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Stochastically perturbed models, where the white noise type stochastic perturbations are proportional to the current system state, the most realistically describe real-life biosystems. However, such models essentially have no equilibrium states apart from one at the origin. This feature makes analysis of such models extremely difficult. Probably, the best result that can be found for such models is finding of accurate estimations of a region in the model phase space that serves as an attractor for model trajectories. In this paper, we consider a classical stochastically perturbed Lotka–Volterra model of competing or symbiotic populations, where the white noise type perturbations are proportional to the current system state. Using the direct Lyapunov method in a combination with a recently developed technique, we establish global asymptotic properties of this model. In order to do this, we, firstly, construct a Lyapunov function that is applicable to the both competing (and globally stable) and symbiotic deterministic Lotka–Volterra models. Then, applying this Lyapunov function to the stochastically perturbed model, we show that solutions with positive initial conditions converge to a certain compact region in the model phase space and oscillate around this region thereafter. The direct Lyapunov method allows to find estimates for this region. We also show that if the magnitude of the noise exceeds a certain critical level, then some or all species extinct via process of the stochastic stabilization ('stabilization by noise'). The approach applied in this paper allows to obtain necessary conditions for the extinction. Sufficient conditions for the extinction (that for this model occurs via the process that is known as the 'stochastic stabilization', or the 'stabilization by noise') are found applying the Khasminskii-type Lyapunov functions. [ABSTRACT FROM AUTHOR]

Altay Prefecture, a typical arid region in northwestern China, has experienced the climate transition from warming-drying to warming-wetting since 1980s and has attracted widespread attention. Nonetheless, it is still unclear how climate change has influenced the distribution of vegetation in this region. In this paper, a reaction–diffusion model of the climate–vegetation system is proposed to study the impact of climate change (precipitation, temperature and carbon dioxide concentration) on vegetation patterns in Altay Prefecture. Our results indicate that the tendency of vegetation growth in Altay Prefecture improved gradually from 1985 to 2010. Under the current climate conditions, the increase of precipitation results in the change of vegetation pattern structures, and eventually vegetation coverage tends to be uniform. Moreover, we found that there exists an optimal temperature where the spot vegetation pattern structure remains stable. Furthermore, the increase in carbon dioxide concentration induces vegetation pattern transition. Based on four climate change scenarios of the Coupled Model Intercomparison Project Phase 6 (CMIP6), we used the power law range (PLR) to predict the optimal scenario for the sustainable development of the vegetation ecosystem in Altay Prefecture. [ABSTRACT FROM AUTHOR]

This paper describes computer models of three interventions used for treating refractory pulmonary hypertension (RPH). These procedures create either an atrial septal defect, a ventricular septal defect or, in the case of a Potts shunt, a patent ductus arteriosus. The aim in all three cases is to generate a right-to-left shunt, allowing for either pressure or volume unloading of the right side of the heart in the setting of right ventricular failure, while maintaining cardiac output. These shunts are created, however, at the expense of introducing de-oxygenated blood into the systemic circulation, thereby lowering the systemic arterial oxygen saturation. The models developed in this paper are based on compartmental descriptions of human hemodynamics and oxygen transport. An important parameter included in our models is the cross-sectional area of the surgically created defect. Numerical simulations are performed to compare different interventions and various shunt sizes and to assess their impact on hemodynamic variables and oxygen saturations. We also create a model for exercise and use it to study exercise tolerance in simulated pre-intervention and post-intervention RPH patients. [ABSTRACT FROM AUTHOR]

Inhibiting a signalling pathway concerns controlling the cellular processes of a cancer cell's viability, cell division and death. Assay protocols created to see if the molecular structures of the drugs being tested have the desired inhibition qualities often show great variability across experiments, and it is imperative to diminish the effects of such variability while inferences are drawn. In this paper, we propose the study of experimental data through the lenses of a mathematical model depicting the inhibition mechanism and the activation-inhibition dynamics. The method is exemplified through assay data obtained from an experimental study of the inhibition of the chemokine receptor 4 (CXCR4) and chemokine ligand 12 (CXCL12) signalling pathway of melanoma cells. The quantitative analysis is conducted as a two step process: (i) deriving theoretically from the model the cell viability as a function of time depending on several parameters; (ii) estimating the values of the parameters by using the experimental data. The cell viability is obtained as a function of concentration of the inhibitor and time, thus providing a comprehensive characterization of the potential therapeutic effect of the considered inhibitor, e.g. |$IC_{50}$| can be computed for any time point. [ABSTRACT FROM AUTHOR]

This paper focuses on tracing the connectivity of white matter fascicles in the brain. In particular, a generalized order algorithm based on mixture of non-central Wishart distribution model is proposed for this purpose. The proposed algorithm utilizes the generalization of integer order based approach with the mixture of non-central Wishart distribution model. Pseudo super anomalous behavior of water diffusion inside human brain is the prime motivation of the the present study. We have shown results on multiple synthetic simulations with fibers orientations in two and three directions in each voxel as well as experiments on real data. Synthetic simulations were performed with varying noise levels and diffusion weighting gradient i.e. |$b-$| values. The proposed model performed outstanding especially for distinguishing closely oriented fibers. [ABSTRACT FROM AUTHOR]

A traditional method of in vitro cell culture involves a monolayer of cells at the base of a petri dish filled with culture medium. While the primary role of the culture medium is to supply nutrients to the cells, drug or other solutes may be added, depending on the purpose of the experiment. Metabolism by cells of oxygen, nutrients and drug is typically governed by Michaelis–Menten (M-M) kinetics. In this paper, a mathematical model of solute transport with M-M kinetics is developed. Upon non-dimensionalization, the reaction/diffusion system is re-characterized in terms of Volterra integral equations, where a parameter $\beta $ , the ratio of the initial solute concentration to the M-M constant, proves important: $\beta \ll 1$ is relevant to drug metabolism for the liver, whereas $\beta \gg 1$ is more appropriate in the case of oxygen metabolism. Regular perturbation expansions for both cases are obtained. A small-time expansion and steady-state solution are also presented. All results are compared against the numerical solution of the Volterra integral equations, and excellent agreement is found. The utility of the model and analytical solutions are discussed in the context of assisting experimental researchers to better understand the environment within in vitro cell culture experiments. [ABSTRACT FROM AUTHOR]

Our aim in this paper is to study a mathematical model for high grade gliomas, taking into account lactates kinetics, as well as chemotherapy and antiangiogenic treatment. In particular, we prove the existence and uniqueness of biologically relevant solutions. We also perform numerical simulations based on different therapeutical situations that can be found in the literature. These simulations are consistent with what is expected in these situations. [ABSTRACT FROM AUTHOR]

The aim of the paper is to apply the stochastic optimal control problem in order to optimize the number of individual which will have the pre-exposure prophylaxis (PReP) treatment in the stochastic model for HIV/AIDS with PReP. By using the stochastic maximum principle, we derive the stochastic optimal control of PReP for the unconstrained control problem. Furthermore, by combining the stochastic maximum principle with a version of the Lagrange multiplier method, we solve the PReP problem for two different types of budget constrains with a given constrain for the costs (possible of different kind, transportation, price of the treatment, etc.). Obtained results for the different percentage of the individuals who got the vaccine, as well as results for unconstrained and constrained problems, are illustrated by a numerical example. [ABSTRACT FROM AUTHOR]

This paper reports a minimal model simulating the growth of a Lewy body (LB). To the best of our knowledge, this is the first model simulating LB growth. The LB is assumed to consist of a central spherical core, which is composed of membrane fragments and various dysfunctional intracellular organelles, and a halo, which is composed of alpha-synuclein (α-syn) fibrils. Membrane fragments and α-syn monomers are assumed to be produced in the soma at constant rates. The growth of the core and the halo are simulated by the Finke–Watzky model. Analytical (closed-form) solutions describing the growth of the core and the halo are obtained. A sensitivity analysis in terms of model parameters is performed. [ABSTRACT FROM AUTHOR]

Mycobacterium tuberculosis (TB) infection can involve all immune system components and can result in different disease outcomes. The antibiotic TB drugs require strict adherence to prevent both disease relapse and mutation of drug- and multidrug-resistant strains. To overcome the constraints of pathogen-directed therapy, host-directed therapy has attracted more attention in recent years as an adjunct therapy to enhance host immunity to fight against this intractable pathogen. The goal of this paper is to investigate in-host TB models to provide insights into therapy development. Focusing on therapy-targeting parameters, the parameter regions for different disease outcomes are identified from an established ODE model. Interestingly, the ODE model also demonstrates that the immune responses can both benefit and impede disease progression, depending on the number of bacteria engulfed and released by macrophages. We then develop two Itô SDE models, which consider the impact of demographic variations at the cellular level and environmental variations during therapies along with demographic variations. The SDE model with demographic variation suggests that stochastic fluctuations at the cellular level have significant influences on (1) the T-cell population in all parameter regions, (2) the bacterial population when parameters located in the region with multiple disease outcomes and (3) the uninfected macrophage population in the parameter region representing active disease. Further, considering environmental variations from therapies, the second SDE model suggests that disease progression can slow down if therapies (1) can have fast return rates and (2) can bring parameter values into the disease clearance regions. [ABSTRACT FROM AUTHOR]

In this paper, we propose and analyse a compartmental model of COVID-19 to predict and control the outbreak. We first formulate a comprehensive mathematical model for the dynamical transmission of COVID-19 in the context of sub-Saharan Africa. We provide the basic properties of the model and compute the basic reproduction number |$\mathcal {R}_0$| when the parameter values are constant. After, assuming continuous measurement of the weekly number of newly COVID-19 detected cases, newly deceased individuals and newly recovered individuals, the Ensemble of Kalman filter (EnKf) approach is used to estimate the unmeasured variables and unknown parameters, which are assumed to be time-dependent using real data of COVID-19. We calibrated the proposed model to fit the weekly data in Cameroon and Gabon before, during and after the lockdown. We present the forecasts of the current pandemic in these countries using the estimated parameter values and the estimated variables as initial conditions. During the estimation period, our findings suggest that |$\mathcal {R}_0 \approx 1.8377 $| in Cameroon, while |$\mathcal {R}_0 \approx 1.0379$| in Gabon meaning that the disease will not die out without any control measures in theses countries. Also, the number of undetected cases remains high in both countries, which could be the source of the new wave of COVID-19 pandemic. Short-term predictions firstly show that one can use the EnKf to predict the COVID-19 in Sub-Saharan Africa and that the second vague of the COVID-19 pandemic will still increase in the future in Gabon and in Cameroon. A comparison between the basic reproduction number from human individuals |$\mathcal {R}_{0h}$| and from the SARS-CoV-2 in the environment |$\mathcal {R}_{0v}$| has been done in Cameroon and Gabon. A comparative study during the estimation period shows that the transmissions from the free SARS-CoV-2 in the environment is greater than that from the infected individuals in Cameroon with |$\mathcal {R}_{0h}$| = 0.05721 and |$\mathcal {R}_{0v}$| = 1.78051. This imply that Cameroonian apply distancing measures between individual more than with the free SARS-CoV-2 in the environment. But, the opposite is observed in Gabon with |$\mathcal {R}_{0h}$| = 0.63899 and |$\mathcal {R}_{0v}$| = 0.39894. So, it is important to increase the awareness campaigns to reduce contacts from individual to individual in Gabon. However, long-term predictions reveal that the COVID-19 detected cases will play an important role in the spread of the disease. Further, we found that there is a necessity to increase timely the surveillance by using an awareness program and a detection process, and the eradication of the pandemic is highly dependent on the control measures taken by each government. [ABSTRACT FROM AUTHOR]

In this paper, three stochastic mathematical models are developed for the spread of the coronavirus disease (COVID-19). These models take into account the known special characteristics of this disease such as the existence of infectious undetected cases and the different social and infectiousness conditions of infected people. In particular, they include a novel approach that considers the social structure, the fraction of detected cases over the real total infected cases, the influx of undetected infected people from outside the borders, as well as contact-tracing and quarantine period for travellers. Two of these models are discrete time–discrete state space models (one is simplified and the other is complete) while the third one is a continuous time–continuous state space stochastic integro-differential model obtained by a formal passing to the limit from the proposed simplified discrete model. From a numerical point of view, the particular case of Lebanon has been studied and its reported data have been used to estimate the complete discrete model parameters, which can be of interest in estimating the spread of COVID-19 in other countries. The obtained simulation results have shown a good agreement with the reported data. Moreover, a parameters' analysis is presented in order to better understand the role of some of the parameters. This may help policy makers in deciding on different social distancing measures. [ABSTRACT FROM AUTHOR]

The collection of 3D cell tracking data from live images of micro-tissues is a recent innovation made possible due to advances in imaging techniques. As such there is increased interest in studying cell motility in 3D in vitro model systems but a lack of rigorous methodology for analysing the resulting data sets. One such instance of the use of these in vitro models is in the study of cancerous tumours. Growing multicellular tumour spheroids in vitro allows for modelling of the tumour microenvironment and the study of tumour cell behaviours, such as migration, which improves understanding of these cells and in turn could potentially improve cancer treatments. In this paper, we present a workflow for the rigorous analysis of 3D cell tracking data, based on the persistent random walk model, but adaptable to other biologically informed mathematical models. We use statistical measures to assess the fit of the model to the motility data and to estimate model parameters and provide confidence intervals for those parameters, to allow for parametrization of the model taking correlation in the data into account. We use in silico simulations to validate the workflow in 3D before testing our method on cell tracking data taken from in vitro experiments on glioblastoma tumour cells, a brain cancer with a very poor prognosis. The presented approach is intended to be accessible to both modellers and experimentalists alike in that it provides tools for uncovering features of the data set that may suggest amendments to future experiments or modelling attempts. [ABSTRACT FROM AUTHOR]

This paper focuses on the derivation and simulation of mathematical models describing new plasma fraction in blood for patients undergoing simultaneous extracorporeal membrane oxygenation and therapeutic plasma exchange. Models for plasma exchange with either veno-arterial or veno-venous extracorporeal membrane oxygenation are considered. Two classes of models are derived for each case, one in the form of an algebraic delay equation and another in the form of a system of delay differential equations. In special cases, our models reduce to single compartment ones for plasma exchange that have been validated with experimental data (Randerson et al. , 1982, Artif. Organs , 6, 43–49). We also show that the algebraic differential equations are forward Euler discretizations of the delay differential equations, with timesteps equal to transit times through model compartments. Numerical simulations are performed to compare different model types, to investigate the impact of plasma device port switching on the efficiency of the exchange process, and to study the sensitivity of the models to their parameters. [ABSTRACT FROM AUTHOR]

In 1987, Seymour Glagov observed that arteries went through a two-stage remodeling process as a result of plaque growth: first, a compensatory phase where the lumen area remains approximately constant and second, an encroachment phase where the lumen area decreases over time. In this paper, we investigate the effect of growth anisotropy on Glagov remodeling in five different cases: pure radial, pure circumferential, pure axial, isotropic and general anisotropic growth where the elements of the growth tensor are chosen to minimize the total energy. We suggest that the nature of anisotropy is inclined towards the growth direction that requires the least amount of energy. Our framework is the theory of morphoelasticity on an axisymmetric arterial domain. For each case, we explore their specific effect on the Glagov curves. For the latter two cases, we also provide the changes in collagen fiber orientation and length in the intima, media and adventitia. In addition, we compare the total energy produced by growth in radial, circumferential and axial direction and deduce that using a radially dominant anisotropic growth leads to lower strain energy than isotropic growth. [ABSTRACT FROM AUTHOR]

In this paper, we study a single serotype transmission model of dengue to determine the optimal vaccination age for Dengvaxia. The transmission dynamics are modelled with an age-dependent force of infection. The force of infection for each serotype is derived from the serological profile of dengue in Brazil without serotype distinction and from serotype-specific reported cases. The risk due to an infection is measured by the probability of requiring hospitalization based on Brazilian Ministry of Health data. The optimal vaccination age is determined for any number and combination of the four distinct dengue virus serotypes DENv1–4. The lifetime expected risk is adapted to include antibody dependent enhancement (ADE) and permanent cross-immunity after two heterologous infections. The risk is assumed to be serostatus-dependent. The optimal vaccination age is computed for constant, serostatus-specific vaccine efficacies. Additionally, the vaccination age is restricted to conform to the licence of Dengvaxia in Brazil and the achievable and minimal lifetime expected risks are compared. The optimal vaccination age obtained for the risk of hospitalization varies significantly with the assumptions relating to ADE and cross-immunity. Risk-free primary infections lead to higher optimal vaccination ages, as do asymptomatic third and fourth infections. Sometimes vaccination is not recommended at all, e.g. for any endemic area with a single serotype if primary infections are risk-free. Restricting the vaccination age to Dengvaxia licensed ages mostly leads to only a slightly higher lifetime expected risk and the vaccine should be administered as close as possible to the optimal vaccination age. [ABSTRACT FROM AUTHOR]

In recent years, biological imaging techniques have advanced significantly and it is now possible to digitally reconstruct microvascular network structures in detail, identifying the smallest capillaries at sub-micron resolution and generating large 3D structural data sets of size >106 vessel segments. However, this relies on ex vivo imaging; corresponding in vivo measures of microvascular structure and flow are limited to larger branching vessels and are not achievable in three dimensions for the smallest vessels. This suggests the use of computational modelling to combine in vivo measures of branching vessel architecture and flows with ex vivo data on complete microvascular structures to predict effective flow and pressures distributions. In this paper, a hybrid discrete–continuum model to predict microcirculatory blood flow based on structural information is developed and compared with existing models for flow and pressure in individual vessels. A continuum-based Darcy model for transport in the capillary bed is coupled via point sources of flux to flows in individual arteriolar vessels, which are described explicitly using Poiseuille's law. The venular drainage is represented as a spatially uniform flow sink. The resulting discrete–continuum framework is parameterized using structural data from the capillary network and compared with a fully discrete flow and pressure solution in three networks derived from observations of the rat mesentery. The discrete–continuum approach is feasible and effective, providing a promising tool for extracting functional transport properties in situations where vascular branching structures are well defined. [ABSTRACT FROM AUTHOR]

Cells adhere to each other and to the extracellular matrix (ECM) through protein molecules on the surface of the cells. The breaking and forming of adhesive bonds, a process critical in cancer invasion and metastasis, can be influenced by the mutation of cancer cells. In this paper, we develop a nonlocal mathematical model describing cancer cell invasion and movement as a result of integrin-controlled cell–cell adhesion and cell–matrix adhesion, for two cancer cell populations with different levels of mutation. The partial differential equations for cell dynamics are coupled with ordinary differential equations describing the ECM degradation and the production and decay of integrins. We use this model to investigate the role of cancer mutation on the possibility of cancer clonal competition with alternating dominance, or even competitive exclusion (phenomena observed experimentally). We discuss different possible cell aggregation patterns, as well as travelling wave patterns. In regard to the travelling waves, we investigate the effect of cancer mutation rate on the speed of cancer invasion. [ABSTRACT FROM AUTHOR]

Respiratory protective devices (RPDs) are critical for reducing the spread of infection via inhalable droplets. In determining the type of RPD to deploy, it is important to know the reduction in the infection rate that the RPD enables for the given pathogen and population. This paper extends a previously developed susceptible-infected-recovered (SIR) epidemic model to analyse the effect of a protection strategy. An approximate solution to the modified SIR equations, which compares well with a full numerical solution to the equations, was used to derive a simple threshold equation for predicting when growth of the infected population will occur for a given protection strategy. The threshold equation is cast in terms of a generalized reproduction number, which contains the characteristics of the RPDs deployed by the susceptible and infected populations, as well as the degree of compliance in wearing the equipment by both populations. An example calculation showed that with 50% of the susceptible population deploying RPDs that transmit 15% of pathogens and an unprotected infected population, an otherwise growing infection rate can be converted to one that decays. When the infected population deploys RPDs, the transmission rate for the RPDs worn by the susceptible population can be higher. [ABSTRACT FROM AUTHOR]

In this paper, we investigate an axisymmetric model of intimal thickening using hyperelasticity theory. Our model describes the growth of the arterial intima due to cell proliferation which, in turn, is driven by the release of a cytokine such as platelet-derived growth factor (PDGF). With the growth rate tied to both local stress and the local concentration of PDGF, we derive a quadruple free boundary problem with different regions of the vessel wall characterized by different homeostatic stress. We compare our model predictions to rabbit and rodent models of atherosclerosis and find that in order to achieve the growth rates reported in the experiments, growth must be mainly cytokine induced rather than stress induced. Our model is also able to reproduce Glagov remodelling where, as a vessel becomes more diseased, the lumen expands before rapidly contracting. [ABSTRACT FROM AUTHOR]

In this paper, we study the sensitivities of electron dose calculations with respect to stopping power and transport coefficients. We focus on the application to radiotherapy simulations. We use a Fokker-Planck approximation to the Boltzmann transport equation. Equations for the sensitivities are derived by the adjoint method. The Fokker-Planck equation and its adjoint are solved numerically in slab geometry using the spherical harmonics expansion (PN) and an Harten-Lax-van Leer finite volume method. Our method is verified by comparison to finite difference approximations of the sensitivities. Finally, we present numerical results of the sensitivities for the normalized average dose deposition depth with respect to the stopping power and the transport coefficients, demonstrating the increase in relative sensitivities as beam energy decreases. This in turn gives estimates on the uncertainty in the normalized average deposition depth, which we present. [ABSTRACT FROM AUTHOR]

The Cytochrome P450 (CYP) system is involved in 90% of the human body's interactions with xenobiotics and due to this, it has become an area of avid research including the creation of transgenic mice. This paper proposes a three-compartment model which is used to explain the drug metabolism in the Hepatic Reductase Null (HRN) mouse developed by the University of Dundee (Henderson, C. J., Otto, D. M. E., Carrie, D., Magnuson, M. A., McLaren, A. W., Rosewell, I. and Wolf, C. R. (2003) Inactivation of the hepatic cytochrome p450 system by conditional deletion of hepatic cytochrome p450 reductase. J. Biol. Chem. 278, 13480-13486). The model is compared with a two-compartment model using experimental data from studies using wild-type and HRN mice. This comparison allowed for metabolic differences between the two types of mice to be isolated. The three sets of drug data (Gefitinib, Midazolam and Thalidomide) showed that the transgenic mouse has a decreased rate of metabolism. [ABSTRACT FROM AUTHOR]

The tumour growth paradox refers to the observation that incomplete treatment of cancers can enhance their growth. As shown here and elsewhere, the existence of cancer stem cells (CSCs) can explain this effect. CSC are less sensitive to treatments, hence any stress applied to the tumour selects for CSC, thereby increasing the fitness of the tumour. In this paper, we use a mathematical model to understand the role of CSC in the progression of cancer. Our model is a rather general system of integro-differential equations for tumour growth and tumour spread. Such a model has never been analysed, and we prove results on local and global existence of solutions, their uniqueness and their boundedness. We show numerically that this model exhibits the tumour growth paradox for all parameters tested. This effect becomes more relevant for small renewal rate of the CSC. [ABSTRACT FROM AUTHOR]

Glioma is a common type of primary brain tumour, with a strongly invasive potential, often exhibiting non-uniform, highly irregular growth. This makes it difficult to assess the degree of extent of the tumour, hence bringing about a supplementary challenge for the treatment. It is therefore necessary to understand the migratory behaviour of glioma in greater detail. In this paper, we propose a multiscale model for glioma growth and migration. Our model couples the microscale dynamics (reduced to the binding of surface receptors to the surrounding tissue) with a kinetic transport equation for the cell density on the mesoscopic level of individual cells. On the latter scale, we also include the proliferation of tumour cells via effects of interaction with the tissue. An adequate parabolic scaling yields a convection-diffusion- reaction equation, for which the coefficients can be explicitly determined from the information about the tissue obtained by diffusion tensor imaging (DTI). Numerical simulations relying on DTI measurements confirm the biological findings that glioma spread along white matter tracts. [ABSTRACT FROM AUTHOR]

A coupled non-Fickian model of a cardiovascular drug delivery system using a biodegradable drugeluting stent is proposed. The numerical results are obtained using an implicit-explicit finite-element method. The influence of vessel stiffness on the transport of drug eluted from the stent is analysed. The results presented in this paper suggest new perspectives to adapt the drug delivery profile to the needs of the patient. [ABSTRACT FROM AUTHOR]

The paper investigates a version of a simple epidemiological model involving only susceptible and infected individuals, where the heterogeneity of the population with respect to susceptibility/ infectiousness is taken into account. A comprehensive analysis of the asymptotic behaviour of the disease is given, based on an explicit aggregation of the model. The results are compared with those of a homogeneous version of the model to highlight the influence of the heterogeneity on the asymptotics. Moreover, the performed analysis reveals in which cases incomplete information about the heterogeneity of the population is sufficient in order to determine the long-run outcome of the disease. Numerical simulation is used to emphasize that, for a given level of prevalence, the evolution of the disease under the influence of heterogeneity may in the long run qualitatively differ from the one 'predicted' by the homogeneous model. Furthermore, it is shown that, in a closed population, the indicator for the survival of the population is in the presence of heterogeneity distinct from the basic reproduction number. [ABSTRACT FROM AUTHOR]

In this paper, we consider the derivation of macroscopic equations appropriate to describe the growth of biological tissue, employing a multiple-scale homogenization method to accommodate explicitly the influence of the underlying microscale structure of the material, and its evolution, on the macroscale dynamics. Such methods have been widely used to study porous and poroelastic materials; however, a distinguishing feature of biological tissue is its ability to remodel continuously in response to local environmental cues. Here, we present the derivation of a model broadly applicable to tissue engineering applications, characterized by cell proliferation and extracellular matrix deposition in porous scaffolds used within tissue culture systems, which we use to study coupling between fluid flow, nutrient transport, and microscale tissue growth. Attention is restricted to surface accretion within a rigid porous medium saturated with a Newtonian fluid; coupling between the various dynamics is achieved by specifying the rate of microscale growth to be dependent upon the uptake of a generic diffusible nutrient. The resulting macroscale model comprises a Darcy-type equation governing fluid flow, with flow characteristics dictated by the assumed periodic microstructure and surface growth rate of the porous medium, coupled to an advection-reaction equation specifying the nutrient concentration. Illustrative numerical simulations are presented to indicate the influence of microscale growth on macroscale dynamics, and to highlight the importance of including experimentally relevant microstructural information to correctly determine flow dynamics and nutrient delivery in tissue engineering applications. [ABSTRACT FROM AUTHOR]

This paper developed equations describing steady-state tau distributions for three versions of the diffusion-reaction model of tau transport: a model with constant kinetic rates, a model that additionally accounts for tau diffusion along microtubules (MTs) and a model with a modulated rate of tau attachment to MTs. We demonstrated that, for the model with constant kinetic rates, the concentration of free tau in the cytoplasm was determined by a single dimensionless parameter that represents the ratio of the diffusion time (the time it takes tau to diffuse from the axon hillock to the axon tip) to the half-life of tau. We also developed a model based on the hypothesis that tau is actively transported. Analytical solutions for some special situations were obtained. The model predictions were compared with experimentally measured tau distributions in axons reported in Black et al. (1996, J. Neurosc., 16, 3601-3619), and based on these comparisons, we discussed the performance of various models. We demonstrated the significance of modulation of the tau attachment rate to MTs in the diffusion-reaction model. On the other hand, the active transport model predictions were consistent with experimental data even with constant kinetic rates. For short axons (up to 600µm in length) the predicted average transport velocity of tau was in the experimentally reported range for both the diffusion-reaction and active transport models, but for the active transport model the average tau velocity was larger. [ABSTRACT FROM AUTHOR]

Low-grade gliomas (LGGs) are a group of primary brain tumours usually encountered in young patient populations. These tumours represent a difficult challenge because many patients survive a decade or more and may be at a higher risk for treatment-related complications. Specifically, radiation therapy is known to have a relevant effect on survival but in many cases it can be deferred to avoid side effects while maintaining its beneficial effect. However, a subset of LGGs manifests more aggressive clinical behaviour and requires earlier intervention. Moreover, the effectiveness of radiotherapy depends on the tumour characteristics. Recently Pallud et al. (2012. Neuro-Oncology, 14, 1-10) studied patients with LGGs treated with radiation therapy as a first-line therapy and obtained the counterintuitive result that tumours with a fast response to the therapy had a worse prognosis than those responding late. In this paper, we construct a mathematical model describing the basic facts of glioma progression and response to radiotherapy. The model provides also an explanation to the observations of Pallud et al. Using the model, we propose radiation fractionation schemes that might be therapeutically useful by helping to evaluate tumour malignancy while at the same time reducing the toxicity associated to the treatment. [ABSTRACT FROM AUTHOR]

Drug-eluting stents have significantly improved the treatment of coronary artery disease. They offer reduced rates of restenosis compared with their bare-metal predecessors and are the current gold standard in percutaneous coronary interventions. Drug-eluting stents have been approved for use in humans since 2002 and yet, despite the intensive research activity over the past decade, the drug release mechanism(s) and the uptake into the arterial wall are still poorly understood. While stent manufacturers have focussed primarily on empirical methods, several mathematical models have appeared in the literature considering the release problem, the uptake problem and also the coupled problem. However, two significant challenges that remain are in understanding the drug release mechanism(s) and also the determination of the various parameters characterizing the system. These include drug diffusion coefficients and dissolution constants in the stent polymer coating as well as drug diffusion coefficients, binding/uptake rates and the magnitude of the transmural convection in the arterial wall. In this paper we attempt to address these problems. We provide analytical solutions which, when compared with appropriate experiments, may allow the various parameters of the system to be estimated via the inverse problem. The analytical solutions which we provide here for drug release in vitro may thus be used as a tool for providing insights into the mechanism(s) of release. [ABSTRACT FROM AUTHOR]

Statistical analysis of viral dynamics in HIV-1 infected patients undergoing structured treatment interruptions were performed using a novel model that accounts for treatment efficiency as well as total CD8+ T cell counts. A brief review of parameter estimates obtained in other studies is given, pointing to a considerable variation in the estimated values. A Bayesian approach to parameter estimation was used with longitudinal measurements of CD4+ and CD8+ T cell counts and HIV RNA. We describe an estimation procedure which uses spline approximations of CD8+ T cells dynamics. This approach reduces the number of parameters that must be estimated and is especially helpful when the CD8+ T cells growth function has a delayed dependence on the past. Seven important parameters related to HIV-1 in-host dynamics were estimated, most of them treated as global parameters across the group of patients. The estimated values were mainly in keeping with the estimates obtained in other reports, but our paper also introduces the estimates of some new parameters which supplement the current knowledge. The method was also tested on a simulated data set. [ABSTRACT FROM AUTHOR]

Social networks are often only partly observed, and it is sometimes desirable to infer global properties of the network from 'egocentric' data. In the current paper, we study different types of egocentric data, and show which global network properties are consistent with data. Two global network properties are considered: the size of the largest connected component (the giant) and the size of an epidemic outbreak taking place on the network. The main conclusion is that, in most cases, egocentric data allow for a large range of possible sizes of the giant and the outbreak, implying that egocentric data carry very little information about these global properties. The asymptotic size of the giant and the outbreak is also characterized, assuming the network is selected uniformly among networks with prescribed egocentric data. [ABSTRACT FROM AUTHOR]