al, 2021 , Willis et al, 2021 , Mun and Geng, 2021 , Al-qaness et al, 2021 , Manenti et al, 2020 , Hu et al, 2020 , Cao et al, 2020 , Mojjada et al, 2020 , Yang et al, 2020 ); (4) to analyze the spatial-temporal characteristics of the epidemic in a specific area ( Lv and Cheng, 2020 , Feng et al, 2020 ); (5) to explore related factors which may affect the development of the epidemic ( Hu et al, 2021 ); (6) to evaluate the effects of different epidemic prevention measures ( Leung et al, 2020 , Hasnain et al, 2020 ). In terms of the research purpose and content, the third, the fourth, and the fifth categories are more relevant to the work carried out in this paper.…”

Section: Related Workmentioning

confidence: 99%

“…Their main contribution is developing a strategy for calibrating and validating a model rather than presenting a fully optimized model or attempting to predict the future course of the COVID-19 pandemic. Considering that the assumption of the classic rate law central to the SIR compartmental models is not always true, Mun and Geng (2021) designed a modified mathematical model for non-first-order kinetics. Especially, they discuss two coefficients associated with the modified epidemic model: transmission rate constant k and transmission reaction order n .…”

Section: Related Workmentioning

confidence: 99%

Analysis on the spatio-temporal characteristics of COVID-19 in mainland China

Jin

Yang

et al. 2021

Process Safety and Environmental Protection

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COVID-19 has brought many unfavorable effects on humankind and taken away many lives. Only by understanding it more profoundly and comprehensively can it be soundly defeated. This paper is dedicated to studying the spatial-temporal characteristics of the epidemic development at the provincial-level in mainland China and the civic-level in Hubei Province. Moreover, a correlation analysis on the possible factors that cause the spatial differences in the epidemic's degree is conducted. After completing these works, three different methods are adopted to fit the daily-change tendencies of the number of confirmed cases in mainland China and Hubei Province. The three methods are the Logical Growth Model (LGM), Polynomial fitting, and Fully Connected Neural Network (FCNN). The analysis results on the spatial-temporal differences and their influencing factors show that: (1) The Chinese government has contained the domestic epidemic in early March 2020, indicating that the number of newly diagnosed cases has almost zero increase since then. (2) Throughout the entire mainland of China, effective manual intervention measures such as community isolation and urban isolation have significantly weakened the influence of the subconscious factors that may impact the spatial differences of the epidemic. (3) The classification results based on the number of confirmed cases also prove the effectiveness of the isolation measures adopted by the governments at all levels in China from another aspect. It is reflected in the small monthly grade changes (even no change) in the provinces of mainland China and the cities in Hubei Province during the study period. Based on the experimental results of curve-fitting and considering the time cost and goodness of fit comprehensively, the Polynomial( Degree = 18) model is recommended in this paper for fitting the daily-change tendency of the number of confirmed cases.

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“…In the early days after the outbreak of COVID-19 epidemic, many scholars focused on biology and virology [4][5][6], or epidemic monitoring and risk management [7][8][9], which contributed greatly to the COVID-19 prevention. Most of the modeling prediction focused on Wuhan, China [10,11], but there's also some research about Europe and Americas [12][13][14].…”

Section: Introductionmentioning

confidence: 99%

Flow and access: Driving forces of COVID-19 spreading in the first stage around Hubei, China

Zhang

Cao²

2023

PLoS ONE

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Background This research takes the six provinces around Hubei Province where the Corona virus disease 2019 (COVID-19) outbreak as the research area, collected the number of cumulative confirmed cases (NCCC) in the first four weeks after the lockdown to explore the spatiotemporal characteristics, and to identify its influencing factors by correlation and regression analysis, finally providing reference for epidemic prevention and control policy. Methods The analysis of variance was used to test the spatiotemporal variability of the NCCC in the six provinces, the Pearson coefficient was taken to find the correlation relationship between the NCCC and multiple factor data in socio-economic, geography and transportation, and the following regression equation was obtained based on regression analysis. Results This study found that there is significant spatial variability in the NCCC among the six provinces and the significant influencing factors are changing along the four weeks. The NCCC in Shaanxi and Chongqing in the West was less than that in the other four provinces, especially in Shaanxi in the northwest, which was significantly different from the four provinces in the East, and has the largest difference with adjacent Henan province (792 cases). Correlation analysis shows that the correlation coefficient of the number of main pass is the largest in the first week, the correlation coefficient of the length of road networks is the largest in the second week, and the NCCC in the third and fourth week is significantly correlated with the average elevation. For all four weeks, the highest correlation coefficient belongs to the average elevation in the third week (r = 0.943, P = 0.005). Regression analysis shows that there is a multiple linear regression relationship between the average elevation, the number of main pass and the NCCC in the first week, there is no multiple linear regression relationship in the second week. The following univariate regression analysis shows that the regression equations of various factors are different. And, there is a multiple linear regression relationship between the average elevation, the length of road networks and the NCCC in the third and fourth week, as well as a multiple linear regression relationship between the average elevation, population and the confirmed cases in the fourth week. Conclusion There are significant spatial differences in the NCCC among the six provinces and the influencing factors varied in different weeks. The average elevation, population, the number of main pass and the length of road networks are significantly correlated with the NCCC. The average elevation, as a geographical variable, affects the two traffic factors: the number of main pass and the length of road networks. Therefore, the NCCC is mainly related to the factor categories of flow and access.

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An epidemic model for non-first-order transmission kinetics

Cited by 5 publications

References 29 publications

Catalyst: Fast and flexible modeling of reaction networks

Catalyst: Fast and flexible modeling of reaction networks

Analysis on the spatio-temporal characteristics of COVID-19 in mainland China

Flow and access: Driving forces of COVID-19 spreading in the first stage around Hubei, China

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