An Epidemic Model with Infection Age and Vaccination Age Structure.

A model of epidemic dynamics is developed that incorporates continuous variables for infection age and vaccination age. The model analyzes pre-symptomatic and symptomatic periods of an infected individual in terms of infection age. This property is shown to be of major importance in the severity of the epidemic, when the infectious period of an infected individual precedes the symptomatic period.

Bifurcation analysis of critical values for wound closure outcomes in wound healing experiments.

A nonlinear partial differential equation containing a nonlocal advection term and a diffusion term is analyzed to study wound closure outcomes in wound healing experiments. There is an extensive literature of similar models for wound healing experiments. In this paper we study the character of wound closure in these experiments in terms of the sensing radius of cells and the force of cell-cell adhesion.

The force of cell-cell adhesion in determining the outcome in a nonlocal advection diffusion model of wound healing.

A model of wound healing is presented to investigate the connection of the force of cell-cell adhesion to the sensing radius of cells in their spatial environment. The model consists of a partial differential equation with nonlocal advection and diffusion terms, describing the movement of cells in a spatial environment. The model is applied to biological wound healing experiments to understand incomplete wound closure.

Modeling Vaccine Efficacy for COVID-19 Outbreak in New York City.

In this article we study the efficacy of vaccination in epidemiological reconstructions of COVID-19 epidemics from reported cases data. Given an epidemiological model, we developed in previous studies a method that allowed the computation of an instantaneous transmission rate that produced an exact fit of reported cases data of the COVID-19 outbreak. In this article, we improve the method by incorporating vaccination data.

A COVID-19 Epidemic Model Predicting the Effectiveness of Vaccination in the US.

A model of a COVID-19 epidemic is used to predict the effectiveness of vaccination in the US. The model incorporates key features of COVID-19 epidemics: asymptomatic and symptomatic infectiousness, reported and unreported cases data, and social measures implemented to decrease infection transmission. The model analyzes the effectiveness of vaccination in terms of vaccination efficiency, vaccination scheduling, and relaxation of social measures that decrease disease transmission.

Predicting the cumulative number of cases for the COVID-19 epidemic in China from early data.

We model the COVID-19 coronavirus epidemic in China. We use early reported case data to predict the cumulative number of reported cases to a final size. The key features of our model are the timing of implementation of major public policies restricting social movement, the identification and isolation of unreported cases, and the impact of asymptomatic infectious cases.

Modelling the aqueous transport of an infectious pathogen in regional communities: application to the cholera outbreak in Haiti.

A mathematical model is developed to describe the dynamics of the spread of a waterborne disease among communities located along a flowing waterway. The model is formulated as a system of reaction-diffusion-advection partial differential equations in this spatial setting. The compartments of the model consist of susceptible, infected, and recovered individuals in the communities along the waterway, together with a term representing the pathogen load in each community and a term representing the spatial concentration of pathogens flowing along the waterway.

Understanding Unreported Cases in the COVID-19 Epidemic Outbreak in Wuhan, China, and the Importance of Major Public Health Interventions.

We develop a mathematical model to provide epidemic predictions for the COVID-19 epidemic in Wuhan, China. We use reported case data up to 31 January 2020 from the Chinese Center for Disease Control and Prevention and the Wuhan Municipal Health Commission to parameterize the model. From the parameterized model, we identify the number of unreported cases.

Predicting the long-term impact of voluntary medical male circumcision on HIV incidence among men who have sex with men in Beijing, China.

Using a deterministic compartmental modeling procedure to fit prevalence from 2005-2015, we projected new HIV cases during 2016-2026 under different coverage rates ranging from 0.0001 (at baseline) to 0.15 (an optimistic assumption) with simulations on varying transmission rates, model calibration to match historical data, and sensitivity analyses for different assumptions.

Spatial models of vector-host epidemics with directed movement of vectors over long distances.

We investigate a time-dependent spatial vector-host epidemic model with non-coincident domains for the vector and host populations. The host population resides in small non-overlapping sub-regions, while the vector population resides throughout a much larger region. The dynamics of the populations are modeled by a reaction-diffusion-advection compartmental system of partial differential equations.

Modeling economic and epidemiological impact of voluntary medical male circumcision among men who have sex with men in Beijing, China.

Voluntary medical male circumcision (VMMC) among men who have sex with men (MSM) may protect against HIV acquisition. We conducted a series of analyses to assess if expanded VMMC might reduce HIV incidence among MSM effectively and economically. We used a deterministic compartmental model to project new HIV cases (2016-2026) under annual VMMC coverage rates (λ) ranging from 0.

A dynamic model of CT scans for quantifying doubling time of ground glass opacities using histogram analysis.

We quantify a recent five-category CT histogram based classification of ground glass opacities using a dynamic mathematical model for the spatial-temporal evolution of malignant nodules. Our mathematical model takes the form of a spatially structured partial differential equation with a logistic crowding term. We present the results of extensive simulations and validate our model using patient data obtained from clinical CT images from patients with benign and malignant lesions.

Final size of a multi-group SIR epidemic model: Irreducible and non-irreducible modes of transmission.

A model of an epidemic outbreak incorporating multiple subgroups of susceptible and infected individuals is investigated. The asymptotic behavior of the model is analyzed and it is proved that the infected classes all converge to 0. A computational algorithm is developed for the cumulative final size of infected individuals over the course of the epidemic.

The parameter identification problem for SIR epidemic models: identifying unreported cases.

A SIR epidemic model is analyzed with respect to identification of its parameters, based upon reported case data from public health sources. The objective of the analysis is to understand the relation of unreported cases to reported cases. In many epidemic diseases the ratio of unreported to reported cases is very high, and of major importance in implementing measures for controlling the epidemic.

Optimal control applied to community-acquired methicillin-resistant Staphylococcus aureus in hospitals.

Optimal control methods are applied to a deterministic mathematical model to characterize the factors contributing to the replacement of hospital-acquired methicillin-resistant Staphylococcus aureus (HA-MRSA) with community-acquired methicillin-resistant Staphylococcus aureus (CA-MRSA), and quantify the effectiveness of three interventions aimed at limiting the spread of CA-MRSA in healthcare settings. Characterizations of the optimal control strategies are established, and numerical simulations are provided to illustrate the results.

Modeling contact tracing in outbreaks with application to Ebola.

Contact tracing is an important control strategy for containing Ebola epidemics. From a modeling perspective, explicitly incorporating contact tracing with disease dynamics presents challenges, and population level effects of contact tracing are difficult to determine. In this work, we formulate and analyze a mechanistic SEIR type outbreak model which considers the key features of contact tracing, and we characterize the impact of contact tracing on the effective reproduction number, Re, of Ebola.

A nosocomial epidemic model with infection of patients due to contaminated rooms.

A model of epidemic bacterial infections in hospitals is developed. The model incorporates the infection of patients and the contamination of healthcare workers due to environmental causes. The model is analyzed with respect to the asymptotic behavior of solutions.

A model of the 2014 ebola epidemic in west Africa with contact tracing.

A differential equations model is developed for the 2014 Ebola epidemics in Sierra Leone and Liberia. The model describes the dynamic interactions of the susceptible and infected populations of these countries. The model incorporates the principle features of contact tracing, namely, the number of contacts per identified infectious case, the likelihood that a traced contact is infectious, and the efficiency of the contact tracing process.

Host demise as a beneficial function of indigenous microbiota in human hosts.

Unlabelled: The age structure of human populations is exceptional among animal species. Unlike with most species, human juvenility is extremely extended, and death is not coincident with the end of the reproductive period. We examine the age structure of early humans with models that reveal an extraordinary balance of human fertility and mortality.

Modeling the impact on HIV incidence of combination prevention strategies among men who have sex with men in Beijing, China.

Objective: To project the HIV/AIDS epidemics among men who have sex with men (MSM) under different combinations of HIV testing and linkage to care (TLC) interventions including antiretroviral therapy (ART) in Beijing, China.

Design: Mathematical modeling.

Methods: Using a mathematical model to fit prevalence estimates from 2000-2010, we projected trends in HIV prevalence and incidence during 2011-2020 under five scenarios: (S1) current intervention levels by averaging 2000-2010 coverage; (S2) increased ART coverage with current TLC; (S3) increased TLC/ART coverage; (S4) increased condom use; and (S5) increased TLC/ART plus increased condom use.

Alzheimer's disease: analysis of a mathematical model incorporating the role of prions.

We introduce a mathematical model of the in vivo progression of Alzheimer's disease with focus on the role of prions in memory impairment. Our model consists of differential equations that describe the dynamic formation of β-amyloid plaques based on the concentrations of Aβ oligomers, PrP(C) proteins, and the Aβ-x-Aβ-PrP(C)complex, which are hypothesized to be responsible for synaptic toxicity. We prove the well-posedness of the model and provided stability results for its unique equilibrium, when the polymerization rate of Aβ-amyloid is constant and also when it is described by a power law.

A non-local evolution equation model of cell-cell adhesion in higher dimensional space.

A model for cell-cell adhesion, based on an equation originally proposed by Armstrong et al. [A continuum approach to modelling cell-cell adhesion, J. Theor.

Docetaxel-resistance in prostate cancer: evaluating associated phenotypic changes and potential for resistance transfer via exosomes.

Background: Hormone-refractory prostate cancer remains hindered by inevitable progression of resistance to first-line treatment with docetaxel. Recent studies suggest that phenotypic changes associated with cancer may be transferred from cell-to-cell via microvesicles/exosomes. Here we aimed to investigate phenotypic changes associated with docetaxel-resistance in order to help determine the complexity of this problem and to assess the relevance of secreted exosomes in prostate cancer.

The contribution of age structure to cell population responses to targeted therapeutics.

Cells grown in culture act as a model system for analyzing the effects of anticancer compounds, which may affect cell behavior in a cell cycle position-dependent manner. Cell synchronization techniques have been generally employed to minimize the variation in cell cycle position. However, synchronization techniques are cumbersome and imprecise and the agents used to synchronize the cells potentially have other unknown effects on the cells.

Efficacy of infection control interventions in reducing the spread of multidrug-resistant organisms in the hospital setting.

Multidrug-resistant organisms (MDRO) continue to spread in hospitals globally, but the population-level impact of recommended preventive strategies and the relative benefit of individual strategies targeting all MDRO in the hospital setting are unclear. To explore the dynamics of MDRO transmission in the hospital, we develop a model extending data from clinical individual-level studies to quantify the impact of hand hygiene, contact precautions, reducing antimicrobial exposure and screening surveillance cultures in decreasing the prevalence of MDRO colonization and infection. The effect of an ongoing increase in the influx of patients colonized with MDRO into the hospital setting is also quantified.