Glenn Webb - Academia.edu (original) (raw)

Papers by Glenn Webb

arXiv (Cornell University), May 27, 2016

Background: A deterministic model is developed for the spatial spread of an epidemic disease in a... more Background: A deterministic model is developed for the spatial spread of an epidemic disease in a geographical setting. The disease is borne by vectors to susceptible hosts through criss-cross dynamics. The model is focused on an epidemic outbreak that initiates from a small number of cases in a small sub-region of the geographical setting. Methods: Partial differential equations are formulated to describe the interaction of the model compartments. Results: The partial differential equations of the model are analyzed and proven to be well-posed. The epidemic outcomes of the model are correlated to the spatially dependent parameters and initial conditions of the model. Conclusions: A version of the model is applied to the 2015-2016 Zika outbreak in the Rio de Janeiro Municipality in Brazil.

Journal of Mathematical Biology

Mathematical Biosciences and Engineering

A model of wound healing is presented to investigate the connection of the force of cell-cell adh... more 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. The analysis demonstrates that for each value of the force of adhesion parameter, there is a critical value of the sensing radius above which complete wound healing does not occur.

Biology, 2022

In this article we study the efficacy of vaccination in epidemiological reconstructions of COVID-... more 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. More precisely, we develop a model in which vaccination is variable in its effectiveness. We develop a new technique to compute the transmission rate in this model, which produces an exact fit to reported cases data, while quantifying the efficacy of the vaccine and the daily number of vaccinated. We apply our method to the reported cases data and vaccination data of New York City.

The Art of Theoretical Biology, 2020

Mathematical models of complex dynamic biological processes sometimes involve systems of partial ... more Mathematical models of complex dynamic biological processes sometimes involve systems of partial differemtial eqaations for production, growth, decay, interaction, and spatial movement.

The Art of Theoretical Biology, 2020

Discrete and Continuous Dynamical Systems - Series B, 2017

Mathematical models of antibiotic resistant infection epidemics in hospital intensive care units ... more Mathematical models of antibiotic resistant infection epidemics in hospital intensive care units are developed with two modeling methods, individual based models and differential equations based models. Both models dynamically track uninfected patients, patients infected with a nonresistant bacterial strain not on antibiotics, patients infected with a nonresistant bacterial strain on antibiotics, and patients infected with a resistant bacterial strain. The outputs of the two modeling methods are shown to be complementary with respect to a common parameterization, which justifies the differential equations modeling approach for very small patient populations present in an intensive care unit. The model outputs are classified with respect to parameters to distinguish the extinction or endemicity of the bacterial strains. The role of stewardship of antibiotic use is analyzed for mitigation of these nosocomial epidemics.

Journal of Biological Dynamics, 2016

Optimal control methods are applied to a deterministic mathematical model to characterize the fac... more 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.

Mathematical Modelling of Natural Phenomena, 2010

Background: Community-acquired methicillin-resistant Staphylococcus aureus (CA-MRSA), a novel str... more Background: Community-acquired methicillin-resistant Staphylococcus aureus (CA-MRSA), a novel strain of MRSA, has recently emerged and rapidly spread in the community. Invasion into the hospital setting with replacement of the hospital-acquired MRSA (HA-MRSA) has also been documented. Co-colonization with both CA-MRSA and HA-MRSA would have important clinical implications given differences in antimicrobial susceptibility profiles and the potential for exchange of genetic information. Methods: A deterministic mathematical model was developed to characterize the transmission dynamics of HA-MRSA and CA-MRSA in the hospital setting and to quantify the emergence of co-colonization with both strains Results: The model analysis shows that the state of co-colonization becomes endemic over time and that typically there is no competitive exclusion of either strain. Increasing the length of stay or rate of hospital entry among patients colonized with CA-MRSA leads to a rapid increase in the co-colonized state. Compared to MRSA decolonization strategy, improving hand hygiene compliance has the greatest impact on decreasing the prevalence of HA-MRSA, CA-MRSA and the co-colonized state. Conclusions: The model predicts that with the expanding community reservoir of CA-MRSA, the majority of hospitalized patients will become colonized with both CA-MRSA and HA-MRSA.

Journal of Thoracic Oncology, 2012

Based on promising preclinical efficacy of bortezomib in mesothelioma, a single-arm phase II tria... more Based on promising preclinical efficacy of bortezomib in mesothelioma, a single-arm phase II trial (Ireland Cooperative Oncology Research Group 05-10 study), with Simon's two-stage design, was undertaken to assess efficacy of bortezomib monotherapy in the first-line (poor performance status) and second-line settings. The Bcl-2 homology domain 3-only protein Noxa has been implicated as a key inducer of apoptosis by bortezomib. Thus, in a biomarker research substudy, we hypothesized that deficiency in Noxa expression might correlate with resistance. In the second-line setting, 23 patients were enrolled. Partial response was confirmed in one patient (4.8%) who received four cycles of bortezomib. One patient had stable disease; however, progression occurred in the majority of patients within the first two cycles. Median progression-free survival and overall survival were 2.1 and 5.8 months, respectively. In the first-line setting, ten patients were accrued, and there was no evidence of objective response. In the tumor analysis, expression of Noxa was seen in all biopsies. Bortezomib monotherapy exhibits insufficient activity to warrant further investigation in unselected patients with mesothelioma.

Journal of Biological Chemistry, 2012

Background: The P-glycoprotein is expressed in many human cancers, where it contributes to multi-... more Background: The P-glycoprotein is expressed in many human cancers, where it contributes to multi-drug resistance phenomenon. Results: Both TnTs and microparticles contribute to the transfer of P-gp in MCF-7. Conclusion: Our findings supply new mechanistic evidences for the extragenetic emergence of MDR in cancer cells. Significance: Inhibition of both MPs and TnTs could be included in treatment strategies designed to overcome MDR. Multi-drug resistance (MDR) is a phenomenon by which tumor cells exhibit resistance to a variety of chemically unrelated chemotherapeutic drugs. The classical form of multidrug resistance is connected to overexpression of membrane P-glycoprotein (P-gp), which acts as an energy dependent drug efflux pump. P-glycoprotein expression is known to be controlled by genetic and epigenetic mechanisms. Until now processes of P-gp gene up-regulation and resistant cell selection were considered sufficient to explain the emergence of MDR phenotype within a cell population. Recently, however, "non-genetic" acquisitions of MDR by cell-to-cell P-gp transfers have been pointed out. In the present study we show that intercellular transfers of functional P-gp occur by two different but complementary modalities through donor-recipient cells interactions in the absence of drug selection pressure. P-glycoprotein and drug efflux activity transfers were followed over 7 days by confocal microscopy and flow cytometry in drug-sensitive parental MCF-7 breast cancer cells co-cultured with P-gp overexpressing resistant variants. An early process of remote transfer was established based on the release and binding of P-gp-containing microparticles. Microparticle-mediated transfers were detected after only 4 h of incubation. We also identify an alternative mode of transfer by contact, consisting of cell-to-cell P-gp trafficking by tunneling nanotubes bridging neighboring cells. Our findings supply new mechanistic evidences for the extragenetic emergence of MDR in cancer cells and indicate that new treatment strategies designed to overcome MDR may include inhibition of both microparticles and Tunneling nanotube-mediated intercellular P-gp transfers. of the Interreg IVA project Admin (Trans-Channel Advanced Microscopy network). □ S This article contains supplemental Fig. 1 and supplemental videos 1 and 2. 1 Recipient of a fellowship from the Conseil Regional de Haute-Normandie.

Emerging Infectious Diseases, 1997

Computational and Mathematical Methods in Medicine, 2009

We develop a state space model documenting Gompertz behaviour of tumour growth. The state space m... more We develop a state space model documenting Gompertz behaviour of tumour growth. The state space model consists of two sub-models: a stochastic system model that is an extension of the deterministic model proposed by Gyllenberg and Webb (1991), and an observation model that is a statistical model based on data for the total number of tumour cells over time. In the stochastic system model we derive through stochastic equations the probability distributions of the numbers of different types of tumour cells. Combining with the statistic model, we use these distribution results to develop a generalized Bayesian method and a Gibbs sampling procedure to estimate the unknown parameters and to predict the state variables (number of tumour cells). We apply these models and methods to real data and to computer simulated data to illustrate the usefulness of the models, the methods, and the procedures.

Bulletin of Mathematical Biology, 2004

Bajaria et al. during interruptions. Simulations predict that short-term viral suppression with v... more Bajaria et al. during interruptions. Simulations predict that short-term viral suppression with varying interruption strategies does not guarantee long-term clinical benefit.

ABSTRACT Materials and methods A deterministic HIV/AIDS model was developed in which a Bernoulli ... more ABSTRACT Materials and methods A deterministic HIV/AIDS model was developed in which a Bernoulli process was used to assess the relationship between per-act and per-partner probabilities of anal intercourse transmission over a given number of sex acts. The model incorporated condom use, HIV testing, risk-reduction and antiretroviral therapy as control strategies of preventing HIV transmission (Figure 1). Data for estimating parameters came from national and local HIV reporting and sentinel surveillance networks, Chinese free ART project database, local epidemiological studies and existing literature. Markov-Chain Monte-Carlo simulation was also carried out using the Metropolis-Hastings algorithm to estimate mean values of some parameters. Figure 1. Schematic diagram of compartments for uninfected and infected MSM with or without receiving HIV testing, risk reduction, and antiretroviral therapy (ART). S –uninfected, susceptible MSM; I-infected MSM. Subscript N presents those were not tested; T presents those were tested; R represents those received risk reduction; A represents those received ART. Superscript 1 refers to CD4 count ≥350 cells/mm3 and 2 refers to CD4 count<350. alpha: recruitment rate per year into target population; Mu: natural removal rate from compartment; kappa i (1; 2; 3): testing rates; lota i (1; 2; 3): linkage-to-risk reduction rates; rho i (1; 2) : progression rates of untreated infected MSM; tau i (1; 2) : treatment rates; theta i (1; 2) : drop out rates from ART; delta i (1) : progression rate for those on ART.

Clinical Infectious Diseases, 2009

Background. Methicillin-resistant Staphylococcus aureus (MRSA) has traditionally been associated ... more Background. Methicillin-resistant Staphylococcus aureus (MRSA) has traditionally been associated with infections in hospitals. Recently, a new strain of MRSA has emerged and rapidly spread in the community, causing serious infections among young, healthy individuals. Preliminary reports imply that a particular clone (USA300) of a community-acquired MRSA (CA-MRSA) strain is infiltrating hospitals and replacing the traditional hospitalacquired MRSA strains. If true, this event would have serious consequences, because CA-MRSA infections in hospitals would occur among a more debilitated, older patient population. Methods. A deterministic mathematical model was developed to characterize the factors contributing to the replacement of hospital-acquired MRSA with CA-MRSA and to quantify the effectiveness of interventions aimed at limiting the spread of CA-MRSA in health care settings. Results. The model strongly suggests that CA-MRSA will become the dominant MRSA strain in hospitals and health care facilities. This reversal of dominant strain will occur as a result of the documented expanding community reservoir and increasing influx into the hospital of individuals who harbor CA-MRSA. Competitive exclusion of hospital-acquired MRSA by CA-MRSA will occur, with increased severity of CA-MRSA infections resulting in longer hospitalizations and a larger in-hospital reservoir of CA-MRSA. Conclusions. Improving compliance with hand hygiene and screening for and decolonization of CA-MRSA carriers are effective strategies. However, hand hygiene has the greatest return of benefits and, if compliance is optimized, other strategies may have minimal added benefit.

Journal of Biological Dynamics, 2010

Modelling the invasion of community-acquired methicillin-resistant Staphylococcus aureus into the... more Modelling the invasion of community-acquired methicillin-resistant Staphylococcus aureus into the hospital setting, Clin. Infect. Dis. 48 (2009), pp. 274-284] proposed a deterministic mathematical model to characterize the factors contributing to the replacement of hospital-acquired methicillin-resistant Staphylococcus aureus (HA-MRSA) with the community-acquired MRSA (CA-MRSA) and to quantify the effectiveness of interventions aimed at limiting the spread of CA-MRSA in the hospital setting. Numerical simulations of the model strongly suggest that CA-MRSA will become the dominant MRSA strain in the hospital setting. In this companion paper, we provide steady-state analysis and more numerical simulations of the model. It is shown that when no colonized or infected patients enter the hospital, competitive exclusion of HA-MRSA by CA-MRSA will occur with increased severity of CA-MRSA infections resulting in longer hospitalizations and a larger in-hospital reservoir of CA-MRSA. Improving compliance with hand hygiene and decolonization of CA-MRSA carriers are effective control strategies.

This article aims to study the COVID-19 data for New York City. We use both the daily number of s... more This article aims to study the COVID-19 data for New York City. We use both the daily number of second does vaccination and the daily number of reported cases for New York City. This article provides a method to combine an epidemic model and such data. We explore the influence of vaccine efficacy on our results.

Computational and Mathematical Methods in Medicine, 2009

Transforming growth factor (TGF)-β is known to have properties of both a tumour suppressor and a ... more Transforming growth factor (TGF)-β is known to have properties of both a tumour suppressor and a tumour promoter. While it inhibits cell proliferation, it also increases cell motility and decreases cell–cell adhesion. Coupling mathematical modelling and experiments, we investigate the growth and motility of oncogene-expressing human mammary epithelial cells under exposure to TGF-β. We use a version of the well-known Fisher–Kolmogorov equation, and prescribe a procedure for its parametrisation. We quantify the simultaneous effects of TGF-β to increase the tendency of individual cells and cell clusters to move randomly and to decrease overall population growth. We demonstrate that in experiments with TGF-β treated cellsin vitro, TGF-β increases cell motility by a factor of 2 and decreases cell proliferation by a factor of 1/2 in comparison with untreated cells.

arXiv (Cornell University), May 27, 2016

Background: A deterministic model is developed for the spatial spread of an epidemic disease in a... more Background: A deterministic model is developed for the spatial spread of an epidemic disease in a geographical setting. The disease is borne by vectors to susceptible hosts through criss-cross dynamics. The model is focused on an epidemic outbreak that initiates from a small number of cases in a small sub-region of the geographical setting. Methods: Partial differential equations are formulated to describe the interaction of the model compartments. Results: The partial differential equations of the model are analyzed and proven to be well-posed. The epidemic outcomes of the model are correlated to the spatially dependent parameters and initial conditions of the model. Conclusions: A version of the model is applied to the 2015-2016 Zika outbreak in the Rio de Janeiro Municipality in Brazil.

Journal of Mathematical Biology

Mathematical Biosciences and Engineering

A model of wound healing is presented to investigate the connection of the force of cell-cell adh... more 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. The analysis demonstrates that for each value of the force of adhesion parameter, there is a critical value of the sensing radius above which complete wound healing does not occur.

Biology, 2022

In this article we study the efficacy of vaccination in epidemiological reconstructions of COVID-... more 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. More precisely, we develop a model in which vaccination is variable in its effectiveness. We develop a new technique to compute the transmission rate in this model, which produces an exact fit to reported cases data, while quantifying the efficacy of the vaccine and the daily number of vaccinated. We apply our method to the reported cases data and vaccination data of New York City.

The Art of Theoretical Biology, 2020

Mathematical models of complex dynamic biological processes sometimes involve systems of partial ... more Mathematical models of complex dynamic biological processes sometimes involve systems of partial differemtial eqaations for production, growth, decay, interaction, and spatial movement.

The Art of Theoretical Biology, 2020

Discrete and Continuous Dynamical Systems - Series B, 2017

Mathematical models of antibiotic resistant infection epidemics in hospital intensive care units ... more Mathematical models of antibiotic resistant infection epidemics in hospital intensive care units are developed with two modeling methods, individual based models and differential equations based models. Both models dynamically track uninfected patients, patients infected with a nonresistant bacterial strain not on antibiotics, patients infected with a nonresistant bacterial strain on antibiotics, and patients infected with a resistant bacterial strain. The outputs of the two modeling methods are shown to be complementary with respect to a common parameterization, which justifies the differential equations modeling approach for very small patient populations present in an intensive care unit. The model outputs are classified with respect to parameters to distinguish the extinction or endemicity of the bacterial strains. The role of stewardship of antibiotic use is analyzed for mitigation of these nosocomial epidemics.

Journal of Biological Dynamics, 2016

Optimal control methods are applied to a deterministic mathematical model to characterize the fac... more 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.

Mathematical Modelling of Natural Phenomena, 2010

Background: Community-acquired methicillin-resistant Staphylococcus aureus (CA-MRSA), a novel str... more Background: Community-acquired methicillin-resistant Staphylococcus aureus (CA-MRSA), a novel strain of MRSA, has recently emerged and rapidly spread in the community. Invasion into the hospital setting with replacement of the hospital-acquired MRSA (HA-MRSA) has also been documented. Co-colonization with both CA-MRSA and HA-MRSA would have important clinical implications given differences in antimicrobial susceptibility profiles and the potential for exchange of genetic information. Methods: A deterministic mathematical model was developed to characterize the transmission dynamics of HA-MRSA and CA-MRSA in the hospital setting and to quantify the emergence of co-colonization with both strains Results: The model analysis shows that the state of co-colonization becomes endemic over time and that typically there is no competitive exclusion of either strain. Increasing the length of stay or rate of hospital entry among patients colonized with CA-MRSA leads to a rapid increase in the co-colonized state. Compared to MRSA decolonization strategy, improving hand hygiene compliance has the greatest impact on decreasing the prevalence of HA-MRSA, CA-MRSA and the co-colonized state. Conclusions: The model predicts that with the expanding community reservoir of CA-MRSA, the majority of hospitalized patients will become colonized with both CA-MRSA and HA-MRSA.

Journal of Thoracic Oncology, 2012

Based on promising preclinical efficacy of bortezomib in mesothelioma, a single-arm phase II tria... more Based on promising preclinical efficacy of bortezomib in mesothelioma, a single-arm phase II trial (Ireland Cooperative Oncology Research Group 05-10 study), with Simon's two-stage design, was undertaken to assess efficacy of bortezomib monotherapy in the first-line (poor performance status) and second-line settings. The Bcl-2 homology domain 3-only protein Noxa has been implicated as a key inducer of apoptosis by bortezomib. Thus, in a biomarker research substudy, we hypothesized that deficiency in Noxa expression might correlate with resistance. In the second-line setting, 23 patients were enrolled. Partial response was confirmed in one patient (4.8%) who received four cycles of bortezomib. One patient had stable disease; however, progression occurred in the majority of patients within the first two cycles. Median progression-free survival and overall survival were 2.1 and 5.8 months, respectively. In the first-line setting, ten patients were accrued, and there was no evidence of objective response. In the tumor analysis, expression of Noxa was seen in all biopsies. Bortezomib monotherapy exhibits insufficient activity to warrant further investigation in unselected patients with mesothelioma.

Journal of Biological Chemistry, 2012

Background: The P-glycoprotein is expressed in many human cancers, where it contributes to multi-... more Background: The P-glycoprotein is expressed in many human cancers, where it contributes to multi-drug resistance phenomenon. Results: Both TnTs and microparticles contribute to the transfer of P-gp in MCF-7. Conclusion: Our findings supply new mechanistic evidences for the extragenetic emergence of MDR in cancer cells. Significance: Inhibition of both MPs and TnTs could be included in treatment strategies designed to overcome MDR. Multi-drug resistance (MDR) is a phenomenon by which tumor cells exhibit resistance to a variety of chemically unrelated chemotherapeutic drugs. The classical form of multidrug resistance is connected to overexpression of membrane P-glycoprotein (P-gp), which acts as an energy dependent drug efflux pump. P-glycoprotein expression is known to be controlled by genetic and epigenetic mechanisms. Until now processes of P-gp gene up-regulation and resistant cell selection were considered sufficient to explain the emergence of MDR phenotype within a cell population. Recently, however, "non-genetic" acquisitions of MDR by cell-to-cell P-gp transfers have been pointed out. In the present study we show that intercellular transfers of functional P-gp occur by two different but complementary modalities through donor-recipient cells interactions in the absence of drug selection pressure. P-glycoprotein and drug efflux activity transfers were followed over 7 days by confocal microscopy and flow cytometry in drug-sensitive parental MCF-7 breast cancer cells co-cultured with P-gp overexpressing resistant variants. An early process of remote transfer was established based on the release and binding of P-gp-containing microparticles. Microparticle-mediated transfers were detected after only 4 h of incubation. We also identify an alternative mode of transfer by contact, consisting of cell-to-cell P-gp trafficking by tunneling nanotubes bridging neighboring cells. Our findings supply new mechanistic evidences for the extragenetic emergence of MDR in cancer cells and indicate that new treatment strategies designed to overcome MDR may include inhibition of both microparticles and Tunneling nanotube-mediated intercellular P-gp transfers. of the Interreg IVA project Admin (Trans-Channel Advanced Microscopy network). □ S This article contains supplemental Fig. 1 and supplemental videos 1 and 2. 1 Recipient of a fellowship from the Conseil Regional de Haute-Normandie.

Emerging Infectious Diseases, 1997

Computational and Mathematical Methods in Medicine, 2009

We develop a state space model documenting Gompertz behaviour of tumour growth. The state space m... more We develop a state space model documenting Gompertz behaviour of tumour growth. The state space model consists of two sub-models: a stochastic system model that is an extension of the deterministic model proposed by Gyllenberg and Webb (1991), and an observation model that is a statistical model based on data for the total number of tumour cells over time. In the stochastic system model we derive through stochastic equations the probability distributions of the numbers of different types of tumour cells. Combining with the statistic model, we use these distribution results to develop a generalized Bayesian method and a Gibbs sampling procedure to estimate the unknown parameters and to predict the state variables (number of tumour cells). We apply these models and methods to real data and to computer simulated data to illustrate the usefulness of the models, the methods, and the procedures.

Bulletin of Mathematical Biology, 2004

Bajaria et al. during interruptions. Simulations predict that short-term viral suppression with v... more Bajaria et al. during interruptions. Simulations predict that short-term viral suppression with varying interruption strategies does not guarantee long-term clinical benefit.

ABSTRACT Materials and methods A deterministic HIV/AIDS model was developed in which a Bernoulli ... more ABSTRACT Materials and methods A deterministic HIV/AIDS model was developed in which a Bernoulli process was used to assess the relationship between per-act and per-partner probabilities of anal intercourse transmission over a given number of sex acts. The model incorporated condom use, HIV testing, risk-reduction and antiretroviral therapy as control strategies of preventing HIV transmission (Figure 1). Data for estimating parameters came from national and local HIV reporting and sentinel surveillance networks, Chinese free ART project database, local epidemiological studies and existing literature. Markov-Chain Monte-Carlo simulation was also carried out using the Metropolis-Hastings algorithm to estimate mean values of some parameters. Figure 1. Schematic diagram of compartments for uninfected and infected MSM with or without receiving HIV testing, risk reduction, and antiretroviral therapy (ART). S –uninfected, susceptible MSM; I-infected MSM. Subscript N presents those were not tested; T presents those were tested; R represents those received risk reduction; A represents those received ART. Superscript 1 refers to CD4 count ≥350 cells/mm3 and 2 refers to CD4 count<350. alpha: recruitment rate per year into target population; Mu: natural removal rate from compartment; kappa i (1; 2; 3): testing rates; lota i (1; 2; 3): linkage-to-risk reduction rates; rho i (1; 2) : progression rates of untreated infected MSM; tau i (1; 2) : treatment rates; theta i (1; 2) : drop out rates from ART; delta i (1) : progression rate for those on ART.

Clinical Infectious Diseases, 2009

Background. Methicillin-resistant Staphylococcus aureus (MRSA) has traditionally been associated ... more Background. Methicillin-resistant Staphylococcus aureus (MRSA) has traditionally been associated with infections in hospitals. Recently, a new strain of MRSA has emerged and rapidly spread in the community, causing serious infections among young, healthy individuals. Preliminary reports imply that a particular clone (USA300) of a community-acquired MRSA (CA-MRSA) strain is infiltrating hospitals and replacing the traditional hospitalacquired MRSA strains. If true, this event would have serious consequences, because CA-MRSA infections in hospitals would occur among a more debilitated, older patient population. Methods. A deterministic mathematical model was developed to characterize the factors contributing to the replacement of hospital-acquired MRSA with CA-MRSA and to quantify the effectiveness of interventions aimed at limiting the spread of CA-MRSA in health care settings. Results. The model strongly suggests that CA-MRSA will become the dominant MRSA strain in hospitals and health care facilities. This reversal of dominant strain will occur as a result of the documented expanding community reservoir and increasing influx into the hospital of individuals who harbor CA-MRSA. Competitive exclusion of hospital-acquired MRSA by CA-MRSA will occur, with increased severity of CA-MRSA infections resulting in longer hospitalizations and a larger in-hospital reservoir of CA-MRSA. Conclusions. Improving compliance with hand hygiene and screening for and decolonization of CA-MRSA carriers are effective strategies. However, hand hygiene has the greatest return of benefits and, if compliance is optimized, other strategies may have minimal added benefit.

Journal of Biological Dynamics, 2010

Modelling the invasion of community-acquired methicillin-resistant Staphylococcus aureus into the... more Modelling the invasion of community-acquired methicillin-resistant Staphylococcus aureus into the hospital setting, Clin. Infect. Dis. 48 (2009), pp. 274-284] proposed a deterministic mathematical model to characterize the factors contributing to the replacement of hospital-acquired methicillin-resistant Staphylococcus aureus (HA-MRSA) with the community-acquired MRSA (CA-MRSA) and to quantify the effectiveness of interventions aimed at limiting the spread of CA-MRSA in the hospital setting. Numerical simulations of the model strongly suggest that CA-MRSA will become the dominant MRSA strain in the hospital setting. In this companion paper, we provide steady-state analysis and more numerical simulations of the model. It is shown that when no colonized or infected patients enter the hospital, competitive exclusion of HA-MRSA by CA-MRSA will occur with increased severity of CA-MRSA infections resulting in longer hospitalizations and a larger in-hospital reservoir of CA-MRSA. Improving compliance with hand hygiene and decolonization of CA-MRSA carriers are effective control strategies.

This article aims to study the COVID-19 data for New York City. We use both the daily number of s... more This article aims to study the COVID-19 data for New York City. We use both the daily number of second does vaccination and the daily number of reported cases for New York City. This article provides a method to combine an epidemic model and such data. We explore the influence of vaccine efficacy on our results.

Computational and Mathematical Methods in Medicine, 2009

Transforming growth factor (TGF)-β is known to have properties of both a tumour suppressor and a ... more Transforming growth factor (TGF)-β is known to have properties of both a tumour suppressor and a tumour promoter. While it inhibits cell proliferation, it also increases cell motility and decreases cell–cell adhesion. Coupling mathematical modelling and experiments, we investigate the growth and motility of oncogene-expressing human mammary epithelial cells under exposure to TGF-β. We use a version of the well-known Fisher–Kolmogorov equation, and prescribe a procedure for its parametrisation. We quantify the simultaneous effects of TGF-β to increase the tendency of individual cells and cell clusters to move randomly and to decrease overall population growth. We demonstrate that in experiments with TGF-β treated cellsin vitro, TGF-β increases cell motility by a factor of 2 and decreases cell proliferation by a factor of 1/2 in comparison with untreated cells.