3,256 research outputs found
Computational Methods and Results for Structured Multiscale Models of Tumor Invasion
We present multiscale models of cancer tumor invasion with components at the
molecular, cellular, and tissue levels. We provide biological justifications
for the model components, present computational results from the model, and
discuss the scientific-computing methodology used to solve the model equations.
The models and methodology presented in this paper form the basis for
developing and treating increasingly complex, mechanistic models of tumor
invasion that will be more predictive and less phenomenological. Because many
of the features of the cancer models, such as taxis, aging and growth, are seen
in other biological systems, the models and methods discussed here also provide
a template for handling a broader range of biological problems
Numerical simulation of a susceptible-exposed-infectious space-continuous model for the spread of rabies in raccoons across a realistic landscape
We introduce a numerical model for the spread of a lethal infectious disease in wildlife. The reference model is a Susceptible-Exposed-Infectious system where the spatial component of the dynamics is modelled by a diffusion process. The goal is to develop a model to be used for real geographical scenarios, so we do not rely upon simplifying assumptions on the shape of the region of interest. For this reason, space discretization is carried out with the finite element method on an unstructured triangulation. A diffusion term is designed to take into account landscape heterogeneities such as mountains and waterways. Numerical simulations are carried out for rabies epidemics among raccoons in New York state. A qualitative comparison of numerical results to available data from real-world epidemics is discussed
Mixed approximation of a population diffusion equation
AbstractA numerical method is proposed to approximate the solution of a nonlinear and nonlocal system of integro-differential equations describing age-dependent population dynamics with spatial diffusion. A finite difference method along the characteristic age-time direction combined with mixed finite elements in the spatial variable is used for the approximation. Optimal order error estimates are derived for the relevant variables. Using nonnegativity of the discrete solution, a stability of the method is also proved
Numerical approximation of density dependent diffusion in age-structured population dynamics
summary:We study a numerical method for the diffusion of an age-structured population in a spatial environment. We extend the method proposed in [2] for linear diffusion problem, to the nonlinear case, where the diffusion coefficients depend on the total population. We integrate separately the age and time variables by finite differences and we discretize the space variable by finite elements. We provide stability and convergence results and we illustrate our approach with some numerical result
The cultural psychology of obesity: diffusion of pathological norms from Western to East Asian societies
We examine the accelerating worldwide obesity epidemic using a mathematical model relating a cognitive hypothalamic-pituitary-adrenal axis tuned by embedding cultural context to a signal of chronic, structured, psychosocial threat. The obesity epidemic emerges as a distorted physiological image of ratcheting social pathology involving massive, policy-driven, economic and social 'structural adjustment' causing increasing individual, family, and community insecurity. The resulting, broadly developmental, disorder, while stratified by expected divisions of class, ethnicity, and culture, is nonetheless relentlessly engulfing even affluent majority populations across the globe. The progression of analogous epidemics in affluent Western and East Asian socieities is particularly noteworthy since these enjoy markedly different cultural structures known to influence even such fundamental psychophysical phenomena as change blindness. Indeed, until recently population patterns of obesity were quite different for these cultures. We attribute the entrainment of East Asian societies into the obesity epidemic to the diffusion of Western socioeconomic practices whose imposed resource uncertainties and exacerbation of social and economic divisions constitute powerful threat signals. We find that individual-oriented 'therapeutic' interventions will be largely ineffective since the therapeutic process itself (e.g. relinace on drug treatments) embodies the very threats causing the epidemic
Epidemic processes in complex networks
In recent years the research community has accumulated overwhelming evidence
for the emergence of complex and heterogeneous connectivity patterns in a wide
range of biological and sociotechnical systems. The complex properties of
real-world networks have a profound impact on the behavior of equilibrium and
nonequilibrium phenomena occurring in various systems, and the study of
epidemic spreading is central to our understanding of the unfolding of
dynamical processes in complex networks. The theoretical analysis of epidemic
spreading in heterogeneous networks requires the development of novel
analytical frameworks, and it has produced results of conceptual and practical
relevance. A coherent and comprehensive review of the vast research activity
concerning epidemic processes is presented, detailing the successful
theoretical approaches as well as making their limits and assumptions clear.
Physicists, mathematicians, epidemiologists, computer, and social scientists
share a common interest in studying epidemic spreading and rely on similar
models for the description of the diffusion of pathogens, knowledge, and
innovation. For this reason, while focusing on the main results and the
paradigmatic models in infectious disease modeling, the major results
concerning generalized social contagion processes are also presented. Finally,
the research activity at the forefront in the study of epidemic spreading in
coevolving, coupled, and time-varying networks is reported.Comment: 62 pages, 15 figures, final versio
A numerical method for the stability analysis of linear age-structured models with nonlocal diffusion
We numerically investigate the stability of linear age-structured population
models with nonlocal diffusion, which arise naturally in describing dynamics of
infectious diseases. Compared to Laplace diffusion, the analysis of models with
nonlocal diffusion is more challenging since the associated semigroups have no
regularizing properties in the spatial variable. Nevertheless, the asymptotic
stability of the null equilibrium is determined by the spectrum of the
infinitesimal generator associated to the semigroup. We propose to approximate
the leading part of this spectrum by first reformulating the problem via
integration of the age-state and then by discretizing the generator combining a
spectral projection in space with a pseudospectral collocation in age. A
rigorous convergence analysis is provided in the case of separable model
coefficients. Results are confirmed experimentally and numerical tests are
presented also for the more general instance.Comment: 23 pages, 11 figure
Nonlocal Models in Biology and Life Sciences: Sources, Developments, and Applications
Nonlocality is important in realistic mathematical models of physical and
biological systems at small-length scales. It characterizes the properties of
two individuals located in different locations. This review illustrates
different nonlocal mathematical models applied to biology and life sciences.
The major focus has been given to sources, developments, and applications of
such models. Among other things, a systematic discussion has been provided for
the conditions of pattern formations in biological systems of population
dynamics. Special attention has also been given to nonlocal interactions on
networks, network coupling and integration, including models for brain dynamics
that provide us with an important tool to better understand neurodegenerative
diseases. In addition, we have discussed nonlocal modelling approaches for
cancer stem cells and tumor cells that are widely applied in the cell migration
processes, growth, and avascular tumors in any organ. Furthermore, the
discussed nonlocal continuum models can go sufficiently smaller scales applied
to nanotechnology to build biosensors to sense biomaterial and its
concentration. Piezoelectric and other smart materials are among them, and
these devices are becoming increasingly important in the digital and physical
world that is intrinsically interconnected with biological systems.
Additionally, we have reviewed a nonlocal theory of peridynamics, which deals
with continuous and discrete media and applies to model the relationship
between fracture and healing in cortical bone, tissue growth and shrinkage, and
other areas increasingly important in biomedical and bioengineering
applications. Finally, we provided a comprehensive summary of emerging trends
and highlighted future directions in this rapidly expanding field.Comment: 71 page
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