Epidemiologic data suggest that schools and daycare facilities likely play a major role in the dissemination of influenza. Pathogen transmission within such small, inhomogenously mixed populations is difficult to model using traditional approaches. We developed simulation based mathematical tool to investigate the effects of social contact networks on pathogen dissemination in a setting analogous to a daycare center or grade school. Here we show that interventions that decrease mixing within child care facilities, including limiting the size of social clusters, reducing the contact frequency between social clusters, and eliminating large gatherings, could diminish pathogen dissemination. Moreover, these measures may amplify the effectiveness of vaccination or antiviral prophylaxis, even if the vaccine is not uniformly effective or antiviral compliance is incomplete. Similar considerations should apply to other small, imperfectly mixed populations, such as offices and schools.

Hematologic disorders such as the myelodysplastic syndromes (MDS) are discussed. The lingering controversies related to various diseases are highlighted. A simple biomathematical model of bone marrow - peripheral blood dynamics in the normal state is proposed and used to investigate cell behavior in normal hematopoiesis from a mathematical viewpoint. Analysis of the steady state and properties of the model are used to make postulations about the phenomenon of massive apoptosis in MDS. Simulations of the model show situations in which homeostatic equilibrium can be achieved and maintained. Consequently, it is postulated that hematopoietic growth factors may possess the capabilities of preventing oscillatory dynamics and enhancing faster evolution towards homeostatic equilibrium.

Epidermal wound healing is a complex process that repairs injured tissue. The complexity of this process increases when bacteria are present in a wound; the bacteria interaction determines whether infection sets in. Because of underlying physiological problems infected wounds do not follow the normal healing pattern. In this paper we present a mathematical model of the healing of both infected and uninfected wounds. At the core of our model is an account of the initiation of angiogenesis by macrophage-derived growth factors. We express the model as a system of reaction-diffusion equations, and we present results of computations for a version of the model with one spatial dimension.

Solid tumors and hematological cancers contain small population of tumor cells that are believed to play a critical role in the development and progression of the disease. These cells, named Cancer Stem Cells (CSCs), have been found in leukemia, myeloma, breast, prostate, pancreas, colon, brain and lung cancers. It is also thought that CSCs drive the metastatic spread of cancer. The CSC compartment features a specific and phenotypically defined cell population characterized with self-renewal (through mutations), quiescence or slow cycling, overexpression of anti-apoptotic proteins, multidrug resistance and impaired differentiation. CSCs show resistance to a number of conventional therapies, and it is believed that this explains why it is difficult to completely eradicate the disease and why recurrence is an ever-present threat. A hierarchical phenomenological model is proposed based on eight compartments following the stem cell lineage at the normal and cancer cell levels. As an empirical test, the tumor grading and progression, typically collected in the pathologic lab, is used to correlate the outcome of this model with the tumor development stages. In addition, the model is able to quantitatively account for the temporal development of the population of observed cell types. Two types of therapeutic treatment models are considered, with dose-density chemotherapy (a pulsatile scenario) as well as continuous, metronomic delivery. The drug hit is considered at the stem cell progenitor and early differentiated specialized cell levels for both normal and cancer cells, while the quiescent stem cell and fully differentiated compartments are considered favorable outcome for cancer treatment. Circulating progenitors are neglected in this analysis. The model provides a number of experimentally testable predictions. The relative importance of the cell kill and survival is demonstrated through a deterministic parametric study. The significance of the stem cell compartment is underlined based on this simulation study. This predictive mathematical model for cancer stem cell hypothesis is used to understand tumor responses to chemotherapeutic agents and judge the efficacy.

In this paper, we look at a model depicting the relationship of cancer cells in different development stages with immune cells and a cell cycle specific chemotherapy drug. The model includes a constant delay in the mitotic phase. By applying optimal control theory, we seek to minimize the cost associated with the chemotherapy drug and to minimize the number of tumor cells. Global existence of a solution has been shown for this model and existence of an optimal control has also been proven. Optimality conditions and characterization of the control are discussed.

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.

Motivated by structured parasite populations in aquaculture we consider a class of size-structured population models, where individuals may be recruited into the population with distributed states at birth. The mathematical model which describes the evolution of such a population is a first-order nonlinear partial integro-differential equation of hyperbolic type. First, we use positive perturbation arguments and utilise results from the spectral theory of semigroups to establish conditions for the existence of a positive equilibrium solution of our model. Then, we formulate conditions that guarantee that the linearised system is governed by a positive quasicontraction semigroup on the biologically relevant state space. We also show that the governing linear semigroup is eventually compact, hence growth properties of the semigroup are determined by the spectrum of its generator. In the case of a separable fertility function, we deduce a characteristic equation, and investigate the stability of equilibrium solutions in the general case using positive perturbation arguments.

In proteomics study, Imaging Mass Spectrometry (IMS) is an emerging and very promising new technique for protein analysis from intact biological tissues. Though it has shown great potential and is very promising for rapid mapping of protein localization and the detection of sizeable differences in protein expression, challenges remain in data processing due to the difficulty of high dimensionality and the fact that the number of input variables in prediction model is significantly larger than the number of observations. To obtain a complete overview of IMS data and find trace features based on both spectral and spatial patterns, one faces a global optimization problem. In this paper, we propose a weighted elastic net (WEN) model based on IMS data processing needs of using both the spectral and spatial information for biomarker selection and classification. Properties including variable selection accuracy of the WEN model are discussed. Experimental IMS data analysis results show that such a model not only reduces the number of side features but also helps new biomarkers discovery.

Natural immunity to breast and prostate cancers is predicted by a novel, saturated ordered mutation model fitted to USA (SEER) incidence data, a prediction consistent with the latest ideas in immunosurveillance. For example, the prevalence of natural immunity to breast cancer in the white female risk population is predicted to be 76.5%; this immunity may be genetic and, therefore, inherited. The modeling also predicts that 6.9% of White Females are born with a mutation necessary to cause breast cancer (the hereditary form) and, therefore, are at the highest risk of developing it. By contrast, 16.6% of White Females are born without any such mutation but are nonetheless susceptible to developing breast cancer (the sporadic form). The modeling determines the required number of ordered mutations for a cell to become cancerous as well as the mean time between consecutive mutations for both the sporadic and hereditary forms of the disease. The mean time between consecutive breast cancer mutations was found to vary between 2.59 - 2.97 years, suggesting that such mutations are rare events and establishing an upper bound on the lifetime of a breast cell. The prevalence of immunity to breast cancer is predicted to be 79.7% in Blacks, 86.5% in Asians, and 85.8% in Indians. Similarly, the prevalence of immunity to prostate cancer is predicted to be 67.4% for Whites, 50.5% for Blacks, 77.7% for Asians, and 78.6% for Indians. It is of paramount importance to delineate the mechanism underlying immunity to these cancers.

Real-world medical decisions rarely involve binary Ðsole condition present or absent- patterns of patient pathophysiology. Similarly, provider interventions are rarely unitary in nature: the clinician often undertakes multiple interventions simultaneously. Conventional approaches towards complex physiologic derangements and their associated management focus on the frequencies of joint appearances, treating the individual derangements of physiology or elements of intervention as conceptually isolated. This framework is ill suited to capture either the integrated patterns of derangement displayed by a particular patient or the integrated patterns of provider intervention. Here we illustrate the application of a different approach-that of symbolic dynamics-in which the integrated pattern of each patients derangement, and the associated provider response, are captured by defining words based on the elements of the pattern of failure. We will use as an example provider practices in the context of mechanical ventilation- a common, potentially harmful, and complex life support technology. We also delineate other domains in which symbolic dynamics approaches might aid in quantitating practice patterns, assessing quality of care, and identifying best practices.

This paper extends the volume filling chemotaxis model [18, 26] by taking into account the cell population interactions. The extended chemotaxis models have nonlinear diffusion and chemotactic sensitivity depending on cell population density, which is a modification of the classical Keller-Segel model in which the diffusion and chemotactic sensitivity are constants (linear). The existence and boundedness of global solutions of these models are discussed and the numerical pattern formations are shown. The further improvement is proposed in the end.

Early studies of the novel swine-origin 2009 influenza A (H1N1) epidemic indicate clinical attack rates in children much higher than in adults. Non-medical interventions such as school closings are constrained by their large socio-economic costs. Here we develop a mathematical model to ascertain the roles of pre-symptomatic influenza transmission as well as symptoms surveillance of children to assess the utility of school closures. Our model analysis indicates that school closings are advisable when pre-symptomatic transmission is significant or when removal of symptomatic children is inefficient. Our objective is to provide a rational basis for school closings decisions dependent on virulence characteristics and local surveillance implementation, applicable to the current epidemic and future epidemics.

In this paper we study the error rate of RNA synthesis in the look-ahead model for the random walk of RNA polymerase along DNA during transcription. The model’s central assumption is the existence of a window of activity in which ribonucleoside triphosphates (rNTPs) bind reversibly to the template DNA strand before being hydrolyzed and linked covalently to the nascent RNA chain. An unknown, but important, integer parameter of this model is the window size w. Here, we use mathematical analysis and computer simulation to study the rate at which transcriptional errors occur as a function of w. We find dramatic reduction in the error rate of transcription as w increases, especially for small values of w. The error reduction method provided by look-ahead occurs before hydrolysis and covalent linkage of rNTP to the nascent RNA chain, and is therefore distinct from error correction mechanisms that have previously been considered.