The COVID-19 pandemic has proved to be one of the most disruptive public health emergencies in recent memory. Among non-pharmaceutical interventions, social distancing and lockdown measures are some of the most common tools employed by governments around the world to combat the disease. While mathematical models of COVID-19 are ubiquitous, few have leveraged network theory in a general way to explain the mechanics of social distancing. In this paper, we build on existing network models for heterogeneous, clustered networks with random link activation/deletion dynamics to put forth realistic mechanisms of social distancing using piecewise constant activation/deletion rates. We find our models are capable of rich qualitative behavior, and offer meaningful insight with relatively few intervention parameters. In particular, we find that the severity of social distancing interventions and when they begin have more impact than how long it takes for the interventions to take full effect.

Increasingly-sophisticated parameter-sensitivity analysis techniques continue to be developed, and each technique comes with its own set of advantages and disadvantages. Selecting which parameter-sensitivity method to use for a particular model, however, is not a straightforward task. In this work, we present a multi-method framework that incorporates three global sensitivity analysis methods: two variance-based methods and one derivative-based method. The two variance-based methods are Sobol's method and MeFAST. The derivative-based method is known as DGSM (Derivative-based Global Sensitivity Measures). MeFAST (Multi test eFAST) is a new parameter sensitivity analysis implementation we built upon the eFAST (Extended Fourier Amplitude Sensitivity Test) algorithm. The improvements incorporated into MeFAST address some important aspects of prior eFAST implementations. We present an intuitive description of each implemented algorithm along with MATLAB codes and a guide to tuning algorithm hyper-parameters for better efficiency. We demonstrate the full methodology and workflow using two example mathematical models of different complexity: the first is a model of HIV disease progression and the second is a model of tumor growth. The computational framework we provide generates graphics for visualizing and comparing the results of all three sensitivity analysis algorithms (DGSM, Sobol, and MeFAST). This algorithm output comparison tool allows one to make a more informed decision when assessing which parameters most importantly influence model outcomes.

Environmental stochasticity affects population dynamics in a variety of ways, including the possibility of drastic modifications in the stability properties of the ecosystem. In this work, we investigate a case of coupled host-parasitoid dynamics adopting Beddington's conceptual two-dimensional map. We stochastically perturb some of the parameters controlling either the host dynamics or the host-parasitoid interaction, observing a dramatic change in the system dynamics with the emergence of on-off intermittency, a behavior characterized by the irregular alternation between quiescent phases and sudden population bursts. This phenomenon is herein offered as a qualitative, environmental-based description of population outbreaks.

Even though most axonal cargos are synthesized in the soma, the concentration of many of these cargos is larger at the presynaptic terminal than in the soma. This requires transport of these cargos from the soma to the presynaptic terminal or other active sites in the axon. Axons utilize both bidirectional (for example, slow axonal transport) and unidirectional (for example, fast anterograde axonal transport) modes of cargo transport. Bidirectional transport seems to be less efficient because it requires more time and takes more energy to deliver cargos. In this paper, we studied a family of models which differ by the modes of axonal cargo transport (such as anterograde and retrograde motor-driven transport and passive diffusion) as well as by the presence or absence of pausing states. The models are studied to investigate their ability to describe axonal transport against the cargo concentration gradient. We argue that bidirectional axonal transport is described by a higher-order mathematical model, which allows imposing cargo concentration not only at the axon hillock but also at the axon terminal. The unidirectional transport model allows only for the imposition of cargo concentration at the axon hillock. Due to the great lengths of the axons, anterograde transport mostly relies on molecular motors, such as kinesins, to deliver cargos synthesized in the soma to the terminal and other active sites in the axon. Retrograde transport can be also motor-driven, in which case cargos are transported by dynein motors. If cargo concentration at the axon tip is higher than at the axon hillock, retrograde transport can also occur by cargo diffusion. However, because many axonal cargos are large or they assemble in multiprotein complexes for axonal transport, the diffusivity of such cargos is very small. We investigated the case of a small cargo diffusivity using a perturbation technique and found that for this case the effect of diffusion is limited to a very thin diffusion boundary layer near the axon tip. If cargo diffusivity is decreased in the model, we show that without motor-driven retrograde transport the model is unable to describe a high cargo concentration at the axon tip. To the best of our knowledge, our paper presents the first explanation for the utilization of seemingly inefficient bidirectional transport in neurons.

The coupled reaction-diffusion transport of glucose and oxygen into a core-shell geometry is modeled using dimensionless parameterization. The consumption of oxygen and glucose are coupled by a metabolic modulation function. The results are fit to a Bayesian-Ridge model that can be easily applied to generate large data sets spanning the parameter space. The non-linear correlation between the oxygen and glucose concentrations are presented and the effect of system parameters is explored. The maximum radius of a viable system is shown to decrease by up to 13.8% with high glucose saturation.

The epithelial mesenchymal transition (EMT) is a process by which cells lose their adhesive nature and gain the migratory properties associated with mesenchymal cells. This transition allows cells to migrate away from a primary tumor while maintaining their newly acquired invasive behavior, suggesting that there is a bistable switch between the epithelial and mesenchymal phenotypes. In recent experimental work, we found evidence of this bistability in the MCF7 breast carcinoma cell line (Gasior et al., 2019). Underlying the complex processes governing EMT, we identify a feedback loop between E-cadherin, a protein involved in cellular adhesion, and Slug, a transcription factor that is upregulated during EMT. Here, we present a simple mathematical model that examines the relationship between E-cadherin and Slug in response to pro-epithelial and pro-mesenchymal factors, cell-cell contact and TGF-β, respectively. We hypothesize that cell-cell contact is a critical component in the transition from the epithelial to the mesenchymal phenotype and that it is possible to initiate EMT with the loss of cell-cell contact or the activation of the TGF-β signaling pathway. We propose a reversible bistable switch in response to a loss of cell-cell contact but an irreversible bistable switch when the cell is exposed to TGF-β. Taken together, this model shows that acquiring and retaining invasive behavior by cells with high levels of cell-cell contact is not impossible but, instead, depends on the cooperation between the two switches. The predictions of this model for E-cadherin and Slug levels were compared against relative gene expression data from our recent experiments with MCF7 cells (Gasior et al., 2019). Our model works well to predict E-cadherin and Slug mRNA expression in low confluence experiments, while also highlighting issues that arise when comparing experimental results to theoretical predictions.

A new flight mode in birds that decreases the energy costs is described. This flight mode consists basically of a powered-glide phase and a climb phase. These phases constitute a cycle that is continually performed. The powered-glide phase shows a reduced wing flapping for generating thrust at an intermediate level. Other than a glide with a fixed wing posture, there is an energy support in the powered glide. It is shown that powered-gliding/climbing flight enables a decrease of the energy costs to yield a low fuel consumption. The powered-glide phase is determinative for achieving the decrease of the energy costs. The results based on this effect suggest that powered-gliding/climbing flight shows the lowest fuel consumption per range when compared with other travel flight modes including the flight at constant altitude. It has been found that birds perform continual altitude changes in long-distance flights rather than flying at a constant altitude. There is evidence based on observations and measurements that the descents in these altitude changes take place as powered glides. This suggests that long-distance flights with altitude changes consist of powered-gliding/climbing flight with repeated cycles.

Noise affects all biological processes from molecules to cells, organisms and populations. Although the effect of noise on these processes is highly variable, evidence is accumulating which shows natural stochastic fluctuations (noise) can facilitate biological functions. Herein, we investigate the effect of noise on the transport of intermediate filaments in cells by comparing the stochastic and deterministic formalizations of the bidirectional transport of intermediate filaments, long elastic polymers transported along microtubules by antagonistic motor proteins (Dallon et al., 2019; Portet et al., 2019). By numerically exploring discrepancies in timescales and attractors between both formalizations, we characterize the impact of stochastic fluctuations on the individual and ensemble transport. Biologically, we find that noise promotes the collective movement of intermediate filaments and increases the efficiency of its regulation by the biochemical properties of motor-cargo interactions. While stochastic fluctuations reduce the impact of the initial distributions of motor proteins in cells, the number of binding sites and the affinity of motor-cargo interactions are the key parameters controlling transport efficiency and efficacy.

The classic Hawk-Dove game is a symmetric game in that it does not distinguish between the winners and losers of Hawk-Hawk or Dove-Dove contests. Either of the two interacting Hawks or the two interacting Doves have the same probability to win/lose the contest. In addition, all pairwise interactions take the same time and after disbanding, the individuals pair instantaneously again. This article develops an asymmetric version of the Hawk-Dove model where all costs are measured by the time lost. These times are strategy dependent and measure the length of the conflict and, when a fight occurs between two interacting Hawks, the time an individual needs to recover and pair again. These recovery times depend on whether the Hawk won or lost the contest so that we consider an asymmetric Hawk-Dove game where we distinguish between winners and losers. However, the payoff matrix for this game does not correspond to the standard bimatrix game, because some entries are undefined. To calculate strategy payoffs we consider not only costs and benefits obtained from pairwise contests but also costs when individuals are disbanded. Depending on the interacting and recovery times, the evolutionary outcomes are: Hawk only, both Hawk and Dove, and a mixed strategy. This shows that measuring the cost in time lost leads to a new prediction since, in the classic (symmetric) Hawk-Dove model that does assume positive cost (C>0), both Hawk and Dove strategy is never an evolutionary outcome.

Different biological models are used to study physical behaviors in neural networks. So far, various models of neural network components such as neurons, synapses, and astrocytes have been proposed. An astrocyte is one of the crucial parts introduced in multiple models. A model of astrocytes used as a good reference in various papers is the Li-Rinzel calcium model. This paper presents a real-time analog circuit of the Li-Rinzel calcium model based on common-mode (CM) in 180 nm CMOS technology. To the best of our knowledge, this work is the first report to introduce a real-time analog circuit of Li-Rinzel model in an integrated standard CMOS technology. The careful design of equations and low power consumption are essential features of this circuit. The real-time behavior is also crucial compared with the accelerated time circuits presented so far.

T cell therapy has become a new therapeutic opportunity against solid cancers. Predicting T cell behaviour and efficacy would help therapy optimization and clinical implementation. In this work, we model responsiveness of mouse prostate adenocarcinoma to T cell-based therapies. The mathematical model is based on a Cahn-Hilliard diffuse interface description of the tumour, coupled with Keller-Segel type equations describing immune components dynamics. The model is fed by pre-clinical magnetic resonance imaging data describing anatomical features of prostate adenocarcinoma developed in the context of the Transgenic Adenocarcinoma of the Mouse Prostate model. We perform computational simulations based on the finite element method to describe tumor growth dynamics in relation to local T cells concentrations. We report that when we include in the model the possibility to activate tumor-associated vessels and by that increase the number of T cells within the tumor mass, the model predicts higher therapeutic effects (tumor regression) shortly after therapy administration. The simulated results are found in agreement with reported experimental data. Thus, this diffuse-interface mathematical model well predicts T cell behavior in vivo and represents a proof-of-concept for the role such predictive strategies may play in optimization of immunotherapy against cancer.

We present a modelling and simulation framework for the dynamics of ovarian follicles and key hormones along the hypothalamic-pituitary-gonadal axis throughout consecutive human menstrual cycles. All simulation results (hormone concentrations and ovarian follicle sizes) are in biological units and can easily be compared to clinical data. The model takes into account variability in follicles' response to stimulating hormones, which introduces variability between cycles. The growth of ovarian follicles in waves is an emergent property in our model simulations and further supports the hypothesis that follicular waves are also present in humans. We use Approximate Bayesian Computation and cluster analysis to construct a population of virtual subjects and to study parameter distributions and sensitivities. The model can be used to compare and optimize treatment protocols for ovarian hyperstimulation, thus potentially forming the integral part of a clinical decision support system in reproductive endocrinology.

Solid tumour growth depends on a host of factors which affect the cell life cycle and extracellular matrix vascularization that leads to a favourable environment. The whole solid tumour can either grow or wither in response to the action of the immune system and therapeutics. A personalised mathematical model of such behaviour must consider both the intra- and inter-cellular dynamics and the mechanics of the solid tumour and its microenvironment. However, such wide range of spatial and temporal scales can hardly be modelled in a single model, and require the so-called multiscale models, defined as orchestrations of single-scale component models, connected by relation models that transform the data for one scale to another. While multiscale models are becoming common, there is a well-established engineering approach to the definition of the scale separation, e.g., how the spatiotemporal continuum is split in the various component models. In most studies scale separation is defined as natural, linked to anatomical concepts such as organ, tissue, or cell; but these do not provide reliable definition of scales: for examples skeletal organs can be as large as 500 mm (femur), or as small as 3 mm (stapes). Here we apply a recently proposed scale-separation approach based on the actual experimental and computational limitations to a patient-specific model of the growth of neuroblastoma. The resulting multiscale model can be properly informed with the available experimental data and solved in a reasonable timeframe with the available computational resources.

PURPOSE: Tumor oxygenation is one of the key features influencing the response of cells to radiation and chemo therapies. This study presents a novel in silico tumor model simulating realistic 3D microvascular structures and related oxygenation maps, featuring regions with different levels and typologies of hypoxia (chronic, acute and anemic). Such model, if integrated into a treatment planning system, could allow evaluations and comparisons of various scenarios when deciding the therapy to administer. METHODS AND MATERIALS: Spherical tumors between 0.6 and 1.5 cm in diameter encompassed uniformly by vascular trees generated starting from pseudo-fractal principles were simulated with a voxel resolution of 10 µm. The approach ensures a continuous transition from a well-perfused rim to a core with poor vascularization. The oxygen diffusion equation in the tumor is solved by a finite difference method. Several quantities, such as the fractal dimension (FD), the microvascular density (MVD) and the hypoxic fraction (HF) were assessed and compared. RESULTS: Different tumors with various degrees of chronic hypoxia were simulated by varying the tumor size and the number of bifurcations in the vascular networks. The simulations showed that for the case of chronically hypoxic tumors, in well-oxygenated volumes FD = 2.53 ± 0.07, MVD = 3460 ± 2180 vessels/mm3 and HF = 4.0 ± 3.4%, while in hypoxic volumes FD = 2.34 ± 0.09, MVD = 365 ± 156 vessels/mm3, HF = 49.8 ± 18.3%. The superimposition of acute or anemic hypoxia accentuated the oxygen deprivation in the core of the volumes. CONCLUSIONS: Tumors varying in diameter and extension of their vasculature were simulated, showing features that define two distinctive subvolumes in terms of oxygenation. The model could be regarded as a testbed for simulations of key radiobiological features governing the tumor response to radio- and chemotherapy and thus for treatment outcome simulations.

Many marine and terrestrial species live in groups, whose sizes and dynamics can vary depending on the type and strength of their social interactions. Typical examples of such groups in vertebrates are schools of fish or flocks of bird. Natural habitats can encompass a wide range of spatial heterogeneities, which can also shape the structure of animal groups, depending on the interplay between the attraction/repulsion of environmental cues and social interactions. A key issue in modern applied ecology and conservation is the need to understand the relationship between these ethological and ecological scales in order to account for the social behaviour of animals in their natural environments. Here, we introduce a modeling approach which studies animal groups within heterogeneous habitats constituted by a set of aggregative sites. The model properties are investigated considering the case study of tropical tuna schools and their associative behavior with floating objects, a question of global concern, given the thousands of floating objects deployed by industrial tropical tuna fisheries worldwide. The effects of increasing numbers of aggregative sites (floating objects) on tuna schools are studied. This study offers a general modeling framework to study social species in their habitats, accounting for both ethological and ecological drivers of animal group dynamics.

Chronic wasting disease (CWD) is a fatal disease of cervid species that continues to spread across North America and now in Europe. It poses a threat to cervid populations and the local ecological and economic communities that depend on them. Although empirical studies have shown that host home range overlap and male dispersal are important in the spread of disease, there are few mechanistic models explicitly considering those factors. We built a spatio-temporal, differential equation model for CWD spreading with restricted movement of hosts within home ranges. The model incorporates both direct and environmental transmission within and between groups as well as male dispersal. We compared the relative influence of host density, sex ratio, home range size, and male dispersal distance on the spreading speed using sensitivity analysis. We also assessed the effect of landscape heterogeneity, quantified as edge density, on the spreading speed of CWD because it jointly alters the host density and home range size. Our model binds the theoretical study of CWD spreading speed together with empirical studies on deer home ranges and sets a base for models in 2D space to evaluate management and control strategies.