1,195 research outputs found
The auxiliary region method: A hybrid method for coupling PDE- and Brownian-based dynamics for reaction-diffusion systems
Reaction-diffusion systems are used to represent many biological and physical
phenomena. They model the random motion of particles (diffusion) and
interactions between them (reactions). Such systems can be modelled at multiple
scales with varying degrees of accuracy and computational efficiency. When
representing genuinely multiscale phenomena, fine-scale models can be
prohibitively expensive, whereas coarser models, although cheaper, often lack
sufficient detail to accurately represent the phenomenon at hand. Spatial
hybrid methods couple two or more of these representations in order to improve
efficiency without compromising accuracy.
In this paper, we present a novel spatial hybrid method, which we call the
auxiliary region method (ARM), which couples PDE and Brownian-based
representations of reaction-diffusion systems. Numerical PDE solutions on one
side of an interface are coupled to Brownian-based dynamics on the other side
using compartment-based "auxiliary regions". We demonstrate that the hybrid
method is able to simulate reaction-diffusion dynamics for a number of
different test problems with high accuracy. Further, we undertake error
analysis on the ARM which demonstrates that it is robust to changes in the free
parameters in the model, where previous coupling algorithms are not. In
particular, we envisage that the method will be applicable for a wide range of
spatial multi-scales problems including, filopodial dynamics, intracellular
signalling, embryogenesis and travelling wave phenomena.Comment: 29 pages, 14 figures, 2 table
Incorporating domain growth into hybrid methods for reaction-diffusion systems
Reaction–diffusion mechanisms are a robust paradigm that can be used to represent many biological and physical phenomena over multiple spatial scales. Applications include intracellular dynamics, the migration of cells and the patterns formed by vegetation in semi-arid landscapes. Moreover, domain growth is an important process for embryonic growth and wound healing. There are many numerical modelling frameworks capable of simulating such systems on growing domains; however, each of these may be well suited to different spatial scales and particle numbers. Recently, spatially extended hybrid methods on static domains have been produced to bridge the gap between these different modelling paradigms in order to represent multi-scale phenomena. However, such methods have not been developed with domain growth in mind. In this paper, we develop three hybrid methods on growing domains, extending three of the prominent static-domain hybrid methods. We also provide detailed algorithms to allow others to employ them. We demonstrate that the methods are able to accurately model three representative reaction–diffusion systems accurately and without bias
Unbiased on lattice domain growth
Domain growth is a key process in many areas of biology, including embryonic development, the growth of tissue, and limb regeneration. As a result, mechanisms for incorporating it into traditional models for cell movement, interaction, and proliferation are of great importance. A previously well-used method to incorporate domain growth into on-lattice reaction-diffusion models causes a buildup of particles on the boundaries of the domain, which is particularly evident when diffusion is low in comparison to the rate of domain growth. Here we present an alternative method which addresses this unphysical buildup of particles at the boundaries and demonstrate that it is accurate for scenarios in which the previous method fails. Further, we discuss for which parameter regimes it is feasible to continue using the original method due to diffusion dominating the domain growth mechanism
Unbiased on lattice domain growth
Domain growth is a key process in many areas of biology, including embryonic development, the growth of tissue, and limb regeneration. As a result, mechanisms for incorporating it into traditional models for cell movement, interaction, and proliferation are of great importance. A previously well-used method to incorporate domain growth into on-lattice reaction-diffusion models causes a buildup of particles on the boundaries of the domain, which is particularly evident when diffusion is low in comparison to the rate of domain growth. Here we present an alternative method which addresses this unphysical buildup of particles at the boundaries and demonstrate that it is accurate for scenarios in which the previous method fails. Further, we discuss for which parameter regimes it is feasible to continue using the original method due to diffusion dominating the domain growth mechanism
Critical weaknesses in shielding strategies for COVID-19
The COVID-19 pandemic, caused by the coronavirus SARS-CoV-2, has led to a
wide range of non-pharmaceutical interventions being implemented around the
world to curb transmission. However, the economic and social costs of some of
these measures, especially lockdowns, has been high. An alternative and widely
discussed public health strategy for the COVID-19 pandemic would have been to
'shield' those most vulnerable to COVID-19 (minimising their contacts with
others), while allowing infection to spread among lower risk individuals with
the aim of reaching herd immunity. Here we retrospectively explore the
effectiveness of this strategy using a stochastic SEIR framework, showing that
even under the unrealistic assumption of perfect shielding, hospitals would
have been rapidly overwhelmed with many avoidable deaths among lower risk
individuals. Crucially, even a small (20%) reduction in the effectiveness of
shielding would have likely led to a large increase (>150%) in the number of
deaths compared to perfect shielding. Our findings demonstrate that shielding
the vulnerable while allowing infections to spread among the wider population
would not have been a viable public health strategy for COVID-19 and is
unlikely to be effective for future pandemics
Plasticity in transmission strategies of the malaria parasite, Plasmodium chabaudi : environmental and genetic effects
Parasites may alter their behaviour to cope with changes in the within-host environment. In particular, investment in transmission may alter in response to the availability of parasite resources or host immune responses. However, experimental and theoretical studies have drawn conflicting conclusions regarding parasites' optimal (adaptive) responses to deterioration in habitat quality. We analyse data from acute infections with six genotypes of the rodent malaria species to quantify how investment in transmission (gametocytes) is influenced by the within-host environment. Using a minimum of modelling assumptions, we find that proportional investment in gametocytogenesis increases sharply with host anaemia and also increases at low parasite densities. Further, stronger dependence of investment on parasite density is associated with greater virulence of the parasite genotype. Our study provides a robust quantitative framework for studying parasites' responses to the host environment and whether these responses are adaptive, which is crucial for predicting the short-term and evolutionary impact of transmission-blocking treatments for parasitic diseases
Spatially extended hybrid methods:A review
Many biological and physical systems exhibit behaviour at multiple spatial,
temporal or population scales. Multiscale processes provide challenges when
they are to be simulated using numerical techniques. While coarser methods such
as partial differential equations are typically fast to simulate, they lack the
individual-level detail that may be required in regions of low concentration or
small spatial scale. However, to simulate at such an individual-level
throughout a domain and in regions where concentrations are high can be
computationally expensive. Spatially-coupled hybrid methods provide a bridge,
allowing for multiple representations of the same species in one spatial domain
by partitioning space into distinct modelling subdomains. Over the past twenty
years, such hybrid methods have risen to prominence, leading to what is now a
very active research area across multiple disciplines including chemistry,
physics and mathematics.
There are three main motivations for undertaking this review. Firstly, we
have collated a large number of spatially-extended hybrid methods and presented
them in a single coherent document, while comparing and contrasting them, so
that anyone with a need for a multi-scale hybrid method will be able to find
the most appropriate one for their need. Secondly, we have provided canonical
examples with algorithms and accompanying code, serving to demonstrate how
these types of methods work in practice. Finally, we have presented papers that
employ these methods on real biological and physical problems, demonstrating
their utility. We also consider some open research questions in the area of
hybrid method development and the future directions for the field.Comment: 43 Pages, 13 Figures, 4 Table
The blending region hybrid framework for the simulation of stochastic reaction-diffusion processes
The simulation of stochastic reaction-diffusion systems using fine-grained
representations can become computationally prohibitive when particle numbers
become large. If particle numbers are sufficiently high then it may be possible
to ignore stochastic fluctuations and use a more efficient coarse-grained
simulation approach. Nevertheless, for multiscale systems which exhibit
significant spatial variation in concentration, a coarse-grained approach may
not be appropriate throughout the simulation domain. Such scenarios suggest a
hybrid paradigm in which a computationally cheap, coarse-grained model is
coupled to a more expensive, but more detailed fine-grained model enabling the
accurate simulation of the fine-scale dynamics at a reasonable computational
cost.
In this paper, in order to couple two representations of reaction-diffusion
at distinct spatial scales, we allow them to overlap in a "blending region".
Both modelling paradigms provide a valid representation of the particle density
in this region. From one end of the blending region to the other, control of
the implementation of diffusion is passed from one modelling paradigm to
another through the use of complementary "blending functions" which scale up or
down the contribution of each model to the overall diffusion. We establish the
reliability of our novel hybrid paradigm by demonstrating its simulation on
four exemplar reaction-diffusion scenarios.Comment: 36 pages, 30 figure
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