Mathematical medicine and biology : a journal of the IMA最新文献

The ability to predict clinically relevant exposure to potentially hazardous compounds that can leach from polymeric components can help reduce testing needed to evaluate the biocompatibility of medical devices. In this manuscript, we compare two physics-based exposure models: 1) a simple, one-component model that assumes the only barrier to leaching is the migration of the compound through the polymer matrix and 2) a more clinically relevant, two-component model that also considers partitioning across the polymer-tissue interface and migration in the tissue away from the interface. Using data from the literature, the variation of the model parameters with key material properties were established, enabling the models to be applied to a wide range of combinations of leachable compound, polymer matrix and tissue type. Exposure predictions based on the models suggest that the models are indistinguishable over much of the range of clinically relevant scenarios. However, for systems with low partitioning and/or slow tissue diffusion, the two-component model predicted up to three orders of magnitude less mass release over the same time period. Thus, despite the added complexity, in some scenarios it can be beneficial to use the two-component model to provide more clinically relevant estimates of exposure to leachable substances from implanted devices.

Glioblastoma multiforme is a highly aggressive form of brain cancer, with a median survival time for diagnosed patients of 15 months. Treatment of this cancer is typically a combination of radiation, chemotherapy and surgical removal of the tumour. However, the highly invasive and diffuse nature of glioblastoma makes surgical intrusions difficult, and the diffusive properties of glioblastoma are poorly understood. In this paper, we introduce a stochastic interacting particle system as a model of in vitro glioblastoma migration, along with a maximum likelihood-algorithm designed for inference using microscopy imaging data. The inference method is evaluated on in silico simulation of cancer cell migration, and then applied to a real data set. We find that the inference method performs with a high degree of accuracy on the in silico data, and achieve promising results given the in vitro data set.

Epidemic models of susceptibles, exposed, infected, recovered and deceased (SΕIRD) presume homogeneity, constant rates and fixed, bilinear structure. They produce short-range, single-peak responses, hardly attained under restrictive measures. Tuned via uncertain I,R,D data, they cannot faithfully represent long-range evolution. A robust epidemic model is presented that relates infected with the entry rate to health care units (HCUs) via population averages. Model uncertainty is circumvented by not presuming any specific model structure, or constant rates. The model is tuned via data of low uncertainty, by direct monitoring: (a) of entries to HCUs (accurately known, in contrast to delayed and non-reliable I,R,D data) and (b) of scaled model parameters, representing population averages. The model encompasses random propagation of infections, delayed, randomly distributed entries to HCUs and varying exodus of non-hospitalized, as disease severity subdues. It closely follows multi-pattern growth of epidemics with possible recurrency, viral strains and mutations, varying environmental conditions, immunity levels, control measures and efficacy thereof, including vaccination. The results enable real-time identification of infected and infection rate. They allow design of resilient, cost-effective policy in real time, targeting directly the key variable to be controlled (entries to HCUs) below current HCU capacity. As demonstrated in ex post case studies, the policy can lead to lower overall cost of epidemics, by balancing the trade-off between the social cost of infected and the economic contraction associated with social distancing and mobility restriction measures.

Experimental and theoretical properties of amino acids as building blocks of peptides and proteins have been extensively researched. Each such method assigns a number to each amino acid, and one such assignment is called amino-acid scale. Their usage in bioinformatics to explain and predict behaviour of peptides and proteins is of essential value. The number of such scales is very large. There are more than a hundred scales related just to hydrophobicity. A large number of scales can be a computational burden for algorithms that try to define peptide descriptors combining several of these scales. Hence, it is of interest to construct a smaller, but still representative set of scales. Here, we present software that does this. We test it on the set of scales using a database constructed by Kawashima and collaborators and show that it is possible to significantly reduce the number of scales observed without losing much of the information. An algorithm is implemented in C#. As a result, we provide a smaller database that might be a very useful tool for the analyses and construction of new peptides. Another interesting application of this database would be to compare the artificial intelligence construction of peptides having as an input the complete Kawashima database and this reduced one. Obtaining in both cases similar results would give much credibility to the constructs of such AI algorithms.

Viral infection develops in the organism due to virus replication inside infected cells and its transmission from infected to uninfected cells through the extracellular matrix or cell junctions. In this work, we model infection spreading in tissue with a delay reaction-diffusion system of equations for the concentrations of uninfected cells, infected cells and virus. We prove the wave existence, determine its speed of propagation and introduce a simplified one-equation model obtained from the complete model using a quasi-stationary approximation.

Since 2019, a new strain of coronavirus has challenged global health systems. Due its fragile healthcare systems, Africa was predicted to be the most affected continent. However, past experiences of African countries with epidemics and other factors, including actions taken by governments, have contributed to reducing the spread of SARS-CoV-2. This study aims to assess the marginal impact of non-pharmaceutical interventions in fifteen African countries during the pre-vaccination period. To describe the transmission dynamics and control of SARS-CoV-2 spread, an extended time-dependent SEIR model was used. The transmission rate of each infectious stage was obtained using a logistic model with NPI intensity as a covariate. The results revealed that the effects of NPIs varied between countries. Overall, restrictive measures related to assembly had, in most countries, the largest reducing effects on the pre-symptomatic and mild transmission, while the transmission by severe individuals is influenced by privacy measures (more than $10%$). Countries should develop efficient alternatives to assembly restrictions to preserve the economic sector. This involves e.g. training in digital tools and strengthening digital infrastructures.

Myeloproliferative neoplasms (MPN) are blood cancers that appear after acquiring a driver mutation in a hematopoietic stem cell. These hematological malignancies result in the overproduction of mature blood cells and, if not treated, induce a risk of cardiovascular events and thrombosis. Pegylated IFN$alpha $ is commonly used to treat MPN, but no clear guidelines exist concerning the dose prescribed to patients. We applied a model selection procedure and ran a hierarchical Bayesian inference method to decipher how dose variations impact the response to the therapy. We inferred that IFN$alpha $ acts on mutated stem cells by inducing their differentiation into progenitor cells; the higher the dose, the higher the effect. We found that the treatment can induce long-term remission when a sufficient (patient-dependent) dose is reached. We determined this minimal dose for individuals in a cohort of patients and estimated the most suitable starting dose to give to a new patient to increase the chances of being cured.

We discuss the mathematical modelling of two of the main mechanisms that pushed forward the emergence of multicellularity: phenotype divergence in cell differentiation and between-cell cooperation. In line with the atavistic theory of cancer, this disease being specific of multicellular animals, we set special emphasis on how both mechanisms appear to be reversed, however not totally impaired, rather hijacked, in tumour cell populations. Two settings are considered: the completely innovating, tinkering, situation of the emergence of multicellularity in the evolution of species, which we assume to be constrained by external pressure on the cell populations, and the completely planned-in the body plan-situation of the physiological construction of a developing multicellular animal from the zygote, or of bet hedging in tumours, assumed to be of clonal formation, although the body plan is largely-but not completely-lost in its constituting cells. We show how cancer impacts these two settings and we sketch mathematical models for them. We present here our contribution to the question at stake with a background from biology, from mathematics and from philosophy of science.

A risk factor model of body mass index (BMI) is an important building block of health simulations aimed at estimating government policy effects with regard to overweight and obesity. We created a model that generates representative population level distributions and that also mimics realistic BMI trajectories at an individual level so that policies aimed at individuals can be simulated. The model is constructed by combining several datasets. First, the population level distribution is extracted from a large, cross-sectional dataset. The trend in this distribution is estimated from historical data. In addition, longitudinal data are used to model how individuals move along typical trajectories over time. The model faithfully describes the population level distribution of BMI, stratified by sex, level of education and age. It is able to generate life course trajectories for individuals which seem plausible, but it does not capture extreme fluctuations, such as rapid weight loss.

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.