Minimal reaction schemes for pattern formation.

We link continuum models of reaction-diffusion systems that exhibit diffusion-driven instability to constraints on the particle-scale interactions underpinning this instability. While innumerable biological, chemical and physical patterns have been studied through the lens of Alan Turing's reaction-diffusion pattern-forming mechanism, the connections between models of pattern formation and the nature of the particle interactions generating them have been relatively understudied in comparison with the substantial efforts that have been focused on understanding proposed continuum systems. To derive the necessary reactant combinations for the most parsimonious reaction schemes, we analyse the emergent continuum models in terms of possible generating elementary reaction schemes. This analysis results in the complete list of such schemes containing the fewest reactions; these are the simplest possible hypothetical mass-action models for a pattern-forming system of two interacting species.

Mathematical methods for scaling from within-host to population-scale in infectious disease systems.

Mathematical modellers model infectious disease dynamics at different scales. Within-host models represent the spread of pathogens inside an individual, whilst between-host models track transmission between individuals. However, pathogen dynamics at one scale affect those at another. This has led to the development of multiscale models that connect within-host and between-host dynamics. In this article, we systematically review the literature on multiscale infectious disease modelling according to PRISMA guidelines, dividing previously published models into five categories governing their methodological approaches (Garira (2017)), explaining their benefits and limitations. We provide a primer on developing multiscale models of infectious diseases.

Rapid mechanosensitive migration and dispersal of newly divided mesenchymal cells aid their recruitment into dermal condensates.

Embryonic mesenchymal cells are dispersed within an extracellular matrix but can coalesce to form condensates with key developmental roles. Cells within condensates undergo fate and morphological changes and induce cell fate changes in nearby epithelia to produce structures including hair follicles, feathers, or intestinal villi. Here, by imaging mouse and chicken embryonic skin, we find that mesenchymal cells undergo much of their dispersal in early interphase, in a stereotyped process of displacement driven by 3 hours of rapid and persistent migration followed by a long period of low motility. The cell division plane and the elevated migration speed and persistence of newly born mesenchymal cells are mechanosensitive, aligning with tissue tension, and are reliant on active WNT secretion. This behaviour disperses mesenchymal cells and allows daughters of recent divisions to travel long distances to enter dermal condensates, demonstrating an unanticipated effect of cell cycle subphase on core mesenchymal behaviour.

Swapping in lattice-based cell migration models.

Cell migration is frequently modeled using on-lattice agent-based models (ABMs) that employ the excluded volume interaction. However, cells are also capable of exhibiting more complex cell-cell interactions, such as adhesion, repulsion, pulling, pushing, and swapping. Although the first four of these have already been incorporated into mathematical models for cell migration, swapping has not been well studied in this context. In this paper, we develop an ABM for cell movement in which an active agent can "swap" its position with another agent in its neighborhood with a given swapping probability. We consider a two-species system for which we derive the corresponding macroscopic model and compare it with the average behavior of the ABM. We see good agreement between the ABM and the macroscopic density. We also analyze the movement of agents at an individual level in the single-species as well as two-species scenarios to quantify the effects of swapping on an agent's motility.

Stochastic drift in discrete waves of nonlocally interacting particles.

In this paper, we investigate a generalized model of N particles undergoing second-order nonlocal interactions on a lattice. Our results have applications across many research areas, including the modeling of migration, information dynamics, and Muller's ratchet-the irreversible accumulation of deleterious mutations in an evolving population. Strikingly, numerical simulations of the model are observed to deviate significantly from its mean-field approximation even for large population sizes. We show that the disagreement between deterministic and stochastic solutions stems from finite-size effects that change the propagation speed and cause the position of the wave to fluctuate. These effects are shown to decay anomalously as (lnN)^{-2} and (lnN)^{-3}, respectively-much slower than the usual N^{-1/2} factor. Our results suggest that the accumulation of deleterious mutations in a Muller's ratchet and the loss of awareness in a population may occur much faster than predicted by the corresponding deterministic models. The general applicability of our model suggests that this unexpected scaling could be important in a wide range of real-world applications.

Equivalence framework for an age-structured multistage representation of the cell cycle.

We develop theoretical equivalences between stochastic and deterministic models for populations of individual cells stratified by age. Specifically, we develop a hierarchical system of equations describing the full dynamics of an age-structured multistage Markov process for approximating cell cycle time distributions. We further demonstrate that the resulting mean behavior is equivalent, over large timescales, to the classical McKendrick-von Foerster integropartial differential equation. We conclude by extending this framework to a spatial context, facilitating the modeling of traveling wave phenomena and cell-mediated pattern formation. More generally, this methodology may be extended to myriad reaction-diffusion processes for which the age of individuals is relevant to the dynamics.

Pleiotropic constraints promote the evolution of cooperation in cellular groups.

The evolution of cooperation in cellular groups is threatened by lineages of cheaters that proliferate at the expense of the group. These cell lineages occur within microbial communities, and multicellular organisms in the form of tumours and cancer. In contrast to an earlier study, here we show how the evolution of pleiotropic genetic architectures-which link the expression of cooperative and private traits-can protect against cheater lineages and allow cooperation to evolve. We develop an age-structured model of cellular groups and show that cooperation breaks down more slowly within groups that tie expression to a private trait than in groups that do not. We then show that this results in group selection for pleiotropy, which strongly promotes cooperation by limiting the emergence of cheater lineages. These results predict that pleiotropy will rapidly evolve, so long as groups persist long enough for cheater lineages to threaten cooperation. Our results hold when pleiotropic links can be undermined by mutations, when pleiotropy is itself costly, and in mixed-genotype groups such as those that occur in microbes. Finally, we consider features of multicellular organisms-a germ line and delayed reproductive maturity-and show that pleiotropy is again predicted to be important for maintaining cooperation. The study of cancer in multicellular organisms provides the best evidence for pleiotropic constraints, where abberant cell proliferation is linked to apoptosis, senescence, and terminal differentiation. Alongside development from a single cell, we propose that the evolution of pleiotropic constraints has been critical for cooperation in many cellular groups.

Misinformation can prevent the suppression of epidemics.

The effectiveness of non-pharmaceutical interventions, such as mask-wearing and social distancing, as control measures for pandemic disease relies upon a conscientious and well-informed public who are aware of and prepared to follow advice. Unfortunately, public health messages can be undermined by competing misinformation and conspiracy theories, spread virally through communities that are already distrustful of expert opinion. In this article, we propose and analyse a simple model of the interaction between disease spread and awareness dynamics in a heterogeneous population composed of both trusting individuals who seek better quality information and will take precautionary measures, and distrusting individuals who reject better quality information and have overall riskier behaviour. We show that, as the density of the distrusting population increases, the model passes through a phase transition to a state in which major outbreaks cannot be suppressed. Our work highlights the urgent need for effective interventions to increase trust and inform the public.

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.

Vaccinating adolescents against SARS-CoV-2 in England: a risk-benefit analysis.

OBJECTIVE: To offer a quantitative risk-benefit analysis of two doses of SARS-CoV-2 vaccination among adolescents in England. SETTING: England. DESIGN: Following the risk-benefit analysis methodology carried out by the US Centers for Disease Control, we calculated historical rates of hospital admission, Intensive Care Unit admission and death for ascertained SARS-CoV-2 cases in children aged 12-17 in England. We then used these rates alongside a range of estimates for incidence of long COVID, vaccine efficacy and vaccine-induced myocarditis, to estimate hospital and Intensive Care Unit admissions, deaths and cases of long COVID over a period of 16 weeks under assumptions of high and low case incidence. PARTICIPANTS: All 12-17 year olds with a record of confirmed SARS-CoV-2 infection in England between 1 July 2020 and 31 March 2021 using national linked electronic health records, accessed through the British Heart Foundation Data Science Centre. MAIN OUTCOME MEASURES: Hospitalisations, Intensive Care Unit admissions, deaths and cases of long COVID averted by vaccinating all 12-17 year olds in England over a 16-week period under different estimates of future case incidence. RESULTS: At high future case incidence of 1000/100,000 population/week over 16 weeks, vaccination could avert 4430 hospital admissions and 36 deaths over 16 weeks. At the low incidence of 50/100,000/week, vaccination could avert 70 hospital admissions and two deaths over 16 weeks. The benefit of vaccination in terms of hospitalisations in adolescents outweighs risks unless case rates are sustainably very low (below 30/100,000 teenagers/week). Benefit of vaccination exists at any case rate for the outcomes of death and long COVID, since neither have been associated with vaccination to date. CONCLUSIONS: Given the current (as at 15 September 2021) high case rates (680/100,000 population/week in 10-19 year olds) in England, our findings support vaccination of adolescents against SARS-CoV2.

Tackling the pandemic with (biased) data.

Data are crucial for understanding and addressing the pandemic, but there are pitfalls.

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.

Synchronized oscillations in growing cell populations are explained by demographic noise.

Understanding synchrony in growing populations is important for applications as diverse as epidemiology and cancer treatment. Recent experiments employing fluorescent reporters in melanoma cell lines have uncovered growing subpopulations exhibiting sustained oscillations, with nearby cells appearing to synchronize their cycles. In this study, we demonstrate that the behavior observed is consistent with long-lasting transient phenomenon initiated and amplified by the finite-sample effects and demographic noise. We present a novel mathematical analysis of a multistage model of cell growth, which accurately reproduces the synchronized oscillations. As part of the analysis, we elucidate the transient and asymptotic phases of the dynamics and derive an analytical formula to quantify the effect of demographic noise in the appearance of the oscillations. The implications of these findings are broad, such as providing insight into experimental protocols that are used to study the growth of asynchronous populations and, in particular, those investigations relating to anticancer drug discovery.

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.