Digital Commons Network^™

Exact Solution Structure And Dynamic Preservation In A Nonstandard Finite-Difference Formulation Of The Sir Model, Ramsha Shafqat, Wutiphol Sintunavarat

Mathematical Modelling and Numerical Simulation with Applications

A new nonstandard finite difference method is developed for discretizing the classical Susceptible--Infected--Removed (SIR) epidemic model. In the proposed approach, the first derivatives in the continuous SIR system are replaced by two carefully constructed nonstandard denominator functions, yielding a dynamically consistent discrete model with improved numerical stability while preserving consistency with the original continuous system. It is proved that the proposed scheme preserves the fundamental dynamical properties and qualitative behavior of the continuous SIR model, including positivity and the long-term dynamics of the population classes. Moreover, the resulting discrete system admits explicit analytical solutions, providing further insight into the model …

Modelling Acute Haemorrhagic Conjunctivitis In East Africa: An Integrated Approach To Transmission Dynamics And Outbreak Response Strategies, Geofrey Wingi Sikazwe

Tanzania Journal of Science

Acute hemorrhagic conjunctivitis (AHC) poses a significant global health risk, with the potential for rapid spread during outbreaks. For instance, a localized outbreak in Yunnan Province, China, recorded infection rates of up to 48%, illustrating how transmission can intensify under favourable epidemiological and environmental conditions. Existing mathematical models of AHC transmission overlook seasonal variations, a critical factor in epidemic spread. This study combines species distribution models (SDMs) and epidemiological modelling to analyse key drivers of AHC in East Africa. We use the SEIR type (Susceptible-Exposed-Infected-Recovered - incorporating waning immunity) framework with temperature-dependent infectivity rate as the key driver of an …

Therapeutic Outcomes Of Oral Antibiotics For The Treatment Of Methicillin-Resistant Staphylococcus Aureus Urinary Tract Infections: A Multisite, Retrospective Cohort Study Of Linezolid, Trimethoprim–Sulfamethoxazole And Doxycycline, Ryan Mccall, Elena Gatskevich, Steven E. Fiester, Michael Floren, Elisabeth Chandler

Chemistry Publications

Background: Methicillin-resistant Staphylococcus aureus (MRSA) urinary tract infections (UTIs), while relatively uncommon, pose a unique challenge in treatment as only specific intravenous (IV) options are typically utilized, with the efficacy of oral antimicrobials being poorly defined. Methods: The multi-site retrospective cohort study described herein therefore aims to characterize outcomes associated with oral administration of linezolid, trimethoprim-sulfamethoxazole (TMP-SMX), or doxycycline for the treatment of MRSA UTIs. Study participants were adults with culture-positive MRSA UTIs receiving one of the three oral therapies. Exclusion criteria included polymicrobial UTI, concomitant MRSA outside the urinary tract, receipt of non-study anti-MRSA agents for greater than or …

Epidemic Dynamics Under Pulse Population Exchange, Hannah Kravitz, Christina Durón, Moysey Brio

Mathematics and Statistics Faculty Publications and Presentations

Many epidemiological models assume either closed populations or continuous demographic turnover. We consider an intermediate setting in which exchange occurs through discrete pulses. In this paper, we introduce a population-conserving compartmental epidemiological model with pulse population exchange at a set of prescribed times. At each pulse, a fraction of the population in each compartment is replaced by a combination of susceptible and immunized individuals. In contrast to typical pulse birth or pulse vaccination models where only a single compartment undergoes a pulse population change, the pulses in this model have competing effects: removing infectious individuals reduces the force of infection, …

Public-Port Throughput As An Activity Proxy For Near-Port Air Quality And Health: A Transferable Two-Scale Framework (Kaohsiung, 2017–2024), Ping-Jen Wang, Ying-Lin Hsu, Shih-Hao Chang, Bao-Tzung Wu

Journal of Marine Science and Technology–Taiwan

We developed a two-scale time series framework using monthly container throughput (20-foot equivalent units, TEU) as a port activity indicator. Applied to Kaohsiung, Taiwan (2017–2024), we related TEU to near-port NO₂ and PM₂.₅ (monthly) and air quality to outpatient respiratory diagnoses (weekly) across the 2019–2020 sulfur rules and the COVID-19 pandemic. Transfer-function models indicate TEU tends to lead near-port NO₂ by 6–9 months. Structural break tests at policy dates indicate nonsignificant changes in levels and slopes, suggesting gradual rather than abrupt shifts in the activity–pollution linkage. Weekly two-pollutant distributed-lag Poisson models estimated relative risks (lags 0–8) per interquartile range (IQR) …

Gc-Ms Profiling And Antibacterial Activity Of Cold-Macerated Garlic Extracts Against Multidrug-Resistant Uropathogens, Fatima A. Khalaf, Saeed A. Fayadh

Karbala International Journal of Modern Science

The growing number of cases of multidrug-resistant (MDR) urinary tract infections has made the clinical management of urinary tract diseases a significant challenge; therefore, the need for effective adjunctive therapies cannot be overemphasized. This study evaluated the bioactive components and antibacterial efficacy of cold-macerated garlic extracts obtained using distilled water, 70% ethanol and hexane solvents against antimicrobial-resistant urinary isolates. Out of 250 urine samples that were analyzed, 124 (49.6%) showed significant microbial growth, with Escherichia coli being the most frequently isolated organism. The results of the phytochemical screening and Gas Chromatography-Mass Spectrometry (GC-MS) analysis showed that the ethanolic extract had …

2026 Report On The State Of Great Salt Lake Social Science, Creed Jones, Avyrlie Smith, Shae Barber, Stacia Ryder, Mufti Nadimul Quamar Ahmed, Georgie Corkery, Jennifer Givens, Anna Mcentire, Carla Trentelman, Jessica Ulrich-Schad, Kirsten Vinyeta, Bryn Watkins

Publications

Great Salt Lake (GSL) faces rapid decline that presents more than just a hydrological risk; it poses an existential social hazard. As water levels decline, ecosystems, economies, cultures, and societies face irreversible harm. Since the lake reached its lowest levels in 2022, this issue has specifically gained increased attention in Utah and beyond. Given both the degree to which human consumption contributes to the problem, and the potential risks that the drying of the lake poses for community health, social science research is a crucial for informing successful water management policies and mitigating impacts. The purpose of this report is …

The Role Of External Factors In Shaping Carbohydrate Conformational Landscapes, Murat Yaman

Dissertations, Theses, and Capstone Projects

Carbohydrates (glycans) are among the most structurally diverse biomolecules and participate in a wide range of biological processes, including molecular recognition, cell adhesion, immune response, host-pathogen interactions, and cellular signaling. Their biological functions are governed by a complex interplay between sequence, stereochemistry, conformational flexibility, and environmental factors. However, the structural heterogeneity and dynamic nature of glycans present significant challenges for both experimental characterization and theoretical modeling. In particular, the relationships between glycan structure, conformational dynamics, and the resulting potential energy surfaces remain incomplete.

This dissertation investigates how external factors modulate the potential energy surfaces of carbohydrates through a combination of …

Spatial Association Of Acute Respiratory Infection, Diarrhea, And Low Birth Weight With Stunting Prevalence In Indonesia, 2024, Dian Rosadi, Husaini Husaini, Triawanti Triawanti, Musafaah Musafaah

Kesmas

Stunting remains unevenly distributed across Indonesia, but national evidence integrating spatial analysis and spatial regression is limited. This study examined the spatial distribution of stunting and its associations with acute respiratory infection (ARI), diarrhea, and low birth weight (LBW) across Indonesian provinces. An ecological cross-sectional study used data from the 2024 Indonesian Nutritional Status Survey. Stunting-only analyses included all 38 provinces, whereas analyses involving ARI, diarrhea, and LBW included 37 provinces with complete data. Spatial analyses used a row-standardized symmetric four-nearest-neighbor spatial weights matrix and included Global Moran’s I, bivariate spatial analysis, Local Indicators of Spatial Association, ordinary least squares, …

Dynamics Of Swimming Microorganisms At Structured Liquid Crystal Interfaces, Vajra Sabhapathy Badha

Graduate Doctoral Dissertations

Active matter systems are self-driven units that consume energy to generate motion and mechanical stresses, producing non-equilibrium states of broad physical significance. Examples include synthetic microswimmers and migrating cells. Motile bacteria are a widely studied biological example because their self-propelled motion, hydrodynamic interactions, and collective organization are strongly coupled to local environmental conditions. Their swimming is sensitive to interfacial viscoelasticity, ordering, confinement, and hydrodynamic boundary effects, making them useful for investigating how interfaces regulate active biological motion. Because bacterial accumulation and attachment at interfaces are central to colonization and biofilm formation, these interactions are relevant to both active matter physics …

Antifungal Activity Of Isolated Compounds From Centaurea Salicifolia Var. Salicifolia Against Candida Species, Including Multidrug-Resistant C. Auris, C. Inconspicua, And C. Dubliniensis, Seli̇n Tufan, Di̇lek Şatana, Nur Tan

Turkish Journal of Chemistry

Natural compounds obtained from plants have always held great potential for drug discovery and, as such, have drawn the attention of researchers as novel antifungal molecules that can be effective against fungal resistance. The antifungal activity of sesquiterpene lactones has been extensively investigated against various fungal strains, but there is limited data on their antifungal activity against Candida species. Sesquiterpene lactones are abundant in the Asteraceae family, and 90% of identified sesquiterpene lactones have been isolated from members of this family. Three extracts obtained from the aerial parts of Centaurea salicifolia var. salicifolia, which had not been investigated prior to …

Chitosan Microparticle-Based Antibacterial Nasal Barrier Formulation And In Vivo Evaluations, Güli̇z Ak, Ayça Erek, Tuğba Karakayali, Şadi̇ye Çeti̇n, Şenay Şanlier

Turkish Journal of Chemistry

Microorganisms remain a major cause of infectious diseases, emphasizing the need for alternative and complementary antimicrobial strategies. In this context, plant-derived materials have attracted increasing attention for their antimicrobial and protective properties. Chitosan, a biocompatible and cationic biopolymer, has emerged as an effective carrier system for encapsulating such plant-derived components. In this study, chitosan microparticles were prepared through ionic gelation followed by spray drying and loaded with thyme oil and olive leaf extract. The resulting microparticles exhibited an average size of approximately 1.8 μm and a total phenolic content of 23 mg GAE/g. These microparticles were incorporated into a glycerin–starch …

A Poly-L-Lysine-Functionalized Electrochemical Immunosensor Enables Highly Sensitive Detection Of Tumor Necrosis Factor Receptor-Associated Protein 1, Berfi̇n Vural, Mustafa Kemal Sezgi̇ntürk

Turkish Journal of Chemistry

Tumor necrosis factor receptor-associated protein 1 (TRAP-1), a member of the mitochondrial heat shock protein family (HSP90), is essential for protein homeostasis, stress response, and cell cycle. TRAP-1 not only optimizes cellular energy production but also prevents cell death, thereby supporting the survival and proliferation of tumor cells. In addition to cancer, TRAP-1 has been associated with Parkinson’s disease, certain autoimmune disorders, and abnormalities in the kidney and urinary tract. In this study, a unique and useful indium tin oxide-polyethylene terephthalate (ITO–PET)-based electrochemical biosensor is described for detecting the biomarker TRAP-1. The ITO–PET electrode, selected as the working electrode, is …

Rickettsia Africae Discovered In A Short-Term Urban Traveller To South Africa: A Case Report, Zunairah Sikder

Binghamton University Undergraduate Journal

Rickettsia Africae is a pathogen that causes African tick-bite fever (ATBF). Transmission typically occurs from ticks within the Central and South African regions. Previous studies suggested that ATBF is not uncommon amongst travelers to rural sub-Saharan Africa, especially during the rainy months of November through April. However, this case report highlights a woman who contracted ATBF in novel conditions. The 70-year-old woman reported travelling strictly to and from the local church and hotel for her four-day stay in July. After returning to America, the patient experienced extreme irritation on her arm, as well as complaints of headaches. She presented to …

Numerical Analysis Of The Sir Model For Predicting Disease Spread, Victoria Gaibor, Isabel Tejada, Kate Moore

Discovery Day - Daytona Beach

This project, Numerical Solutions of the SIR Model for Predicting Disease Spread, investigates the application of numerical methods to analyze the dynamics of infectious diseases using the classical Susceptible–Infected–Recovered (SIR) model. The SIR model, a system of nonlinear ordinary differential equations, is widely used to describe how diseases such as COVID-19 propagate through a population. The primary objective of this study is to solve the SIR initial value problem using multiple numerical techniques, including Euler’s method, Runge–Kutta methods, and multistep methods, and to compare their accuracy and efficiency. The model is implemented using given initial conditions and parameters, and additional …

The 2025 Measles Outbreak In Texas, Tamer Oraby, Martial L. Ndeffo-Mbah

School of Mathematical & Statistical Sciences Faculty Publications

Background: In 2025, Texas experienced its largest measles outbreak in decades, reporting 762 cases by mid-August. Measles is a highly contagious but vaccine-preventable infection transmitted mainly among unvaccinated individuals and capable of causing severe outcomes.

Methods: We investigate counterfactual measles control scenarios based on daycare and school closures and reactive vaccination of infants and children, including mixed interventions. We analyze the 2025 Texas outbreak using an age-structured multi-stage SEIR model formulated as a system of ordinary differential equations. The model is fit to case data using Bayesian inference to estimate the effective reproduction number and generate posterior predictive trajectories under …

Dynamics Of Microscale Droplets In Respiratory Airways, Md Shamser Ali Javed

Mathematics Theses and Dissertations

We investigate trajectories of microscale evaporating droplets in a stagnation point flow near a wall of a respiratory airway. The configuration is motivated by the problem of advection and deposition of microscale droplets of respiratory fluids in human airways during transmission of infectious diseases such as tuberculosis and COVID-19. Laminar boundary layer equations are solved to describe the air flow while the equations of motion of the droplet include contributions from gravity, aerodynamic drag, and Saffman force. Evaporation is accounted for at both the droplet surface and the wall of the respiratory airway and is shown to delay droplet deposition …

Expression Levels Of Heat Shock Protein 72 And Their Correlation With Biomarkers Of Renal Function Among Hispanic Construction Workers Exposed To Ambient Heat In El Paso, Texas, Maria Fuentes

Open Access Theses & Dissertations

Heat shock proteins (HSP) are intracellular molecular proteins that are upregulated in response to cellular stress, including heat exposure. Through their protective functions, HSP help maintain protein structure, prevent protein denaturation, and preserve cellular homeostasis during states of physiological stress. Because of their cytoprotective properties, HSP have emerged as potential biomarkers for detecting early signs of tissue injury and predicting clinical outcomes associated with heat related illnesses (HRI), including acute kidney injuries (AKI). AKI is a leading cause of hospitalizations due to heat stress exposure and heat stroke. In the absence of early detection and effective therapeutic interventions, AKI may …

Method Validation Of The Cdc Bottle Bioassay And A Historical Record Of Polycyclic Aromatic Hydrocarbons In Glacier National Park, Evah F. Peard

All Graduate Theses and Dissertations, Fall 2023 to Present

Certain contaminants can persist in the environment for long periods of time, build up within living tissues, travel far from their origin, and harm both ecosystems and organisms. This thesis focuses on two types of contaminants: insecticides and polycyclic aromatic hydrocarbons (PAHs). Insecticides are manufactured to control pests while PAHs are found in oil and gas products and can be produced by industry, vehicle engines, and wildfires. Understanding how harmful these contaminants are and where they end up in the environment is critical for protecting environmental health.

First, I evaluated a widely used test developed by the Centers for Disease …

Phytochemical Analysis And Safety Assessment Of Watercress Nasturtium Officinale: Antioxidant Capacity, Heavy Metal Profiling, And Toxicity Using Brine Shrimp Model, Qurrota A’Yunin, Chamini Kasun Hemachandra, Muhaimin Rifa’I, Yoga Dwi Jatmiko, Maftuch Maftuch, Rizky Fadilla Agustin Rangkuti, Cucun Herlina, Zulfa Mahdiatur Rasyida, Moh Dliyauddin

Karbala International Journal of Modern Science

Medicinal plants have attracted growing attention as sources of natural bioactive compounds for sustainable aquaculture and health. This study evaluated the phytochemical composition, antioxidant activity, heavy metal profile, and acute toxicity of watercress (Nasturtium officinale W.T. Aiton) methanol extract using maceration, qualitative and quantitative (TPC, TFC, antioxidant DPPH) phytochemical assay, XRF, and BSLA. Phytochemical screening of plant extracts showed the existence of flavonoids, alkaloids, phenols, tannins, triterpenoids, and saponins, but not steroidal. The TPC and TFC were 20.6 mg GAE/g and 10.8 mg QE/g, respectively. The extract displayed significant antioxidant activity (IC₅₀ = 64.78 µg/mL in DPPH assay). …

Enhanced Transdermal Immunization Via Solid-In-Oil Nanodispersions Incorporating Dendritic Cell-Targeting Peptide, Md Samiul Islam, Md. Shahin Ekka Sarker, Yoshirou Kawaguchi, Rie Wakabayashi, Noriho Kamiya, Muhammad Moniruzzaman, Masahiro Goto

Publications and Research

Transdermal immunization represents a promising needle-free alternative to conventional vaccination. However, efficient antigen delivery and robust immune activation remain major challenges. In this study, a solid-in-oil (S/O) nanodispersion system comprising a dendritic cell-targeting peptide (HR8), ovalbumin (OVA), and an adjuvant was developed for transdermal immunization. The HR8 peptide along with OVA was successfully incorporated into an S/O nanodispersion with an optimal hydrodynamic diameter of particles (< 200 nm) and exhibited stable physical properties for up to 90 days. In vitro and in vivo studies demonstrated enhanced antigen delivery with insignificant skin irritation in C57BL/6N mice. Moreover, in vivo transdermal immunization studies demonstrated that the addition of the HR8 peptide enhanced OVA-specific IgG responses (~1.5-fold). Notably, the HR8 peptide also promoted an approximately 2.5-fold increase in IgG2c levels, suggesting a shift toward a more T helper type 1-biased immune response, as reflected by an increased IgG2c/IgG1 ratio. Overall, these findings demonstrate that the incorporation of HR8 peptide into an S/O nanodispersion enables efficient transdermal antigen delivery and improved immunogenicity, highlighting its potential as a simple, non-invasive, and patient-friendly immunization strategy.

Bridging The Gap In Science Research: Preparing Students For College- Level Research In The Sciences, Victoria Helwig, Yaoguang Li

UConn Library Presentations

Many first-year students enter college unprepared to fully engage with scientific literature and academic library resources. Drawing on experiences from academic librarians working with STEM students, this session explores common gaps in science research skills, including navigating databases, identifying scholarly sources, and understanding the structure of scientific literature. Participants will be introduced to practical strategies and classroom-ready activities to better prepare students for college-level research. Discussion questions: What science research skills do students struggle with most when entering college? How can high school instruction better support these skills? Where can librarians and educators collaborate to support student success?

Comparative Analysis Of Traditional And Deep Learning Time Series Architectures For Influenza A Infectious Disease Forecasting, Edmund Fosu Agyemang, Hansapani Rodrigo, Vincent Agbenyeavu

School of Mathematical & Statistical Sciences Faculty Publications

Influenza A remains a major cause of respiratory mortality worldwide, motivating accurate forecasting to support timely preparedness and resource allocation. This study presents a comparative evaluation of two traditional seasonal time series baselines, ARIMA and Holt–Winters exponential smoothing (ETS), and six deep learning (DL) architectures (Simple RNN, LSTM, GRU, BiLSTM, BiGRU, and a Transformer) for forecasting monthly Influenza A case counts in the United States. Data from January 2009 to December 2023 were analyzed, using January 2009 to December 2022 for training and January 2023 to December 2023 for out-of-sample testing. Models were tuned using a validation split and assessed …

Decoding The Allosteric Grammar Of Protein Kinases: A Dual-Stream Framework Integrating Protein Language Models And Energy Landscape Frustration Analysis, Will Gatlin, Max Ludwick, Lucas Turano, Brandon Foley, Kamila Riedlova, Vít Škrhák, Marian Novotný, David Hoksza, Gennady M. Verkhivker

Mathematics, Physics, and Computer Science Faculty Articles and Research

The spatial and energetic encoding of allosteric regulatory sites remains a major challenge in structural biology, frequently representing a “blind spot” for sequence-based artificial intelligence (AI) models. We present a protein language model (PLM)-guided approach complemented by the energy landscape frustration analysis as a dual-stream framework to investigate the relationship between AI prediction of binding sites and biophysical organization of regulatory pockets across the human kinome. By probing a fine-tuned residue-level PLM classifier across 453 kinase structures, a clear performance gap is discovered between highly predictable orthosteric pockets (Types I, I.5, and II) and poorly resolved distal allosteric sites (Type …

Ecorxchoice.Com— An Sidp-Funded Calculator Integrating Environmental Metrics With Antimicrobial Stewardship, Pamela S. Lee, Hugh Gordon, Theresa Ferguson, Tien Dinh, Misty Vu, Marina Nguyen, Chaynor Hsiao, Gary Fong

Pharmacy Faculty Articles and Research

Healthcare sustainability is a multidisciplinary field that seeks to mitigate healthcare’s environmental consequences. Antimicrobial stewardship and healthcare sustainability both aim to reduce wasteful resource use while maximizing patient safety. However, a strong partnership between antimicrobial stewardship and healthcare sustainability has yet to develop. To facilitate environmentally sustainable decision-making in antimicrobial prescribing, we developed a web-based calculator (EcoRxChoice (www.ecorxchoice.com)) where users can enter different antimicrobial regimens and compare how much plastic waste each regimen creates. This work was supported in part by the Society of Infectious Diseases Pharmacists (SIDP), reflecting SIDP’s commitment to strengthening sustainability as a practical extension of antimicrobial …

A Differential Equation–Based Epidemiological Model Of Post-Operative Chronic Pain In Scoliosis Patients With Data-Driven Analysis, Paige Zhu, Padmanabhan Seshaiyer

CODEE Journal

Chronic post-surgical pain (CPSP) is a common and often overlooked complication following surgical correction of idiopathic scoliosis, impacting long-term patient wellbeing despite improvements in surgical outcomes. This project introduces a novel epidemiological framework to model the progression of CPSP using a compartmental structure. By applying a coupled system of nonlinear differential equations, we simulate pain trajectories over time and assess the effectiveness of surgical interventions. The model is implemented for a single-cohort population and extended to a two-cohort design to compare outcomes between Posterior Spinal Fusion (PSIF) and Vertebral Body Tethering (VBT) procedures. Further stratification by patient age enables us …

A Mathematical Model For Managing Diphtheria Outbreaks In Nigeria Via Vaccination, Enhanced Surveillance, Effective Quarantine, And Social Distancing Measures, Hycienth Ortser Orapine, Nyiutya Cephas Ine, Dekera Jacob Washachi, Ali Audu Baidu, Lubem Matthew Kwaghkor

Mathematical Modelling and Numerical Simulation with Applications

Diphtheria is a highly infectious respiratory and skin disease that poses a significant threat to global public health. In Nigeria, children and adults with low immunity remain at high risk due to recurring annual outbreaks in the last decade, with a death rate of as high as 68.8\%. This paper presents a deterministic compartmental model to evaluate the effectiveness of interventions implemented by the Nigerian government. The model's mathematical and epidemiological validity is established through proofs of non-negativity and boundedness. The basic reproduction number ($R_0$) is derived, and stability analysis confirms that the diphtheria-free equilibrium is locally and globally asymptotically …

Third Butte Rmap Biomonitoring (Phase 3) Report, Ramboll, Atlantic Richfield Company

Silver Bow Creek/Butte Area Superfund Site

No abstract provided.

Dynamical Behavior, Extinction And Persistence In A Stochastic Delayed Two-Strain Epidemic Model With A Generalized Crowley-Martin Incidence Rate, Amina Allali, Dounia Bentaleb, Saida Amine

Mathematical Modelling and Numerical Simulation with Applications

This paper develops and analyzes a novel delayed stochastic SIR epidemic model with two interacting strains and general incidence functions. By establishing the existence and uniqueness of a positive global solution, the well-posedness of the model under stochastic perturbations is ensured. Extinction occurs when the stochastic reproduction number falls below unity, as demonstrated through Itô calculus and martingale convergence theorems, while persistence is guaranteed under the Crowley–Martin incidence when it exceeds one. Numerical experiments based on the Positive Preserving Truncated Euler–Maruyama (PPTEM) scheme confirm the analytical predictions and highlight the influence of time delay and noise intensity on the long-term …

Stochastic Analysis Of Epidemic Size And Peak Infection In An Svir Model With Imperfect Vaccine And External Source Of Infection, María Gamboa Pérez

Mathematical Modelling and Numerical Simulation with Applications

The dynamics of an infectious disease outbreak are studied under a stochastic framework in a closed population where individuals are homogeneously mixed. A vaccination program is implemented in the community prior to the start of the epidemic. The administered vaccine is imperfect, meaning that vaccinated individuals may still become infected upon contact with infected individuals. The mathematical Susceptible-Vaccinated-Infected-Recovered (SVIR) model describing the evolution of the epidemic is formulated as an absorbing, continuous-time, three-dimensional Markov chain with compartments for vaccinated, susceptible, infected and recovered individuals. The aim of this study is to characterize two fundamental epidemiological quantities: the maximum number of …