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Cell dynamics in the vicinity of the vascular wall involves several factors of mechanical or biochemical origins. It is driven by the competition between the drag force of the blood flow and the resistive force generated by the bonds created between the circulating cell and the endothelial wall. Here, we propose a minimal mathematical model for the adhesive interaction between a circulating cell and the blood vessel wall in shear flow when the cell shape is neglected. The bond dynamics in cell adhesion is modeled as a nonlinear Markovian Jump process that takes into account the growth of adhesion complexes. Performing scaling limits in the spirit of Joffe and Metivier (Adv Appl Probab 18(1):20, 1986), Ethier and Kurtz (Markov processes: characterization and convergence, Wiley, New York, 2009), we obtain deterministic and stochastic continuous models, whose analysis allow to identify a threshold shear velocity associated with the transition from cell rolling and firm adhesion. We also give an estimation of the mean stopping time of the cell resulting from this dynamics. We believe these results can have strong implications for the understanding of major biological phenomena such as cell immunity and metastatic development. [ABSTRACT FROM AUTHOR]

We develop new techniques involving group symmetries and complex analysis to obtain exact solutions for the transition probabilities of the M/M/1/k queueing process. These methods are based on the underlying Markovian structure of these random processes and do not involve any generating functions, Laplace transforms, or advanced special functions. Our techniques exploit the intrinsic group symmetries for both the state spaces and the matrix generators of the Markov processes related to the M/M/1/k queue. These results complement and extend the previous transient solutions given by Takács (Introduction to the theory of queues. University texts in the mathematical sciences, Oxford University Press, New York, 1962). Much of the inspiration for this work comes from viewing this queueing process as a fundamental Markovian model for the dynamics of a bike sharing station. The exact transient analysis for a related stopped version of this process can be used to address fundamental decision-making issues for managing bike-sharing services. [ABSTRACT FROM AUTHOR]

A novel optimization algorithm for stable parameter estimation and forecasting from limited incidence data for an emerging outbreak is proposed. The algorithm combines a compartmental model of disease progression with iteratively regularized predictor-corrector numerical scheme aimed at the reconstruction of case reporting ratio, transmission rate, and effective reproduction number. The algorithm is illustrated with real data on COVID-19 pandemic in the states of Georgia and New York, USA. The techniques of functional data analysis are applied for uncertainty quantification in extracted parameters and in future projections of new cases. [ABSTRACT FROM AUTHOR]

Modeling infectious disease dynamics has been critical throughout the COVID-19 pandemic. Of particular interest are the incidence, prevalence, and effective reproductive number (Rt). Estimating these quantities is challenging due to under-ascertainment, unreliable reporting, and time lags between infection, onset, and testing. We propose a Multilevel Epidemic Regression Model to Account for Incomplete Data (MERMAID) to jointly estimate Rt, ascertainment rates, incidence, and prevalence over time in one or multiple regions. Specifically, MERMAID allows for a flexible regression model of Rt that can incorporate geographic and time-varying covariates. To account for under-ascertainment, we (a) model the ascertainment probability over time as a function of testing metrics and (b) jointly model data on confirmed infections and population-based serological surveys. To account for delays between infection, onset, and reporting, we model stochastic lag times as missing data, and develop an EM algorithm to estimate the model parameters. We evaluate the performance of MERMAID in simulation studies, and assess its robustness by conducting sensitivity analyses in a range of scenarios of model misspecifications. We apply the proposed method to analyze COVID-19 daily confirmed infection counts, PCR testing data, and serological survey data across the United States. Based on our model, we estimate an overall COVID-19 prevalence of 12.5% (ranging from 2.4% in Maine to 20.2% in New York) and an overall ascertainment rate of 45.5% (ranging from 22.5% in New York to 81.3% in Rhode Island) in the United States from March to December 2020. for this article, including a standardized description of the materials available for reproducing the work, are available as an online supplement. [ABSTRACT FROM AUTHOR]

Dubins and Savage (How to gamble if you must: inequalities for stochastic processes, McGraw-Hill, New York, 1965) found an optimal strategy for limsup gambling problems in which a player has at most two choices at every state x at most one of which could differ from the point mass δ (x) . Their result is extended here to a family of two-person, zero-sum stochastic games in which each player is similarly restricted. For these games we show that player 1 always has a pure optimal stationary strategy and that player 2 has a pure ϵ -optimal stationary strategy for every ϵ > 0 . However, player 2 has no optimal strategy in general. A generalization to n-person games is formulated and ϵ -equilibria are constructed. [ABSTRACT FROM AUTHOR]

Introduction: Prenatal smoking exposure may lead to permanent changes in neonatal inflammation and immune response that have lifelong implications, including increased risks for atopy and respiratory disorders.Methods: The effect of maternal smoking on neonatal biomarkers of inflammation and immune response was assessed among 3459 singletons and twins in the Upstate KIDS Study. The following inflammatory biomarkers were measured using newborn dried blood spots (DBSs): interleukin (IL)-1α, IL-1 receptor antagonist, IL-6, IL-8, C-reactive protein, and tumor necrosis factor alpha. Immunoglobulins (IgE, IgA, IgM, and IgG subclasses) were also assessed. We used generalized estimating equations to calculate mean differences (β) in biomarker levels by timing of pregnancy smoking, cigarette load, and secondhand smoke exposure after adjusting for sociodemographic and lifestyle factors including maternal body mass index.Results: Of the 344 (12%) women reporting smoking during pregnancy, about 40% continued throughout pregnancy and 13% reported smoking more than 1 pack per day. After covariate adjustment and Bonferroni correction for multiple comparisons, maternal smoking throughout pregnancy remained significantly associated with increased levels of IL-8 (β = 0.20, 95% confidence interval: 0.07, 0.32; p < .003). No significant associations were found with cigarette load or secondhand smoke exposure. Higher IgG3 levels were also associated with maternal smoking throughout pregnancy, although the association became nominally significant after adjustment for covariates (β = 0.09; 95% confidence interval: 0.0007, 0.17; p < .05).Conclusions: Maternal smoking throughout pregnancy was independently associated with increased IL-8 levels in newborns. Importantly, neonates of women who stopped smoking anytime in pregnancy did not have increased IL-8 levels.Implications: This study evaluated a range of inflammatory biomarkers and immunoglobulins in association with maternal smoking and timing/duration of smoking along with secondhand smoke exposure. By using DBSs, we present data from a large cohort of children born in Upstate New York. Our findings suggest that early differences in immunoregulation of neonates exposed to maternal smoking for full duration in utero may already be detected at birth. [ABSTRACT FROM AUTHOR]

Background: Antenatal magnesium in preterm labor for neuroprotection decreases the incidence of cerebral palsy. However, there are no guidelines on the dose and duration of magnesium infusion for neuroprotection. As increased neonatal serum magnesium concentrations may be related to higher risk of morbidity and mortality, the role of total amount of magnesium and maternal serum magnesium concentrations associated with safe neonatal serum magnesium concentrations is not known. Methods: A retrospective study was conducted on 289 mothers who received antenatal magnesium for neuroprotection as a loading dose of 4-6 g infused over 30 min, followed by a maintenance infusion of 1-2 g/h. Total magnesium dose infused to the mother and maternal serum magnesium concentrations were correlated with neonatal serum magnesium concentrations. Results: Of the 289 mothers, 192 mother/baby dyads had all three measurements (maternal total magnesium dose, and maternal and neonatal serum magnesium concentrations). Magnesium infusion was continued beyond 24 h in 60 mothers. Total maternal magnesium dose at 24 and 48 h of infusion correlated with neonatal serum magnesium concentrations (r=0.55, P<0.0001 and r=0.35, P<0.0001, respectively), but not with maternal serum magnesium concentrations (r=0.004, P=0.98 and r=0.14, P=0.21). However, there was no correlation between the maternal and neonatal serum magnesium concentrations (r=0.10, P=0.15). Conclusion: Total dose of magnesium infused to the mother correlates with neonatal serum magnesium concentrations. To keep neonatal serum magnesium concentrations within a range that is effective for neuroprotection and safe for the neonates, the total dose received by the mother needs to be monitored and limited. [ABSTRACT FROM AUTHOR]