Mathematical Modelling with Multidisciplinary Applications (M3A)
http://hdl.handle.net/20.500.11824/13
2022-09-27T17:09:38ZExistence, Uniqueness, and Numerical Modeling of Wine Fermentation Based on Integro-Differential Equations
http://hdl.handle.net/20.500.11824/1502
Existence, Uniqueness, and Numerical Modeling of Wine Fermentation Based on Integro-Differential Equations
Schenk, C.; Schulz, V.
Predictive modeling is key for saving time and resources in manufacturing processes such as fermentation arising in food and chemical manufacturing. To make reliable predictions, realistic models representing the most important process features are required. Several models describing the white wine fermentation process already exist. However, all of these models lack a combination of features, such as the importance of oxygen at the beginning of the process, the consumption of sugar due to yeast activity, and the toxicity of alcohol on the yeast cells combined with the single-cell yeast dynamics. This work introduces a new population balance model representing all these features in one model. It is based on a system of highly nonlinear weakly hyperbolic partial/ordinary integro-differential equations which poses a number of theoretical and numerical challenges. This paper increases the understanding of the latter and of the process itself by combining theoretical with numerical investigations. Existence and uniqueness of solutions to a simplified problem are studied based on semigroup theory. For the numerical solution of the problem, a numerical methodology based on a finite volume scheme combined with a time implicit scheme is derived. The impact of the initial cell distribution on the dynamics is studied. The detailed model is compared to a simpler model based on ordinary differential equations. The observed differences for different initial cell distributions and distinct models turn out to be smaller than expected. The outcomes of this paper are specifically relevant for applied mathematicians, winemakers, and process engineers.
2022-01-01T00:00:00ZFock-space approach to stochastic susceptible-infected-recovered models
http://hdl.handle.net/20.500.11824/1500
Fock-space approach to stochastic susceptible-infected-recovered models
Barros de Souza, D.; Araújo, H.; Duarte-Fillho, G.; Gaffney, E.; Nóbrega Santos, F.; Raposo, E.
We investigate the stochastic susceptible-infected-recovered (SIR) model of infectious disease dynamics in the Fock-space approach. In contrast to conventional SIR models based on ordinary differential equations for the subpopulation sizes of S, I, and R individuals, the stochastic SIR model is driven by a master equation governing the transition probabilities among the system’s states defined by SIR occupation numbers. In the Fock-space approach the master equation is recast in the form of a real-valued Schrödinger-type equation with a second quantization Hamiltonian-like operator describing the infection and recovery processes. We find exact analytic expressions for the Hamiltonian eigenvalues for any population size N. We present small- and large-N results for the average numbers of SIR individuals and basic reproduction number. For small N we also obtain the probability distributions of SIR states, epidemic sizes and durations, which cannot be found from deterministic SIR models. Our Fock-space approach to stochastic SIR models introduces a powerful set of tools to calculate central quantities of epidemic processes, especially for relatively small populations where statistical fluctuations not captured by conventional deterministic SIR models play a crucial role.We investigate the stochastic susceptible-infected-recovered (SIR) model of infectious disease dynamics in the Fock-space approach. In contrast to conventional SIR models based on ordinary differential equations for the subpopulation sizes of S, I, and R individuals, the stochastic SIR model is driven by a master equation governing the transition probabilities among the system’s states defined by SIR occupation numbers. In the Fock-space approach the master equation is recast in the form of a real-valued Schrödinger-type equation with a second quantization Hamiltonian-like operator describing the infection and recovery processes. We find exact analytic expressions for the Hamiltonian eigenvalues for any population size N. We present small- and large-N results for the average numbers of SIR individuals and basic reproduction number. For small N we also obtain the probability distributions of SIR states, epidemic sizes and durations, which cannot be found from deterministic SIR models. Our Fock-space approach to stochastic SIR models introduces a powerful set of tools to calculate central quantities of epidemic processes, especially for relatively small populations where statistical fluctuations not captured by conventional deterministic SIR models play a crucial role.
2022-07-25T00:00:00ZModeling the initial phase of COVID-19 epidemic: The role of age and disease severity in the Basque Country, Spain
http://hdl.handle.net/20.500.11824/1496
Modeling the initial phase of COVID-19 epidemic: The role of age and disease severity in the Basque Country, Spain
Srivastav, A. K.; Stollenwerk, N.; Bidaurrazaga Van-Dierdonck, J.; Mar, J.; Ibarrondo, O.; Aguiar, M.
Declared a pandemic by the World Health Organization (WHO), COVID-19 has spread rapidly around the globe. With eventually substantial global underestimation of infection, by the end of March 2022, more than 470 million cases were confirmed, counting more than 6.1 million deaths worldwide. COVID-19 symptoms range from mild (or no) symptoms to severe illness, with disease severity and death occurring according to a hierarchy of risks, with age and pre-existing health conditions enhancing risks of disease severity. In order to understand the dynamics of disease severity during the initial phase of the pandemic, we propose a modeling framework stratifying the studied population into two groups, older and younger, assuming different risks for severe disease manifestation. The deterministic and the stochastic models are parametrized using epidemiological data for the Basque Country population referring to confirmed cases, hospitalizations and deaths, from February to the end of March 2020. Using similar parameter values, both models were able to describe well the existing data. A detailed sensitivity analysis was performed to identify the key parameters influencing the transmission dynamics of COVID-19 in the population. We observed that the population younger than 60 years old of age would contribute more to the overall force of infection than the older population, as opposed to the already existing age-structured models, opening new ways to understand the effect of population age on disease
severity during the COVID-19 pandemic. With mild/asymptomatic cases significantly influencing the disease spreading and control, our findings support the vaccination strategy prioritising the most vulnerable individuals to reduce hospitalization and deaths, as well as the non-pharmaceutical intervention measures to reduce disease transmission.
2022-07-13T00:00:00ZA phenomenological model for interfacial water near hydrophilic polymers
http://hdl.handle.net/20.500.11824/1493
A phenomenological model for interfacial water near hydrophilic polymers
Earls, A.; Calderer, M.-C.; Desroches, M.; Zarnescu, A.; Rodrigues, S.
We propose a minimalist phenomenological model for the ‘interfacial water’ phenomenon that
occurs near hydrophilic polymeric surfaces. We achieve this by combining a Ginzburg–Landau
approach with Maxwell’s equations which leads us to a well-posed model providing a
macroscopic interpretation of experimental observations. From the derived governing equations,
we estimate the unknown parameters using experimental measurements from the literature. The
resulting profiles of the polarization and electric potential show exponential decay near the
surface, in qualitative agreement with experiments. Furthermore, the model’s quantitative
prediction of the electric potential at the hydrophilic surface is in excellent agreement with
experiments. The proposed model is a first step towards a more complete parsimonious
macroscopic model that will, for example, help to elucidate the effects of interfacial water on
cells (e.g. neuronal excitability), the effects of infrared neural stimulation or the effects of drugs
mediated by interfacial water.
2022-06-30T00:00:00Z