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. The model is applied to the cholera outbreak in Haiti in 2010.

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. Compared with the baseline (λ = 0.0001), we found the new HIV cases would reduce with the increase of coverage rates of the voluntary medical male circumcision (VMMC) among men who have sex wtih men (MSM). The higher the coverage rate, the lower the new HIV incidence would be. As one of the first studies to model the potential impact of VMMC among MSM in China, our model suggested a modest to the significant public health impact of VMMC. Even at just 15% VMMC annual uptake rate, the reduction in new infections is substantial. Therefore, there is a strong need to determine the efficacy of VMMC among MSM, to improve the evidence base for its potential use among MSM in low circumcision settings. Only then can policymakers decide whether to incorporate VMMC into a package of HIV prevention interventions targeting MSM.

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. The disease is transmitted through vector and host populations in criss-cross fashion. We establish global well-posedness and uniform a prior bounds as well as the long-term behavior. The model is applied to simulate the outbreak of bluetongue disease in sheep transmitted by midges infected with bluetongue virus. We show that the long-range directed movement of the midge population, due to wind-aided movement, enhances the transmission of the disease to sheep in distant sites.

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 0.0001 to 0.15. The 'number needed to avert' (NNA) is defined as the cumulative number of VMMCs conducted up to that year divided by the cumulative number of HIV cases averted in that specific year. Compared with the baseline circumcision coverage rate, we projected that new HIV cases would be reduced with increasing coverage. By 2026 (last year simulated), the model generated the lowest ratio (11.10) when the annual circumcision rate was the most optimistic (λ = 0.15). The breakeven point was observed at the year of 2019 with the annual VMMC coverage rate of 0.001. The total cost saved by averting HIV cases would range from 2.5 to 811 million US dollars by the end of 2026 with different hypothetical coverage rates. Our model suggests that acceleration in VMMC implementation among MSM could help stem the HIV/AIDS epidemic.

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.

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.

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. The model is interpreted to provide insight for controlling these nosocomial epidemics.

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. We hypothesize that the age structure of early humans was maintained by mechanisms incorporating the programmed death of senescent individuals, including by means of interactions with their indigenous microorganisms. First, before and during reproductive life, there was selection for microbes that preserve host function through regulation of energy homeostasis, promotion of fecundity, and defense against competing high-grade pathogens. Second, we hypothesize that after reproductive life, there was selection for organisms that contribute to host demise. While deleterious to the individual, the presence of such interplay may be salutary for the overall host population in terms of resource utilization, resistance to periodic diminutions in the food supply, and epidemics due to high-grade pathogens. We provide deterministic mathematical models based on age-structured populations that illustrate the dynamics of such relationships and explore the relevant parameter values within which population viability is maintained. We argue that the age structure of early humans was robust in its balance of the juvenile, reproductive-age, and senescent classes. These concepts are relevant to issues in modern human longevity, including inflammation-induced neoplasia and degenerative diseases of the elderly, which are a legacy of human evolution. IMPORTANCE: The extended longevity of modern humans is a very recent societal artifact, although it is inherent in human evolution. The age structure of early humans was balanced by fertility and mortality, with an exceptionally prolonged juvenility. We examined the role of indigenous microbes in early humans as fundamental contributors to this age structure. We hypothesize that the human microbiome evolved mechanisms specific to the mortality of senescent individuals among early humans because their mortality contributed to the stability of the general population. The hypothesis that we present provides new bases for modern medical problems, such as inflammation-induced neoplasia and degenerative diseases of the elderly. We postulate that these mechanisms evolved because they contributed to the stability of early human populations, but their legacy is now a burden on human longevity in the changed modern world.

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. RESULTS: The basic reproduction number based upon the current level of interventions is significantly higher than 1 (R0 = 2.09; 95% confidence interval (CI), 1.83-2.35), suggesting that the HIV epidemic will continue to increase to 2020. Compared to the 2010 prevalence of 7.8%, the projected HIV prevalence in 2020 for the five prevention scenarios will be: (S1) Current coverage: 21.4% (95% CI, 9.9-31.7%); (S2) Increased ART: 19.9% (95% CI, 9.9-28.4%); (S3) Increased TLC/ART: 14.5% (95% CI, 7.0-23.8%); (S4) Increased condom use: 13.0% (95% CI, 9.8-28.4%); and (S5) Increased TLC/ART and condom use: 8.7% (95% CI, 5.4-11.5%). HIV epidemic will continue to rise (R0 > 1) for S1-S4 even with hyperbolic coverage in the sensitivity analysis, and is expected to decline (R0 = 0.93) for S5. CONCLUSION: Our transmission model suggests that Beijing MSM will have a rapidly rising HIV epidemic. Even enhanced levels of TLC/ART will not interrupt epidemic expansion, despite optimistic assumptions for coverage. Promoting condom use is a crucial component of combination interventions.

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 ß-amyloid plaques based on the concentrations of Aß oligomers, PrP(C) proteins, and the Aß-x-Aß-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 Aß-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. Biol. 243 (2006), pp. 98-113], is considered. The model consists of a nonlinear partial differential equation for the cell density in an N-dimensional infinite domain. It has a non-local flux term which models the component of cell motion attributable to cells having formed bonds with other nearby cells. Using the theory of fractional powers of analytic semigroup generators and working in spaces with bounded uniformly continuous derivatives, the local existence of classical solutions is proved. Positivity and boundedness of solutions is then established, leading to global existence of solutions. Finally, the asymptotic behaviour of solutions about the spatially uniform state is considered. The model is illustrated by simulations that can be applied to in vitro wound closure experiments.

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. An alternative approach is to determine the age structure in the population and account for the cell cycle positional effects post hoc. Here we provide a formalism to use quantifiable lifespans from live cell microscopy experiments to parameterize an age-structured model of cell population response.

Mathematical model of the impact of a nonantibiotic treatment for Clostridium difficile on the endemic prevalence of vancomycin-resistant enterococci in a hospital setting.

INTRODUCTION: Clostridium difficile-associated disease (CDAD) is treated using antibiotics, which often leads to the emergence of antibiotic-resistant bacteria such as vancomycin-resistant enterococci (VRE). This study estimated the impact of a non antibiotic treatment for CDAD on VRE prevalence. METHODS: A previously published model describing the impact of in-hospital antibiotic use on VRE prevalence was adapted to include CDAD treatment. Simulations compared the prevalence of VRE when nonantibiotic versus antibiotic therapy was used. RESULTS: Nonantibiotic treatment in 50% of CDAD patients resulted in an 18% relative reduction in the prevalence of VRE colonization compared with antibiotic use only. Sensitivity analysis found the model to be most sensitive to rates of antibiotic initiation and discontinuation, prevalence of VRE in admitted patients, length of stay of colonized patients, probability of CDAD acquisition, and hand-washing compliance. CONCLUSION: Nonantibiotic treatment of patients hospitalized with CDAD may significantly reduce the incidence of VRE colonization.

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. We find that most recommended strategies have substantial effect in decreasing the prevalence of MDRO over time. However, screening for asymptomatic MDRO colonization among patients who are not receiving antimicrobials is of minimal value in reducing the spread of MDRO.

A mathematical model of bone remodeling dynamics for normal bone cell populations and myeloma bone disease.

BACKGROUND: Multiple myeloma is a hematologic malignancy associated with the development of a destructive osteolytic bone disease. RESULTS: Mathematical models are developed for normal bone remodeling and for the dysregulated bone remodeling that occurs in myeloma bone disease. The models examine the critical signaling between osteoclasts (bone resorption) and osteoblasts (bone formation). The interactions of osteoclasts and osteoblasts are modeled as a system of differential equations for these cell populations, which exhibit stable oscillations in the normal case and unstable oscillations in the myeloma case. In the case of untreated myeloma, osteoclasts increase and osteoblasts decrease, with net bone loss as the tumor grows. The therapeutic effects of targeting both myeloma cells and cells of the bone marrow microenvironment on these dynamics are examined. CONCLUSIONS: The current model accurately reflects myeloma bone disease and illustrates how treatment approaches may be investigated using such computational approaches. REVIEWERS: This article was reviewed by Ariosto Silva and Mark P. Little.

The effect of co-colonization with community-acquired and hospital-acquired methicillin-resistant Staphylococcus aureus strains on competitive exclusion.

We investigate the in-hospital transmission dynamics of two methicillin-resistant Staphylococcus aureus (MRSA) strains: hospital-acquired methicillin resistant S. aureus (HA-MRSA) and community-acquired methicillin-resistant S. aureus (CA-MRSA). Under the assumption that patients can only be colonized with one strain of MRSA at a time, global results show that competitive exclusion occurs between HA-MRSA and CA-MRSA strains; the strain with the larger basic reproduction ratio will become endemic while the other is extinguished due to competition. Because new studies suggest that patients can be concurrently colonized with multiple strains of MRSA, we extend the model to allow patients to be co-colonized with HA-MRSA and CA-MRSA. Using the extended model, we explore the effect of co-colonization on competitive exclusion by determining the invasion reproduction ratios of the boundary equilibria. In contrast to results derived from the assumption that co-colonization does not occur, the extended model rarely exhibits competitive exclusion. More commonly, both strains become endemic in the hospital. When transmission rates are assumed equal and decolonization measures act equally on all strains, competitive exclusion never occurs. Other interesting phenomena are exhibited. For example, solutions can tend toward a co-existence equilibrium, even when the basic reproduction ratio of one of the strains is less than one.

Competition of hospital-acquired and community-acquired methicillin-resistant Staphylococcus aureus strains in hospitals.

Recently, we [E.M.C. D'Agata, G.F. Webb, M.A. Horn, R.C. Moellering Jr., and S. Ruan, Modellingthe invasion of community-acquired methicillin-resistant Staphylococcus aureus into the hospital setting, Clin. Infect. Dis. 48 (2009), pp. 274­284] 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 interventionsaimed 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.

Modeling the invasion of community-acquired methicillin-resistant Staphylococcus aureus into hospitals.

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 hospital-acquired 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.

A mathematical model quantifies proliferation and motility effects of TGF-ß on cancer cells.

Transforming growth factor (TGF)-ß 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-ß. 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-ß 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-ß treated cells in vitro, TGF-ß increases cell motility by a factor of 2 and decreases cell proliferation by a factor of 1/2 in comparison with untreated cells.

A fully continuous individual-based model of tumor cell evolution.

The aim of this work is to develop and study a fully continuous individual-based model (IBM) for cancer tumor invasion into a spatial environment of surrounding tissue. The IBM improves previous spatially discrete models, because it is continuous in all variables (including spatial variables), and thus not constrained to lattice frameworks. The IBM includes four types of individual elements: tumor cells, extracellular macromolecules (MM), a matrix degradative enzyme (MDE), and oxygen. The algorithm underlying the IBM is based on the dynamic interaction of these four elements in the spatial environment, with special consideration of mutation phenotypes. A set of stochastic differential equations is formulated to describe the evolution of the IBM in an equivalent way. The IBM is scaled up to a system of partial differential equations (PDE) representing the limiting behavior of the IBM as the number of cells and molecules approaches infinity. Both models (IBM and PDE) are numerically simulated with two kinds of initial conditions: homogeneous MM distribution and heterogeneous MM distribution. With both kinds of initial MM distributions spatial fingering patterns appear in the tumor growth. The output of both simulations is quite similar.