Overcompensation of transient and permanent death rate increases in age-structured models with cannibalistic interactions.

There has been renewed interest in understanding the mathematical structure of ecological population models that lead to overcompensation, the process by which a population recovers to a higher level after suffering a permanent increase in predation or harvesting. Here, we apply a recently formulated kinetic population theory to formally construct an age-structured single-species population model that includes a cannibalistic interaction in which older individuals prey on younger ones. Depending on the age-dependent structure of this interaction, our model can exhibit transient or steady-state overcompensation of an increased death rate as well as oscillations of the total population, both phenomena that have been observed in ecological systems. Analytic and numerical analysis of our model reveals sufficient conditions for overcompensation and oscillations. We also show how our structured population partial integrodifferential equation (PIDE) model can be reduced to coupled ODE models representing piecewise constant parameter domains, providing additional mathematical insight into the emergence of overcompensation.

Antagonism between ambient ozone increase and urbanization-oriented population migration on Chinese cardiopulmonary mortality.

Ever-increasing ambient ozone (O3) pollution in China has been exacerbating cardiopulmonary premature deaths. However, the urban-rural exposure inequity has seldom been explored. Here, we assess population-scale O3 exposure and mortality burdens between 1990 and 2019 based on integrated pollution tracking and epidemiological evidence. We find Chinese population have been suffering from climbing O3 exposure by 4.3 ± 2.8 ppb per decade as a result of rapid urbanization and growing prosperity of socioeconomic activities. Rural residents are broadly exposed to 9.8 ± 4.1 ppb higher ambient O3 than the adjacent urban citizens, and thus urbanization-oriented migration compromises the exposure-associated mortality on total population. Cardiopulmonary excess premature deaths attributable to long-term O3 exposure, 373,500 (95% uncertainty interval [UI]: 240,600-510,900) in 2019, is underestimated in previous studies due to ignorance of cardiovascular causes. Future O3 pollution policy should focus more on rural population who are facing an aggravating threat of mortality risks to ameliorate environmental health injustice.

Spatial Resolved Surface Ozone with Urban and Rural Differentiation during 1990-2019: A Space-Time Bayesian Neural Network Downscaler.

Long-term exposure to ambient ozone (O3) can lead to a series of chronic diseases and associated premature deaths, and thus population-level environmental health studies hanker after the high-resolution surface O3 concentration database. In response to this demand, we innovatively construct a space-time Bayesian neural network parametric regressor to fuse TOAR historical observations, CMIP6 multimodel simulation ensemble, population distributions, land cover properties, and emission inventories altogether and downscale to 10 km × 10 km spatial resolution with high methodological reliability (R2 = 0.89-0.97, RMSE = 1.97-3.42 ppbV), fair prediction accuracy (R2 = 0.69-0.77, RMSE = 5.63-7.97 ppbV), and commendable spatiotemporal extrapolation capabilities (R2 = 0.62-0.76, RMSE = 5.38-11.7 ppbV). Based on our predictions in 8-h maximum daily average metric, the rural-site surface O3 are 15.1±7.4 ppbV higher than urban globally averaged across 30 historical years during 1990-2019, with developing countries being of the most evident differences. The globe-wide urban surface O3 are climbing by 1.9±2.3 ppbV per decade, except for the decreasing trends in eastern United States. On the other hand, the global rural surface O3 tend to be relatively stable, except for the rising tendencies in China and India. Using CMIP6 model simulations directly without urban-rural differentiation will lead to underestimations of population O3 exposure by 2.0±0.8 ppbV averaged over each historical year. Our original Bayesian neural network framework contributes to the deep-learning-driven environmental studies methodologically by providing a brand-new feasible way to realize data fusion and downscaling, which maintains high interpretability by conforming to the principles of spatial statistics without compromising the prediction accuracy. Moreover, the 30-year highly spatial resolved monthly surface O3 database with multiple metrics fills in the literature gap for long-term surface O3 exposure tracing.

How Naive T-Cell Clone Counts Are Shaped By Heterogeneous Thymic Output and Homeostatic Proliferation.

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.

Why estimating population-based case fatality rates during epidemics may be misleading.

Different ways of calculating mortality ratios during epidemics can yield widely different results, particularly during the COVID-19 pandemic. We formulate both a survival probability model and an associated infection duration-dependent SIR model to define individual- and population-based estimates of dynamic mortality ratios. The key parameters that affect the dynamics of the different mortality estimates are the incubation period and the length of time individuals were infected before confirmation of infection. We stress that none of these ratios are accurately represented by the often misinterpreted case fatality ratio (CFR), the number of deaths to date divided by the total number of infected cases to date. Using available data on the recent SARS-CoV-2 outbreaks and simple assumptions, we estimate and compare the different dynamic mortality ratios and highlight their differences. Informed by our modeling, we propose a more systematic method to determine mortality ratios during epidemic outbreaks and discuss sensitivity to confounding effects and errors in the data.

Why case fatality ratios can be misleading: individual- and population-based mortality estimates and factors influencing them.

Different ways of calculating mortality during epidemics have yielded very different results, particularly during the current COVID-19 pandemic. For example, the 'CFR' has been interchangeably called the case fatality ratio, case fatality rate, and case fatality risk, often without standard mathematical definitions. The most commonly used CFR is the case fatality ratio, typically constructed using the estimated number of deaths to date divided by the estimated total number of confirmed infected cases to date. How does this CFR relate to an infected individual's probability of death? To explore such issues, we formulate both a survival probability model and an associated infection duration-dependent SIR model to define individual- and population-based estimates of dynamic mortality measures to show that neither of these are directly represented by the case fatality ratio. The key parameters that affect the dynamics of different mortality estimates are the incubation period and the time individuals were infected before confirmation of infection. Using data on the recent SARS-CoV-2 outbreaks, we estimate and compare the different dynamic mortality estimates and highlight their differences. Informed by our modeling, we propose more systematic methods to determine mortality during epidemic outbreaks and discuss sensitivity to confounding effects and uncertainties in the data arising from, e.g., undertesting and heterogeneous populations.

PDE MODELS OF ADDER MECHANISMS IN CELLULAR PROLIFERATION.

Cell division is a process that involves many biochemical steps and complex biophysical mechanisms. To simplify the understanding of what triggers cell division, three basic models that subsume more microscopic cellular processes associated with cell division have been proposed. Cells can divide based on the time elapsed since their birth, their size, and/or the volume added since their birth-the timer, sizer, and adder models, respectively. Here, we propose unified adder-sizer models and investigate some of the properties of different adder processes arising in cellular proliferation. Although the adder-sizer model provides a direct way to model cell population structure, we illustrate how it is mathematically related to the well-known model in which cell division depends on age and size. Existence and uniqueness of weak solutions to our 2+1-dimensional PDE model are proved, leading to the convergence of the discretized numerical solutions and allowing us to numerically compute the dynamics of cell population densities. We then generalize our PDE model to incorporate recent experimental findings of a system exhibiting mother-daughter correlations in cellular growth rates. Numerical experiments illustrating possible average cell volume blowup and the dynamical behavior of cell populations with mother-daughter correlated growth rates are carried out. Finally, motivated by new experimental findings, we extend our adder model cases where the controlling variable is the added size between DNA replication initiation points in the cell cycle.