Applied & Industrial Mathematics

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Now showing 1 - 9 of 9

Open Access
A Branch-and-Price Algorithm for Bin Packing Problem
(2015-12-16) Ataei, Masoud; Chen, Michael
Bin Packing Problem examines the minimum number of identical bins needed to pack a set of items of various sizes. Employing branch-and-bound and column generation usually requires designation of the problem-specific branching rules compatible with the nature of the pricing sub-problem of column generation, or alternatively it requires determination of the k-best solutions of knapsack problem at level kth of the tree. Instead, we present a new approach to deal with the pricing sub-problem of column generation which handles two-dimensional knapsack problems. Furthermore, a set of new upper bounds for Bin Packing Problem is introduced in this work which employs solutions of the continuous relaxation of the set-covering formulation of Bin Packing Problem. These high quality upper bounds are computed inexpensively and dominate the ones generated by state-of-the-art methods.
Open Access
Exact Solutions to Lattice Models of Polymer Adsorption
(2023-08-04) Pierce, Colin Brandon; Janse van Rensburg, Esaias J.
Entropy calculations are important in determining the physical properties of a polymeric system. A classical method of modeling polymers is with self-avoiding walks, and entropy may be determined by counting the total number of weighted walks. If directed walks are used, recurrences may be formed and solved to study a variety of physical properties exactly. One solution method is to solve the recurrences with generating functions. Additionally, we may attempt to derive the partition function of the model, which explicitly provides the walk entropy per length. In this thesis, the solution to a variety of polymer models of adsorption are derived with generating functions. The partition functions of these models are then extracted when possible through combinatorial convolution identities or by solving their partial difference equations on the lattice.
Open Access
Incorporating the Pre-symptomatic Stage in the Discrete-Time Kermack-McKendrick Model
(2024-03-16) Singh, Surin Rohan; Wu, Jianhong
Numerous mathematical models have been implemented since the COVID-19 pandemic, with most using large compartmental models which indirectly restrict the generation-time distribution. The continuous-time Kermack-McKendrick epidemic model of 1927 (KM27) allows a random generation-time distribution, but there is a disadvantage where the numerical implementation is too much. Here, the pre-symptomatic stage was further included in the recent discrete-time SEIR KM27 Model formulated in Diekmann (2021). With discrete-time models being general, flexible when including public health interventions and easier to implement computationally than continuous-time models, it is a powerful tool for exploring infectious diseases such as COVID-19. To demonstrate this potential, a numerical investigation is performed on how the incidence-peak size depends on the model components. It was found that compartmental models predicted lower peak sizes with the same reproduction number and initial growth rate than models in which the latent, pre-symptomatically infectious and symptomatically infectious periods have fixed duration.
Open Access
Modelling of Polymer Adsorption and Looping
(2024-03-16) Koumarianos, Sperydon; Madras, Neal; Bergevin, Ozzy
Understanding the physical adsorption behavior of polymers on surfaces is crucial for advancing materials science and developing smart coatings to enhance the bio-compatibility of implanted devices. Applications, ranging from heart stents to brain-integrated microchips,have been experimentally explored to study the adsorption properties of charged polymers onto diverse surfaces. While experimental observations have indicated the presence of loops in adsorbed polymer chains, there remains a need for a comprehensive theoretical model to consistently predict these phenomena. The proposed self-avoiding walk model aims to elucidate the conformations of polymer chains on a surface lattice, emphasizing the entropic competition between flat adsorption and dangly loops during the adsorption process. Focusing on loops formed by adsorbed polymers, the study aims to determine entropically preferred looping structures. These looping structures are relevant to the biocompatibility of materials. The modeling approach involves relating entropy to partition values generated by different macro-states, with a focus on enumerating micro-states to identify the most entropically preferred behavior of adsorbed polymers.
Open Access
Modelling the Effects of Stressors and Treatment in a Honeybee Colony
(2024-03-16) Luik, Thomas Stephen; Heffernan, Jane M.
Honeybees are agriculturally important through their pollination work and production of honey. They are also vulnerable to the accumulation of stressors, which cause drastic colony losses. It is important to understand the effect of stress on a hive so that the cost of testing, treatment, and rest can be evaluated. We have developed a model of honeybee stress and simulated scenarios of testing and treatment regiments. The model tracks importation of stressors through foraging, and quantifies their effect on bee stress. The model is used to determine appropriate times for testing and treatment before, during, and after pollination jobs, and it is used to determine resting periods needed between pollination jobs, depending on testing and treatment use, to minimize the probability of bee loss and maximize profit for a beekeeper. Ultimately, the model will be used to inform testing and treatment strategies that will increase economic profitability for the beekeeping industry, and the agricultural sector as a whole.
Open Access
Quantifying the Effect of Disease Characteristics on the Outcomes of Interventions Using Mathematical Modelling
(2023-08-04) Lisitza, Cassandra Raelene; Moghadas, Seyed
Many emerging diseases have several common features in terms of their natural history; however, they differ in their quantifiable characteristics, such as transmissibility and infectiousness. These characteristics are crucial in determining whether there will be a local outbreak of the disease or if it has the potential to evolve into a global pandemic. Understanding these characteristics is essential in devising public health policies to prevent the repercussions of novel diseases, such as those seen during the COVID-19 pandemic. This thesis presents a general modeling framework for the transmission dynamics of influenza and SARS-CoV2, examining the impact of their characteristics on intervention outcomes. Simulations and sensitivity analysis show that the length and infectiousness profile during various stages of illness significantly affect intervention outcomes. The results suggest that the longer and more infectious pre-symptomatic stage of SARS-CoV-2 compared to influenza may explain the difference in school closure outcomes between the two diseases.
Open Access
The Dynamics of Multi-Drug Resistant Organisms: Modeling Nosocomial Infection Control Measures
(2024-11-07) Donato, Lorianne Elsa; Wu, Jianhong
It has long been a challenge to try and understand how nosocomial infections develops in order to find the most efficient methods to combat it. Though drugs do exist to treat them, they are known to be highly resistant and have proven to be a reoccurring problem in hospitals, posing an increasing medical burden. Infection control measures have been implemented in order to reduce their impact and spread with various degrees of completeness and efficiency. A multi-drug resistant ODE model, featuring three types of infection status and two groupings of patient history classes, is created to model the transmission dynamics of Vancomycin-Resistant Enterococcus and Methicillin-Resistant Staphylococcus Aureus. Analysis of the model is supported with numerical simulations. It is shown that infection control procedures, including the identication of high-risk patient groupings, have a strong effect on the transmission dynamics.
Open Access
The Effects of Pre-Movement on Large Building Evacuations
(2015-12-16) Farnell, Lisa Carroll Ruth; Madras, Neal; Chen, Shengyuan Michael
Evacuation times for buildings with a range of heights and occupant loads were generated by a computer simulation algorithm, assuming simultaneous start. Additional evacuation times were generated for the same buildings with pre-movement times assigned to building occupants. Pre-movement times were assigned based on uniform and gamma distributions. Building evacuation times with pre-movement were compared to those without, to determine the quantitative effects of pre-movement. Using regression analysis, equations were generated to predict the effects of pre-movement for given building heights and occupant loads. Regression equations were shown to reasonably predict the effects of pre-movement for the building cases used for the regression analysis. Additional simulations were performed with and without pre-movement for buildings with alternative heights and occupant loads. The regression function was applied to these additional simulations, and found to predict the effects of pre-movement in these building cases with some accuracy.
Open Access
The Impact of Population Heterogeneities and Disease Interventions on Herd Immunity: A Case Study of the COVID-19 Pandemic in Ontario
(2023-03-28) Liwag, Maria Geneva Roselle Marino; Moghadas, Seyed
In epidemiology, herd immunity refers to the population level of immunity required to prevent or extinguish a large disease outbreak. In models with homogeneously mixing assumptions and without demographic structures, the herd immunity level may be different from that in heterogeneous models. With the COVID-19 pandemic in Ontario as a case study, a comprehensive deterministic mathematical model of disease spread with age and contact pattern variations was developed to examine the required herd immunity for different variants and compare with theoretical values obtained using homogeneous assumptions. The effects of non-pharmaceutical (testing/isolation of silent infections) interventions and vaccination on epidemic progression and herd immunity were investigated. With the inclusion of age and contact pattern structures, the resulting herd immunity level required to end an epidemic under the assumptions of long-term protection (without re-infection) is lower than theoretical values, even for more transmissible variants. While waning immunity and re-infection results in an oscillation in herd immunity levels in the population, subsequent epidemic peaks are less amplified, suggesting that even with increased variant transmissibility, infections of any variant allow for population immunity to rise, leading to an endemic state.

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Browsing Applied & Industrial Mathematics by Subject "Applied mathematics"

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