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Abstract The drug-overdose crisis in the United States continues to intensify. Fatalities have increased 5-fold since 1999 reaching a record high of 108,000 deaths in 2021. The epidemic has unfolded through distinct waves of different drug types, uniquely impacting various age, gender, race, and ethnic groups in specific geographical areas. One major challenge in designing interventions and efficiently delivering treatment is forecasting age-specific overdose patterns at the local level. To address this need, we develop a forecasting method that assimilates observational data obtained from the CDC WONDER database with an age-structured model of addiction and overdose mortality. We apply our method nationwide and to three select areas: Los Angeles County, Cook County, and the five boroughs of New York City, providing forecasts of drug-overdose mortality and estimates of relevant epidemiological quantities, such as mortality and age-specific addiction rates. 

Abstract Drug overdose deaths continue to increase in the United States for all major drug categories. Over the past two decades the total number of overdose fatalities has increased more than fivefold; since 2013 the surge in overdose rates is primarily driven by fentanyl and methamphetamines. Different drug categories and factors such as age, gender, and ethnicity are associated with different overdose mortality characteristics that may also change in time. For example, the average age at death from a drug overdose has decreased from 1940 to 1990 while the overall mortality rate has steadily increased. To provide insight into the population-level dynamics of drug overdose mortality, we develop an age-structured model for drug addiction. Using an augmented ensemble Kalman filter (EnKF), we show through a simple example how our model can be combined with synthetic observation data to estimate mortality rate and an age-distribution parameter. Finally, we use an EnKF to combine our model with observation data on overdose fatalities in the United States from 1999 to 2020 to forecast the evolution of overdose trends and estimate model parameters. 

We examine trends in drug overdose deaths by race, gender, and geography in the United States during the period 2013–2020. Race and gender specific crude rates were extracted from the final National Vital Statistics System multiple cause-of-death mortality files for several jurisdictions and used to calculate the male-to-female ratios of crude rates between 2013 and 2020. We established 2013–2019 temporal trends for four major drug types: psychostimulants with addiction potential (T43.6, such as methamphetamines); heroin (T40.1); natural and semi-synthetic opioids (T40.2, such as those contained in prescription pain-killers); synthetic opioids (T40.4, such as fentanyl and its derivatives) through a quadratic regression and determined whether changes in the pandemic year 2020 were statistically significant. We also identified which race, gender and states were most impacted by drug overdose deaths. Nationwide, the year 2020 saw statistically significant increases in overdose deaths from all drug categories except heroin, surpassing predictions based on 2013–2019 trends. Crude rates for Black individuals of both genders surpassed those for White individuals for fentanyl and psychostimulants in 2018, creating a gap that widened through 2020. In some regions, mortality among White persons decreased while overdose deaths for Black persons kept rising. The largest 2020 mortality statistic is for Black males in the District of Columbia, with a record 134 overdose deaths per 100,000 due to fentanyl, 9.4 times more than the fatality rate among White males. Male overdose crude rates in 2020 remain larger than those of females for all drug categories except in Idaho, Utah and Arkansas where crude rates of overdose deaths by natural and semisynthetic opioids for females exceeded those of males. Drug prevention, mitigation and no-harm strategies should include racial, geographical and gender-specific efforts, to better identify and serve at-risk groups. 

Hematopoiesis has been studied via stem cell labeling using barcodes, viral integration sites (VISs), or in situ methods. Subsequent proliferation and differentiation preserve the tag identity, thus defining a clone of mature cells across multiple cell type or lineages. By tracking the population of clones, measured within samples taken at discrete time points, we infer physiological parameters associated with a hybrid stochastic-deterministic mathematical model of hematopoiesis. We analyze clone population data from Koelle et al. ( Koelle et al., 2017 ) and compare the states of clones (mean and variance of their abundances) and the state-space density of clones with the corresponding quantities predicted from our model. Comparing our model to the tagged granulocyte populations, we find parameters (stem cell carrying capacity, stem cell differentiation rates, and the proliferative potential of progenitor cells, and sample sizes) that provide reasonable fits in three out of four animals. Even though some observed features cannot be quantitatively reproduced by our model, our analyses provides insight into how model parameters influence the underlying mechanisms in hematopoiesis. We discuss additional mechanisms not incorporated in our model. 

We consider age-structured models with an imposed refractory period between births. These models can be used to formulate alternative population control strategies to China’s one-child policy. By allowing any number of births, but with an imposed delay between births, we show how the total population can be decreased and how a relatively older age distribution can be generated. This delay represents a more ‘continuous’ form of population management for which the strict one-child policy is a limiting case. Such a policy approach could be more easily accepted by society. Our analyses provide an initial framework for studying demographics and how social constraints influence population structure. 

Abstract Backtracking of RNA polymerase (RNAP) is an important pausing mechanism during DNA transcription that is part of the error correction process that enhances transcription fidelity. We model the backtracking mechanism of RNAP, which usually happens when the polymerase tries to incorporate a noncognate or ‘mismatched’ nucleotide triphosphate. Previous models have made simplifying assumptions such as neglecting the trailing polymerase behind the backtracking polymerase or assuming that the trailing polymerase is stationary. We derive exact analytic solutions of a stochastic model that includes locally interacting RNAPs by explicitly showing how a trailing RNAP influences the probability that an error is corrected or incorporated by the leading backtracking RNAP. We also provide two related methods for computing the mean times for error correction and incorporation given an initial local RNAP configuration. Using these results, we propose an effective interacting-RNAP lattice that can be readily simulated. 

We develop a statistical model for the testing of disease prevalence in a population. The model assumes a binary test result, positive or negative, but allows for biases in sample selection and both type I (false positive) and type II (false negative) testing errors. Our model also incorporates multiple test types and is able to distinguish between retesting and exclusion after testing. Our quantitative framework allows us to directly interpret testing results as a function of errors and biases. By applying our testing model to COVID-19 testing data and actual case data from specific jurisdictions, we are able to estimate and provide uncertainty quantification of indices that are crucial in a pandemic, such as disease prevalence and fatality ratios. This article is part of the theme issue ‘Data science approach to infectious disease surveillance’. 

The specificity of T cells is that each T cell has only one T cell receptor (TCR). A T cell clone represents a collection of T cells with the same TCR sequence. Thus, the number of different T cell clones in an organism reflects the number of different T cell receptors (TCRs) that arise from recombination of the V(D)J gene segments during T cell development in the thymus. TCR diversity and more specifically, the clone abundance distribution, are important factors in immune functions. Specific recombination patterns occur more frequently than others while subsequent interactions between TCRs and self-antigens are known to trigger proliferation and sustain naive T cell survival. These processes are TCR-dependent, leading to clone-dependent thymic export and naive T cell proliferation rates. We describe the heterogeneous steady-state population of naive T cells (those that have not yet been antigenically triggered) by using a mean-field model of a regulated birth-death-immigration process. After accounting for random sampling, we investigate how TCR-dependent heterogeneities in immigration and proliferation rates affect the shape of clone abundance distributions (the number of different clones that are represented by a specific number of cells, or “clone counts”). By using reasonable physiological parameter values and fitting predicted clone counts to experimentally sampled clone abundances, we show that realistic levels of heterogeneity in immigration rates cause very little change to predicted clone-counts, but that modest heterogeneity in proliferation rates can generate the observed clone abundances. Our analysis provides constraints among physiological parameters that are necessary to yield predictions that qualitatively match the data. Assumptions of the model and potentially other important mechanistic factors are discussed.