Artificial Neural Network Prediction of COVID-19 Daily Infection Count.

This study addresses COVID-19 testing as a nonlinear sampling problem, aiming to uncover the dependence of the true infection count in the population on COVID-19 testing metrics such as testing volume and positivity rates. Employing an artificial neural network, we explore the relationship among daily confirmed case counts, testing data, population statistics, and the actual daily case count. The trained artificial neural network undergoes testing in in-sample, out-of-sample, and several hypothetical scenarios. A substantial focus of this paper lies in the estimation of the daily true case count, which serves as the output set of our training process. To achieve this, we implement a regularized backcasting technique that utilize death counts and the infection fatality ratio (IFR), as the death statistics and serological surveys (providing the IFR) as more reliable COVID-19 data sources. Addressing the impact of factors such as age distribution, vaccination, and emerging variants on the IFR time series is a pivotal aspect of our analysis. We expect our study to enhance our understanding of the genuine implications of the COVID-19 pandemic, subsequently benefiting mitigation strategies.

Logic programming-based Minimal Cut Sets reveal consortium-level therapeutic targets for chronic wound infections.

Minimal Cut Sets (MCSs) identify sets of reactions which, when removed from a metabolic network, disable certain cellular functions. The traditional search for MCSs within genome-scale metabolic models (GSMMs) targets cellular growth, identifies reaction sets resulting in a lethal phenotype if disrupted, and retrieves a list of corresponding gene, mRNA, or enzyme targets. Using the dual link between MCSs and Elementary Flux Modes (EFMs), our logic programming-based tool aspefm was able to compute MCSs of any size from GSMMs in acceptable run times. The tool demonstrated better performance when computing large-sized MCSs than the mixed-integer linear programming methods. We applied the new MCSs methodology to a medically-relevant consortium model of two cross-feeding bacteria, Staphylococcus aureus and Pseudomonas aeruginosa. aspefm constraints were used to bias the computation of MCSs toward exchanged metabolites that could complement lethal phenotypes in individual species. We found that interspecies metabolite exchanges could play an essential role in rescuing single-species growth, for instance inosine could complement lethal reaction knock-outs in the purine synthesis, glycolysis, and pentose phosphate pathways of both bacteria. Finally, MCSs were used to derive a list of promising enzyme targets for consortium-level therapeutic applications that cannot be circumvented via interspecies metabolite exchange.

A taxonomy of multiple stable states in complex ecological communities.

Natural systems are built from multiple interconnected units, making their dynamics, functioning and fragility notoriously hard to predict. A fragility scenario of particular relevance concerns so-called regime shifts: abrupt transitions from healthy to degraded ecosystem states. An explanation for these shifts is that they arise as transitions between alternative stable states, a process that is well-understood in few-species models. However, how multistability upscales with system complexity remains a debated question. Here, we identify that four different multistability regimes generically emerge in models of species-rich communities and other archetypical complex biological systems assuming random interactions. Across the studied models, each regime consistently emerges under a specific interaction scheme and leaves a distinct set of fingerprints in terms of the number of observed states, their species richness and their response to perturbations. Our results help clarify the conditions and types of multistability that can be expected to occur in complex ecological communities.

Advice to a Young Mathematical Biologist.

This paper offers advice to early-mid career researchers in Mathematical Biology from ten past and current Presidents of the Society for Mathematical Biology. The topics covered include deciding if a career in academia is right for you; finding and working with a mentor; building collaborations and working with those from other disciplines; formulating a research question; writing a paper; reviewing papers; networking; writing fellowship or grant proposals; applying for faculty positions; and preparing and giving lectures. While written with mathematical biologists in mind, it is hoped that this paper will be of use to early and mid career researchers across the mathematical, physical and life sciences, as they embark on careers in these disciplines.

On hierarchical competition through reduction of individual growth.

We consider a population organised hierarchically with respect to size in such a way that the growth rate of each individual depends only on the presence of larger individuals. As a concrete example one might think of a forest, in which the incidence of light on a tree (and hence how fast it grows) is affected by shading by taller trees. The classic formulation of a model for such a size-structured population employs a first order quasi-linear partial differential equation equipped with a non-local boundary condition. However, the model can also be formulated as a delay equation, more specifically a scalar renewal equation, for the population birth rate. After discussing the well-posedness of the delay formulation, we analyse how many stationary birth rates the equation can have in terms of the functional parameters of the model. In particular we show that, under reasonable and rather general assumptions, only one stationary birth rate can exist besides the trivial one (associated to the state in which there are no individuals and the population birth rate is zero). We give conditions for this non-trivial stationary birth rate to exist and analyse its stability using the principle of linearised stability for delay equations. Finally, we relate the results to the alternative, partial differential equation formulation of the model.

Untangling the Molecular Interactions Underlying Intracellular Phase Separation Using Combined Global Sensitivity Analyses.

Liquid-liquid phase separation is an intracellular mechanism by which molecules, usually proteins and RNAs, interact and then rapidly demix from the surrounding matrix to form membrane-less compartments necessary for cellular function. Occurring in both the cytoplasm and the nucleus, properties of the resulting droplets depend on a variety of characteristics specific to the molecules involved, such as valency, density, and diffusion within the crowded environment. Capturing these complexities in a biologically relevant model is difficult. To understand the nuanced dynamics between proteins and RNAs as they interact and form droplets, as well as the impact of these interactions on the resulting droplet properties, we turn to sensitivity analysis. In this work, we examine a previously published mathematical model of two RNA species competing for the same protein-binding partner. We use the combined analyses of Morris Method and Sobol' sensitivity analysis to understand the impact of nine molecular parameters, subjected to three different initial conditions, on two observable LLPS outputs: the time of phase separation and the composition of the droplet field. Morris Method is a screening method capable of highlighting the most important parameters impacting a given output, while the variance-based Sobol' analysis can quantify both the importance of a given parameter, as well as the other model parameters it interacts with, to produce the observed phenomena. Combining these two techniques allows Morris Method to identify the most important dynamics and circumvent the large computational expense associated with Sobol', which then provides more nuanced information about parameter relationships. Together, the results of these combined methodologies highlight the complicated protein-RNA relationships underlying both the time of phase separation and the composition of the droplet field. Sobol' sensitivity analysis reveals that observed spatial and temporal dynamics are due, at least in part, to high-level interactions between multiple (3+) parameters. Ultimately, this work discourages using a single measurement to extrapolate the value of any single rate or parameter value, while simultaneously establishing a framework in which to analyze and assess the impact of these small-scale molecular interactions on large-scale droplet properties.

Effect of schooling on flow generated sounds from carangiform swimmers.

Computational models are used to examine the effect of schooling on flow generated noise from fish swimming using their caudal fins. We simulate the flow as well as the far-field hydrodynamic sound generated by the time-varying pressure loading on these carangiform swimmers. The effect of the number of swimmers in the school, the relative phase of fin flapping of the swimmers, and their spatial arrangement is examined. The simulations indicate that the phase of the fin flapping is a dominant factor in the total sound radiated into the far-field by a group of swimmers. For small schools, a suitable choice of relative phase between the swimmers can significantly reduce the overall intensity of the sound radiated to the far-field. The relative positioning of the swimmers is also shown to have an impact on the total radiated noise. For a larger school, even highly uncorrelated phases of fin movement between the swimmers in the school are very effective in significantly reducing the overall intensity of sound radiated into the far-field. The implications of these findings for fish ethology as well as the design and operation of bioinspired vehicles are discussed.

The three-species problem: Incorporating competitive asymmetry and intransitivity in modern coexistence theory.

While natural communities can contain hundreds of species, modern coexistence theory focuses primarily on species pairs. Alternatively, the structural stability approach considers the feasibility of equilibria, gaining scalability to larger communities but sacrificing information about dynamic stability. Three-species competitive communities are a bridge to more-diverse communities. They display novel phenomena while remaining amenable to mathematical analysis, but remain incompletely understood. Here, we combine these approaches to identify the key quantities that determine three-species competition outcomes. We show that pairwise niche overlap and fitness differences are insufficient to completely characterize competitive outcomes, which requires a strictly triplet-wise quantity: cyclic asymmetry, which underlies intransitivity. Low pairwise niche overlap stabilizes the triplet, while high fitness differences promote competitive exclusion. The effect of cyclic asymmetry on stability is complex and depends on pairwise niche overlap. In summary, we elucidate how pairwise niche overlap, fitness differences and cyclic asymmetry determine three-species competition outcomes.

The need for speed - Does the force-velocity property significantly alter strain distributions within skeletal muscle?

Skeletal muscles are complex structures with nonlinear constitutive properties. This complexity often requires finite element (FE) modeling to better understand muscle behavior and response to activation, especially the fiber strain distributions that can be difficult to measure in vivo. However, many FE muscle models designed to study fiber strain do not include force-velocity behavior. To investigate force-velocity property impact on strain distributions within skeletal muscle, we modified a muscle constitutive model with active and passive force-length properties to include force-velocity properties. We implemented the new constitutive model as a plugin for the FE software FEBio and applied it to four geometries: 1) a single element, 2) a multiple-element model representing a single fiber, 3) a model of tapering fibers, and 4) a model representing the bicep femoris long head (BFLH) morphology. Maximum fiber velocity and boundary conditions of the finite element models were varied to test their influence on fiber strain distribution. We found that force-velocity properties in the constitutive model behaved as expected for the single element and multi-element conditions. In the tapered fiber models, fiber strain distributions were impacted by changes in maximum fiber velocity; the range of strains increased with maximum fiber velocity, which was most noted in isometric contraction simulations. In the BFLH model, maximum fiber velocity had minimal impact on strain distributions, even in the context of sprinting. Taken together, the combination of muscle model geometry, activation, and displacement parameters play a critical part in determining the magnitude of impact of force-velocity on strain distribution.

Partial differential equation models for invasive species spread in the presence of spatial heterogeneity.

Models of invasive species spread often assume that landscapes are spatially homogeneous; thus simplifying analysis but potentially reducing accuracy. We extend a recently developed partial differential equation model for invasive conifer spread to account for spatial heterogeneity in parameter values and introduce a method to obtain key outputs (e.g. spread rates) from computational simulations. Simulations produce patterns of spatial spread which appear qualitatively similar to observed patterns in grassland ecosystems invaded by exotic conifers, validating our spatially explicit strategy. We find that incorporating spatial variation in different parameters does not significantly affect the evolution of invasions (which are characterised by a long quiescent period followed by rapid evolution towards to a constant rate of invasion) but that distributional assumptions can have a significant impact on the spread rate of invasions. Our work demonstrates that spatial variation in site-suitability or other parameters can have a significant impact on invasions and must be considered when designing models of invasive species spread.

The Demographic-Wealth model for cliodynamics.

Cliodynamics is a still a relatively new research area with the purpose of investigating and modelling historical processes. One of its first important mathematical models was proposed by Turchin and called "Demographic-Fiscal Model" (DFM). This DFM was one of the first and is one of a few models that link population with state dynamics. In this work, we propose a possible alternative to the classical Turchin DFM, which contributes to further model development and comparison essential for the field of cliodynamics. Our "Demographic-Wealth Model" (DWM) aims to also model link between population and state dynamics but makes different modelling assumptions, particularly about the type of possible taxation. As an important contribution, we employ tools from nonlinear dynamics, e.g., existence theory for periodic orbits as well as analytical and numerical bifurcation analysis, to analyze the DWM. We believe that these tools can also be helpful for many other current and future models in cliodynamics. One particular focus of our analysis is the occurrence of Hopf bifurcations. Therefore, a detailed analysis is developed regarding equilibria and their possible bifurcations. Especially noticeable is the behavior of the so-called coexistence point. While changing different parameters, a variety of Hopf bifurcations occur. In addition, it is indicated, what role Hopf bifurcations may play in the interplay between population and state dynamics. There are critical values of different parameters that yield periodic behavior and limit cycles when exceeded, similar to the "paradox of enrichment" known in ecology. This means that the DWM provides one possible avenue setup to explain in a simple format the existence of secular cycles, which have been observed in historical data. In summary, our model aims to balance simplicity, linking to the underlying processes and the goal to represent secular cycles.

A novel simulation-based analysis of a stochastic HIV model with the time delay using high order spectral collocation technique.

The economic impact of Human Immunodeficiency Virus (HIV) goes beyond individual levels and it has a significant influence on communities and nations worldwide. Studying the transmission patterns in HIV dynamics is crucial for understanding the tracking behavior and informing policymakers about the possible control of this viral infection. Various approaches have been adopted to explore how the virus interacts with the immune system. Models involving differential equations with delays have become prevalent across various scientific and technical domains over the past few decades. In this study, we present a novel mathematical model comprising a system of delay differential equations to describe the dynamics of intramural HIV infection. The model characterizes three distinct cell sub-populations and the HIV virus. By incorporating time delay between the viral entry into target cells and the subsequent production of new virions, our model provides a comprehensive understanding of the infection process. Our study focuses on investigating the stability of two crucial equilibrium states the infection-free and endemic equilibriums. To analyze the infection-free equilibrium, we utilize the LaSalle invariance principle. Further, we prove that if reproduction is less than unity, the disease free equilibrium is locally and globally asymptotically stable. To ensure numerical accuracy and preservation of essential properties from the continuous mathematical model, we use a spectral scheme having a higher-order accuracy. This scheme effectively captures the underlying dynamics and enables efficient numerical simulations.

Mechanistic Modeling of In Vitro Biopharmaceutic Data for a Weak Acid Drug: A Pathway Towards Deriving Fundamental Parameters for Physiologically Based Biopharmaceutic Modeling.

Mechanistic modeling of in vitro experiments using metabolic enzyme systems enables the extrapolation of metabolic clearance for in vitro-in vivo predictions. This is particularly important for successful clearance predictions using physiologically based pharmacokinetic (PBPK) modeling. The concept of mechanistic modeling can also be extended to biopharmaceutics, where in vitro data is used to predict the in vivo pharmacokinetic profile of the drug. This approach further allows for the identification of parameters that are critical for oral drug absorption in vivo. However, the routine use of this analysis approach has been hindered by the lack of an integrated analysis workflow. The objective of this tutorial is to (1) review processes and parameters contributing to oral drug absorption in increasing levels of complexity, (2) outline a general physiologically based biopharmaceutic modeling workflow for weak acids, and (3) illustrate the outlined concepts via an ibuprofen (i.e., a weak, poorly soluble acid) case example in order to provide practical guidance on how to integrate biopharmaceutic and physiological data to better understand oral drug absorption. In the future, we plan to explore the usefulness of this tutorial/roadmap to inform the development of PBPK models for BCS 2 weak bases, by expanding the stepwise modeling approach to accommodate more intricate scenarios, including the presence of diprotic basic compounds and acidifying agents within the formulation.

Global latitudinal gradients and the evolution of body size in dinosaurs and mammals.

Global climate patterns fundamentally shape the distribution of species and ecosystems. For example, Bergmann's rule predicts that homeothermic animals, including birds and mammals, inhabiting cooler climates are generally larger than close relatives from warmer climates. The modern world, however, lacks the comparative data needed to evaluate such macroecological rules rigorously. Here, we test for Bergmann's rule in Mesozoic dinosaurs and mammaliaforms that radiated within relatively temperate global climate regimes. We develop a phylogenetic model that accounts for biases in the fossil record and allows for variable evolutionary dispersal rates. Our analysis also includes new fossil data from the extreme high-latitude Late Cretaceous Arctic Prince Creek Formation. We find no evidence for Bergmann's rule in Mesozoic dinosaurs or mammaliaforms, the ancestors of extant homeothermic birds and mammals. When our model is applied to thousands of extant dinosaur (bird) and mammal species, we find that body size evolution remains independent of latitude. A modest temperature effect is found in extant, but not in Mesozoic, birds, suggesting that body size evolution in modern birds was influenced by Bergmann's rule during Cenozoic climatic change. Our study provides a general approach for studying macroecological rules, highlighting the fossil record's power to address longstanding ecological principles.

Dynamics of Information Flow and Task Allocation of Social Insect Colonies: Impacts of Spatial Interactions and Task Switching.

Models of social interaction dynamics have been powerful tools for understanding the efficiency of information spread and the robustness of task allocation in social insect colonies. How workers spatially distribute within the colony, or spatial heterogeneity degree (SHD), plays a vital role in contact dynamics, influencing information spread and task allocation. We used agent-based models to explore factors affecting spatial heterogeneity and information flow, including the number of task groups, variation in spatial arrangements, and levels of task switching, to study: (1) the impact of multiple task groups on SHD, contact dynamics, and information spread, and (2) the impact of task switching on SHD and contact dynamics. Both models show a strong linear relationship between the dynamics of SHD and contact dynamics, which exists for different initial conditions. The multiple-task-group model without task switching reveals the impacts of the number and spatial arrangements of task locations on information transmission. The task-switching model allows task-switching with a probability through contact between individuals. The model indicates that the task-switching mechanism enables a dynamical state of task-related spatial fidelity at the individual level. This spatial fidelity can assist the colony in redistributing their workforce, with consequent effects on the dynamics of spatial heterogeneity degree. The spatial fidelity of a task group is the proportion of workers who perform that task and have preferential walking styles toward their task location. Our analysis shows that the task switching rate between two tasks is an exponentially decreasing function of the spatial fidelity and contact rate. Higher spatial fidelity leads to more agents aggregating to task location, reducing contact between groups, thus making task switching more difficult. Our results provide important insights into the mechanisms that generate spatial heterogeneity and deepen our understanding of how spatial heterogeneity impacts task allocation, social interaction, and information spread.

Modeling Developmental Changes in Caffeine Clearance Considering Differences between Pre- and Postnatal Period.

Taguchi et al. reported that postmenstrual age (PMA) is a promising factor in describing and understanding the developmental change of caffeine (CAF) clearance. The aim of the present study was to quantify how developmental changes occur and to determine the effect of the length of the gestational period on CAF clearance. We performed a nonlinear mixed effect model (NONMEM) analysis and evaluated the fit of six models. A total of 115 samples were obtained from 52 patients with a mean age of 34.3 ± 18.2 d. The median values of gestational age (GA) and postnatal age (PNA) were 196 and 31 d, respectively. Serum CAF levels corrected for dose per body surface area (BSA) (C/D ratioBSA) were dependent on PMA rather than PNA, which supports the findings of a previous study. NONMEM analysis provided the following final model of oral clearance: CL/F = 0.00603∙WT∙∙0.877GA ≤ 196 L/h. This model takes into account developmental changes during prenatal and postnatal periods separately. The model successfully described the variation in clearance of CAF. Our findings suggest that the dosage of CAF in preterm infants should be determined based not only on body weight (WT) but also on both PNA and GA.

Exploring the potential and challenges of developing physiologically-based toxicokinetic models to support human health risk assessment of microplastic and nanoplastic particles.

Microplastics (MPs) and nanoplastics (NPs) pollution has emerged as a significant and widespread environmental issue. Humans are inevitably exposed to MPs and NPs via ingestion, inhalation, and dermal contacts from various sources. However, mechanistic knowledge of their distribution, interaction, and potency in the body is still lacking. To address this knowledge gap, we have undertaken the task of elucidating the toxicokinetic (TK) behaviors of MPs and NPs, aiming to provide mechanistic information for constructing a conceptual physiologically based toxicokinetic (PBTK) model to support in silico modeling approaches. Our effort involved a thorough examination of the existing literature and data collation on the presence of MPs in the human body and in vitro/ex vivo/in vivo biodistribution across various cells and tissues. By comprehending the absorption, distribution, metabolism, and excretion mechanisms of MPs and NPs in relation to their physicochemical attributes, we established a foundational understanding of the link between external exposure and internal tissue dosimetry. We observed that particle size and surface chemistry have been thoroughly explored in previous experimental studies. However, certain attributes, such as polymer type, shape, and biofilm/biocorona, warrant attention and further examination. We discussed the fundamental disparities in TK properties of MPs/NPs from those of engineered nanoparticles. We proposed a preliminary PBTK framework with several possible modeling approaches and discussed existing challenges for further investigation. Overall, this article provides a comprehensive compilation of existing TK data of MPs/NPs, a critical overview of TK processes and mechanisms, and proposes potential PBTK modeling approaches, particularly regarding their applicability to the human system, and outlines future perspectives for developing PBTK models and their integration into human health risk assessment of MPs and NPs.

Infection-induced increases to population size during cycles in a discrete-time epidemic model.

One-dimensional discrete-time population models, such as those that involve Logistic or Ricker growth, can exhibit periodic and chaotic dynamics. Expanding the system by one dimension to incorporate epidemiological interactions causes an interesting complexity of new behaviors. Here, we examine a discrete-time two-dimensional susceptible-infectious (SI) model with Ricker growth and show that the introduction of infection can not only produce a distinctly different bifurcation structure than that of the underlying disease-free system but also lead to counter-intuitive increases in population size. We use numerical bifurcation analysis to determine the influence of infection on the location and types of bifurcations. In addition, we examine the appearance and extent of a phenomenon known as the 'hydra effect,' i.e., increases in total population size when factors, such as mortality, that act negatively on a population, are increased. Previous work, primarily focused on dynamics at fixed points, showed that the introduction of infection that reduces fecundity to the SI model can lead to a so-called 'infection-induced hydra effect.' Our work shows that even in such a simple two-dimensional SI model, the introduction of infection that alters fecundity or mortality can produce dynamics can lead to the appearance of a hydra effect, particularly when the disease-free population is at a cycle.

Integrating Diversity, Equity, and Inclusion into Preclinical, Clinical, and Public Health Mathematical Models.

Mathematical modelling applied to preclinical, clinical, and public health research is critical for our understanding of a multitude of biological principles. Biology is fundamentally heterogeneous, and mathematical modelling must meet the challenge of variability head on to ensure the principles of diversity, equity, and inclusion (DEI) are integrated into quantitative analyses. Here we provide a follow-up perspective on the DEI plenary session held at the 2023 Society for Mathematical Biology Annual Meeting to discuss key issues for the increased integration of DEI in mathematical modelling in biology.

Suillus: an emerging model for the study of ectomycorrhizal ecology and evolution.

Research on mycorrhizal symbiosis has been slowed by a lack of established study systems. To address this challenge, we have been developing Suillus, a widespread ecologically and economically relevant fungal genus primarily associated with the plant family Pinaceae, into a model system for studying ectomycorrhizal (ECM) associations. Over the last decade, we have compiled extensive genomic resources, culture libraries, a phenotype database, and protocols for manipulating Suillus fungi with and without their tree partners. Our efforts have already resulted in a large number of publicly available genomes, transcriptomes, and respective annotations, as well as advances in our understanding of mycorrhizal partner specificity and host communication, fungal and plant nutrition, environmental adaptation, soil nutrient cycling, interspecific competition, and biological invasions. Here, we highlight the most significant recent findings enabled by Suillus, present a suite of protocols for working with the genus, and discuss how Suillus is emerging as an important model to elucidate the ecology and evolution of ECM interactions.