A comprehensive comparison of ODE solvers for biochemical problems

Postawa, Karol; Szczygieł, Jerzy; Kułażyński, Marek

doi:10.1016/j.renene.2020.04.089

Cited by 21 publications

(18 citation statements)

References 19 publications

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“…This integrator has been used to solve many differential equations in the biology field. However, there are many other efficient integrators with different characteristics [148]. Here we present the results of the numerical simulations for different scenarios varying the inoculation rate, efficacy of the vaccine, percentage of infections that are asymptomatic, and the transmission rates.…”

Section: Resultsmentioning

confidence: 99%

Analysis of Key Factors of a SARS-CoV-2 Vaccination Program: A Mathematical Modeling Approach

2021

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The administration of vaccines against the coronavirus disease 2019 (COVID-19) started in early December of 2020. Currently, there are only a few approved vaccines, each with different efficacies and mechanisms of action. Moreover, vaccination programs in different regions may vary due to differences in implementation, for instance, simply the availability of the vaccine. In this article, we study the impact of the pace of vaccination and the intrinsic efficacy of the vaccine on prevalence, hospitalizations, and deaths related to the SARS-CoV-2 virus. Then we study different potential scenarios regarding the burden of the COVID-19 pandemic in the near future. We construct a compartmental mathematical model and use computational methodologies to study these different scenarios. Thus, we are able to identify some key factors to reach the aims of the vaccination programs. We use some metrics related to the outcomes of the COVID-19 pandemic in order to assess the impact of the efficacy of the vaccine and the pace of the vaccine inoculation. We found that both factors have a high impact on the outcomes. However, the rate of vaccine administration has a higher impact in reducing the burden of the COVID-19 pandemic. This result shows that health institutions need to focus on increasing the vaccine inoculation pace and create awareness in the population about the importance of COVID-19 vaccines.

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Section: Resultsmentioning

confidence: 99%

Analysis of Key Factors of a SARS-CoV-2 Vaccination Program: A Mathematical Modeling Approach

2021

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“…The design and analyses of this study were based on an AD model developed earlier [ 28 , 34 ], that was partially based in its assumptions on the universal ADM1 tool [ 35 ]. The implementation of the ADM1 for the design and control of innovative reactor types lies within its field of application, although it is still not widespread.…”

Section: Methodsmentioning

confidence: 99%

“…The design and analyses of this study were based on an AD model developed earlier [28,34], that was partially based in its assumptions on the universal ADM1 tool [35].…”

Section: Model Characteristics and Implementation Of Process Modificamentioning

confidence: 99%

Innovations in anaerobic digestion: a model-based study

Postawa

Szczygieł

Kułażyński

2021

Biotechnol Biofuels

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Background Increasing the efficiency of the biogas production process is possible by modifying the technological installations of the biogas plant. In this study, specific solutions based on a mathematical model that lead to favorable results were proposed. Three configurations were considered: classical anaerobic digestion (AD) and its two modifications, two-phase AD (TPAD) and autogenerative high-pressure digestion (AHPD). The model has been validated based on measurements from a biogas plant located in Poland. Afterward, the TPAD and AHPD concepts were numerically tested for the same volume and feeding conditions. Results The TPAD system increased the overall biogas production from 9.06 to 9.59%, depending on the feedstock composition, while the content of methane was slightly lower in the whole production chain. On the other hand, the AHPD provided the best purity of the produced fuel, in which a methane content value of 82.13% was reached. At the same time, the overpressure leads to a decrease of around 7.5% in the volumetric production efficiency. The study indicated that the dilution of maize silage with pig manure, instead of water, can have significant benefits in the selected configurations. The content of pig slurry strengthens the impact of the selected process modifications—in the first case, by increasing the production efficiency, and in the second, by improving the methane content in the biogas. Conclusions The proposed mathematical model of the AD process proved to be a valuable tool for the description and design of biogas plant. The analysis shows that the overall impact of the presented process modifications is mutually opposite. The feedstock composition has a moderate and unsteady impact on the production profile, in the tested modifications. The dilution with pig manure, instead of water, leads to a slightly better efficiency in the classical configuration. For the TPAD process, the trend is very similar, but the AHPD biogas plant indicates a reverse tendency. Overall, the recommendation from this article is to use the AHPD concept if the composition of the biogas is the most important. In the case in which the performance is the most important factor, it is favorable to use the TPAD configuration.

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“…To keep all calculations reproducible and equivalent, in all cases the same ODEs solver is utilized-namely ode15s [26]. This algorithm is dedicated to stiff systems, which fits perfectly in the requirements for biological simulation [27]. What's more, it provides relatively high accuracy, with very good performance.…”

Section: Methodsmentioning

confidence: 99%

Methods for anaerobic digestion model fitting—comparison between heuristic and automatic approach

Postawa

Szczygieł

Kułażyński

2020

Biomass Conv. Bioref.

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The article demonstrates if automatic optimization can be better than manual adjustment. The subject of optimization was the temperature-phased anaerobic digestion (TPAD) model. A selection of 3 parameters per each reactor in the process chain was appointed-reaction rate for propionate conversion, acetate conversion, and hydrolysis. Overall, both methods provided very convergent results. However, the total summary error (TSE) for the automatic algorithm was always moderately lower than for manual-the difference varied between 16.16 and 57.05 percentage points. Although the manual method has significant advantages-adjustment was more homogenous and gave more uniform fitting. Finally, cross-validation was performed to unify the values between the experimental series. The result was a total number of 4 values for each optimized constant-for two temperature points in each of two methods. Due to inconclusive information about the accuracy, averaged values were calculated to use in further researches. The recommendation from this article is to connect the best aspect of both methods to achieve the most accurate results. Keywords Biogas • TPAD • Model • Algorithm • Optimization Abbreviations δx The total error for iteration X θ Mean value of constant, from both series and methods f x The fractioning factor for a fraction x fun(k m;pro , k m;ac , k dis) The objective function in the optimization k dis Hydrolysis rate k m;x Uptake rate for substance X k x T Value of constant k x for the temperature T Q gas , Q gas exp Biogas flow for model or experiment Q in Input biomass flow to the reactor S x , S x exp The concentration of substance X, from model or experiment t sr The additional retention time for solids in addition to the hydraulic retention time V Rx The total volume of the reactor X X c Total feeding value of biomass

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A comprehensive comparison of ODE solvers for biochemical problems

Cited by 21 publications

References 19 publications

Analysis of Key Factors of a SARS-CoV-2 Vaccination Program: A Mathematical Modeling Approach

Analysis of Key Factors of a SARS-CoV-2 Vaccination Program: A Mathematical Modeling Approach

Innovations in anaerobic digestion: a model-based study

Methods for anaerobic digestion model fitting—comparison between heuristic and automatic approach

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