Epidemiologic data suggest that schools and daycare facilities likely play a major rolein the dissemination of influenza. Pathogen transmission within such small, inhomogenouslymixed populations is difficult to model using traditional approaches. We developedsimulation based mathematical tool to investigate the effects of social contact networkson pathogen dissemination in a setting analogous to a daycare center or grade school. Herewe show that interventions that decrease mixing within child care facilities, includinglimiting the size of social clusters, reducing the contact frequency between socialclusters, and eliminating large gatherings, could diminish pathogen dissemination.Moreover, these measures may amplify the effectiveness of vaccination or antiviralprophylaxis, even if the vaccine is not uniformly effective or antiviral compliance isincomplete. Similar considerations should apply to other small, imperfectly mixedpopulations, such as offices and schools.

Hematologic disorders such as the myelodysplastic syndromes (MDS) are discussed. Thelingering controversies related to various diseases are highlighted. A simplebiomathematical model of bone marrow - peripheral blood dynamics in the normal state isproposed and used to investigate cell behavior in normal hematopoiesis from a mathematicalviewpoint. Analysis of the steady state and properties of the model are used to makepostulations about the phenomenon of massive apoptosis in MDS. Simulations of the modelshow situations in which homeostatic equilibrium can be achieved and maintained.Consequently, it is postulated that hematopoietic growth factors may possess thecapabilities of preventing oscillatory dynamics and enhancing faster evolution towardshomeostatic equilibrium.

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

Solid tumors and hematological cancers contain small population of tumor cells that arebelieved to play a critical role in the development and progression of the disease. Thesecells, 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 themetastatic spread of cancer. The CSC compartment features a specific and phenotypicallydefined cell population characterized with self-renewal (through mutations), quiescence orslow cycling, overexpression of anti-apoptotic proteins, multidrug resistance and impaireddifferentiation. CSCs show resistance to a number of conventional therapies, and it isbelieved that this explains why it is difficult to completely eradicate the disease andwhy recurrence is an ever-present threat. A hierarchical phenomenological model isproposed based on eight compartments following the stem cell lineage at the normal andcancer cell levels. As an empirical test, the tumor grading and progression, typicallycollected in the pathologic lab, is used to correlate the outcome of this model with thetumor development stages. In addition, the model is able to quantitatively account for thetemporal development of the population of observed cell types. Two types of therapeutictreatment models are considered, with dose-density chemotherapy (a pulsatile scenario) aswell as continuous, metronomic delivery. The drug hit is considered at the stem cellprogenitor and early differentiated specialized cell levels for both normal and cancercells, while the quiescent stem cell and fully differentiated compartments are consideredfavorable outcome for cancer treatment. Circulating progenitors are neglected in thisanalysis. The model provides a number of experimentally testable predictions. The relativeimportance of the cell kill and survival is demonstrated through a deterministicparametric study. The significance of the stem cell compartment is underlined based onthis simulation study. This predictive mathematical model for cancer stem cell hypothesisis used to understand tumor responses to chemotherapeutic agents and judge theefficacy.

In this paper, we look at a model depicting the relationship of cancer cells in differentdevelopment stages with immune cells and a cell cycle specific chemotherapy drug. Themodel 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 thenumber of tumor cells. Global existence of a solution has been shown for this model andexistence of an optimal control has also been proven. Optimality conditions andcharacterization of the control are discussed.

Background: Community-acquired methicillin-resistant Staphylococcusaureus (CA-MRSA), a novel strain of MRSA, has recently emerged and rapidlyspread in the community. Invasion into the hospital setting with replacement of thehospital-acquired MRSA (HA-MRSA) has also been documented. Co-colonization with bothCA-MRSA and HA-MRSA would have important clinical implications given differences inantimicrobial susceptibility profiles and the potential for exchange of geneticinformation.

Methods: A deterministic mathematical model was developed to characterizethe transmission dynamics of HA-MRSA and CA-MRSA in the hospital setting and to quantifythe emergence of co-colonization with both strains

Results: The model analysis shows that the state of co-colonization becomesendemic 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 withCA-MRSA leads to a rapid increase in the co-colonized state. Compared to MRSAdecolonization strategy, improving hand hygiene compliance has the greatest impact ondecreasing the prevalence of HA-MRSA, CA-MRSA and the co-colonized state.

Conclusions: The model predicts that with the expanding community reservoirof CA-MRSA, the majority of hospitalized patients will become colonized with both CA-MRSAand HA-MRSA.

Motivated by structured parasite populations in aquaculture we consider a class ofsize-structured population models, where individuals may be recruited into the populationwith distributed states at birth. The mathematical model which describes the evolution ofsuch a population is a first-order nonlinear partial integro-differential equation ofhyperbolic type. First, we use positive perturbation arguments and utilise results fromthe spectral theory of semigroups to establish conditions for the existence of a positiveequilibrium solution of our model. Then, we formulate conditions that guarantee that thelinearised system is governed by a positive quasicontraction semigroup on the biologicallyrelevant state space. We also show that the governing linear semigroup is eventuallycompact, hence growth properties of the semigroup are determined by the spectrum of itsgenerator. In the case of a separable fertility function, we deduce a characteristicequation, and investigate the stability of equilibrium solutions in the general case usingpositive perturbation arguments.

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

Natural immunity to breast and prostate cancers is predicted by a novel, saturatedordered mutation model fitted to USA (SEER) incidence data, a prediction consistent withthe latest ideas in immunosurveillance. For example, the prevalence of natural immunity tobreast cancer in the white female risk population is predicted to be 76.5%; this immunitymay be genetic and, therefore, inherited. The modeling also predicts that 6.9% of WhiteFemales are born with a mutation necessary to cause breast cancer (the hereditaryform) 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 susceptibleto developing breast cancer (the sporadic form). The modeling determinesthe required number of ordered mutations for a cell to become cancerous as well as themean time between consecutive mutations for both the sporadic and hereditary forms of thedisease. The mean time between consecutive breast cancer mutations was found to varybetween 2.59 - 2.97 years, suggesting that such mutations are rare events and establishingan upper bound on the lifetime of a breast cell. The prevalence of immunity to breastcancer 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% forWhites, 50.5% for Blacks, 77.7% for Asians, and 78.6% for Indians. It is of paramountimportance 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 unitaryin nature: the clinician often undertakes multiple interventions simultaneously.Conventional approaches towards complex physiologic derangements and their associatedmanagement focus on the frequencies of joint appearances, treating the individualderangements of physiology or elements of intervention as conceptually isolated. Thisframework is ill suited to capture either the integrated patterns of derangement displayedby a particular patient or the integrated patterns of provider intervention. Here weillustrate the application of a different approach-that of symbolic dynamics-in which theintegrated pattern of each patients derangement, and the associated provider response, arecaptured by defining words based on the elements of the pattern offailure. We will use as an example provider practices in the context of mechanicalventilation- a common, potentially harmful, and complex life support technology. We alsodelineate other domains in which symbolic dynamics approaches might aid in quantitatingpractice 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. Theextended chemotaxis models have nonlinear diffusion and chemotactic sensitivity dependingon cell population density, which is a modification of the classical Keller-Segel model inwhich the diffusion and chemotactic sensitivity are constants (linear). The existence andboundedness of global solutions of these models are discussed and the numerical patternformations are shown. The further improvement is proposed in the end.

Early studies of the novel swine-origin 2009 influenza A (H1N1) epidemic indicateclinical attack rates in children much higher than in adults. Non-medical interventionssuch as school closings are constrained by their large socio-economic costs. Here wedevelop a mathematical model to ascertain the roles of pre-symptomatic influenzatransmission as well as symptoms surveillance of children to assess the utility of schoolclosures. Our model analysis indicates that school closings are advisable whenpre-symptomatic transmission is significant or when removal of symptomatic children isinefficient. Our objective is to provide a rational basis for school closings decisionsdependent on virulence characteristics and local surveillance implementation, applicableto the current epidemic and future epidemics.

In this paper we study the error rate of RNA synthesis in the look-ahead model for therandom walk of RNA polymerase along DNA during transcription. The model’s centralassumption is the existence of a window of activity in whichribonucleoside triphosphates (rNTPs) bind reversibly to the template DNA strand beforebeing hydrolyzed and linked covalently to the nascent RNA chain. An unknown, butimportant, integer parameter of this model is the window size w. Here, weuse mathematical analysis and computer simulation to study the rate at whichtranscriptional errors occur as a function of w. We find dramaticreduction in the error rate of transcription as w increases, especiallyfor small values of w. The error reduction method provided by look-aheadoccurs before hydrolysis and covalent linkage of rNTP to the nascent RNAchain, and is therefore distinct from error correction mechanisms that have previouslybeen considered.