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

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.

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.

Background: Predicting the endemic/epidemic transition during the temporal evolution of a contagious disease.

Methods: Indicators for detecting the transition endemic/epidemic, with four scalars to be compared, are calculated from the daily reported news cases: coefficient of variation, skewness, kurtosis, and entropy. The indicators selected are related to the shape of the empirical distribution of the new cases observed over 14 days. This duration has been chosen to smooth out the effect of weekends when fewer new cases are registered. For finding a forecasting variable, we have used the principal component analysis (PCA), whose first principal component (a linear combination of the selected indicators) explains a large part of the observed variance and can then be used as a predictor of the phenomenon studied (here the occurrence of an epidemic wave).

Results: A score has been built from the four proposed indicators using the PCA, which allows an acceptable level of forecasting performance by giving a realistic retro-predicted date for the rupture of the stationary endemic model corresponding to the entrance in the epidemic exponential growth phase. This score is applied to the retro-prediction of the limits of the different phases of the COVID-19 outbreak in successive endemic/epidemic transitions for three countries, France, India, and Japan.

Conclusion: We provided a new forecasting method for predicting an epidemic wave occurring after an endemic phase for a contagious disease.

The goal of this work is to understand and quantify how a line with nonlocal diffusion given by an integral enhances a reaction-diffusion process occurring in the surrounding plane. This is part of a long term programme where we aim at modelling, in a mathematically rigorous way, the effect of transportation networks on the speed of biological invasions or propagation of epidemics. We prove the existence of a global propagation speed and characterise in terms of the parameters of the system the situations where such a speed is boosted by the presence of the line. In the course of the study we also uncover unexpected regularity properties of the model. On the quantitative side, the two main parameters are the intensity of the diffusion kernel and the characteristic size of its support. One outcome of this work is that the propagation speed will significantly be enhanced even if only one of the two is large, thus broadening the picture that we have already drawn in our previous works on the subject, with local diffusion modelled by a standard Laplacian. We further investigate the role of the other parameters, enlightening some subtle effects due to the interplay between the diffusion in the half plane and that on the line. Lastly, in the context of propagation of epidemics, we also discuss the model where, instead of a diffusion, displacement on the line comes from a pure transport term.

This paper is concerned with the existence of transition fronts for a one-dimensional two patch model with KPP reaction terms. Density and flux conditions are imposed at the interface between the two patches. We first construct a pair of suitable super- and sub solutions by making full use of information of the leading edges of two KPP fronts and gluing them through the interface conditions. Then, an entire solution obtained thanks to a limiting argument is shown to be a transition front moving from one patch to the other one. This propagating solution admits asymptotic past and future speeds, and it connects two different fronts, each associated with one of the two patches. The paper thus provides the first example of a transition front for a KPP-type two-patch model with interface conditions.

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.