We construct a multi-stage cell lineage model including self-renewal, apoptosis, cell movement and the symmetrical/asymmetrical division of stem cells. The evolution of cell populations can be described by coupled reaction-diffusion partial differential equations, and the propagating wavefront speeds can be obtained analytically and verified by numerical solutions of the equations. The emphasis is on the effect of symmetric/asymmetric division of stem cells on the population and propagating dynamics of cell lineage. It is found that stem cells' asymmetric cell division (ACD) can move the phase boundary of the homogenous solution of the system. The population of the cell lineage will be promoted in presence of ACD. The concentration of stem cells increases with ACD but that of differentiated daughter cells decreases with ACD. In addition, it is found that the propagating speed of the stem cells can be evaluated with ACD. When the daughter cells move fast to a new space, stem cells can catch them up through increasing ACD. Our results may suggest a mechanism of collective migration of cell lineage through cooperation between ACD of stem cells and fast diffusion of the daughter cells.

Oncolytic viruses are a promising new treatment for cancer, whereby viruses are engineered to selectively destroy cancer cells. Mathematical modelling of the dynamics of the virus-tumour system can be modelled to provide insight into the system outcomes under different treatment protocols. In this study key metrics of treatment efficacy were identified and the mathematical model used to develop a decision framework to assess different treatment protocols. The optimal treatment outcome is the interplay between the virus application protocol and the uncertainty about the tumour characteristics. The uncertainty in the model parameters decreases as more data is available for their inference - however to obtain more data more time is required and the tumour then grows in size. Thus, there is an inherent tension whether it is better to wait to know the characteristics of the tumour system better or immediately initiating treatment. It is shown that, for small tumours, parameter inference with limited data does not constrain the choice of treatment protocol and rather only influences longer term decisions.

A principal objective in agriculture is to maximise food production; this is particularly relevant with the added demands of an ever increasing population, coupled with the unpredictability that climate change brings. Further improvements in productivity can only be achieved with an increased understanding of plant and crop processes. In this respect, mathematical modelling of plants and crops plays an important role. In this paper we present a two-scale mathematical model of crop yield that accounts for plant growth and canopy interactions. A system of nonlinear ordinary differential equations (ODEs) is formulated to describe the growth of each individual plant, where equations are coupled via a term that describes plant competition via canopy-canopy interactions. A crop of greenhouse plants is then modelled via an agent based modelling approach in which the growth of each plant is described via our system of ODEs. The model is formulated for the African drought tolerant legume bambara groundnut (Vigna subterranea), which is currently being investigated as a food source in light of climate change and food insecurity challenges. Our model allows us to account for plant diversity and also investigate the effect of individual plant traits (e.g. plant canopy size and planting distance) on the yield of the overall crop. Informed with greenhouse data, model results show that plant positioning relative to other plants has a large impact on individual plant yield. Variation in physiological plant traits from genetic diversity and the environmental effects lead to experimentally observed variations in crop yield. These traits include plant height, plant carrying capacity, leaf accumulation rate and canopy spread. Of these traits plant height and ground cover growth rates are found to have the greatest impact on crop yield. We also consider a range of different planting arrangements (uniform grid, staggered grid, circular rings and random allocation) and find that the staggered grid leads to the greatest crop yield (6% more compared to uniform grid). Whilst formulated specifically for bambara groundnut, the generic formulation of our model means that with changes to certain parameter's, it may be extended to other crop species that form a canopy.

Marine central-place foragers are increasingly faced with altered prey landscapes, necessitating predictions of the impact of such changes on behavior, reproductive success, and population dynamics. We used state-dependent behavioral life history theory implemented via Stochastic Dynamic Programming (SDP) to explore the influence of changes in prey distribution and energy gain from foraging on the behavior and reproductive success of a central place forager during lactation. Our work is motivated by northern fur seals (Callorhinus ursinus) because of the ongoing population decline of the Eastern Pacific stock and projected declines in biomass of walleye pollock (Gadus chalcogrammus), a key fur seal prey species in the eastern Bering Sea. We also explored how changes in female and pup metabolic rates, body size, and lactation duration affected model output to provide insight into traits that might experience selective pressure in response to reductions in prey availability. Simulated females adopted a central-place foraging strategy after an initial extended period spent on land (4.7-8.3 days). Trip durations increased as the high energy prey patch moved farther from land or when the energy gain from foraging decreased. Increases in trip duration adversely affected pup growth rates and wean mass despite attempts to compensate by increasing land durations. Metabolic rate changes had the largest impacts on pup wean mass, with reductions in a pup's metabolic rate allowing females to successfully forage at distances of 600+ km from land for up to 15+ days. Our results indicate that without physiological adaptations, a rookery is unlikely to be viable if the primary foraging grounds are 400 km or farther from the rookery. To achieve pup growth rates characteristic of a population experiencing rapid growth, model results indicate the primary foraging grounds need to be <150 km from the rookery.

Early detection of invaders requires finding small numbers of individuals across large landscapes. It has been argued that the only feasible way to achieve the sampling effort needed for early detection of an invader is to involve volunteer groups (citizen scientists, passive surveyors, etc.). A key concern is that volunteers may have a considerable false-positive and false-negative rate. The question then becomes whether verification of a report from a volunteer is worth the effort. This question is the topic of this paper. Since we are interested in early detection we calculate the Z% upper limit of the one sided confidence interval of the incidence (fraction infected) and use the term maximum expected plausible incidence for this. We compare the maximum plausible incidence when the expert samples on their own, qE∼, and the maximum plausible incidence when the expert only verifies cases reported by the volunteer surveyor to be infected, qV∼. The maximum plausible incidences qE∼ and qV∼. are related as, qV∼=θfp1-θfnqE∼ where θfp and θfn are the false positive and false negative rate of the volunteer surveyor, respectively. We also show that the optimal monitoring programme consists of verifying only the cases reported by the volunteer surveyor if, TXTN<θfp1-θfn, where TN is the time needed for a sample taken by the expert and TX is the time needed for an expert to verify a case reported by a volunteer surveyor. Our results can be used to calculate the maximum plausible incidence of a plant disease based on reports of passive surveyors that have been verified by experts and data from experts sampling on their own. The results can also be used in the development phase of a surveillance project to assess whether including passive surveyor reports is useful in the early detection of exotic invaders.

Measuring the phase synchronization between different brain regions in functional brain networks is a common approach to investigate many psychological disorders such as Attention Deficit Hyperactivity Disorder (ADHD). The emotional processing deficit in ADHD children is one of the main obstacles in their social interactions. In this study, the nonlinear Correlation between Probability of Recurrences (CPR) method is used for the first time to construct functional brain networks of 22 boys with ADHD and 22 healthy ones during watching four visual-emotional stimuli types. Topological features of brain networks, including shortest path length, clustering coefficient, and nodes strengths, are investigated in groups of ADHD and healthy. The results indicate a significantly (P-Values < 0.01) greater average clustering coefficient and lower shortest path length in the brain networks of ADHD individuals than the healthy ones. Accordingly, in the ADHD brain networks, the information exchange in both local and global scales is abnormally more than the healthy ones, leading to a hyper-synchronization in this group. The topological alterations of ADHD brain networks are mainly observed in the brain's frontal and occipital lobes, indicating impaired brain function of this group in emotional and visual processing. This survey demonstrates that the CPR method can be a good candidate for distinguishing the phase interactions of ADHD and healthy brain networks. Therefore, this study can contribute to further insights into the nonlinear dynamics analysis of brain networks in ADHD individuals.

Update of medRxiv. 2022 Jul 29;:

During the COVID-19 pandemic, some countries, such as Australia, China, Iceland, New Zealand, Thailand, and Vietnam successfully implemented an elimination strategy, enacting strict border control and periods of lockdowns to end community transmission. Atlantic Canada and Canada's territories implemented similar policies, and reported long periods with no community cases. In Newfoundland and Labrador (NL), Nova Scotia, and Prince Edward Island a median of 80% or more of daily reported cases were travel-related from July 1, 2020 to May 31, 2021. With increasing vaccination coverage, it may be appropriate to exit an elimination strategy, but most existing epidemiological frameworks are applicable only to situations where most cases occur in the community, and are not appropriate for regions that have implemented an elimination strategy. To inform the pandemic response in regions that are implementing an elimination strategy, we extend importation modelling to consider post-arrival travel restrictions, and pharmaceutical and non-pharmaceutical interventions in the local community. We find that shortly after the Omicron variant had begun spreading in Canada, the expected daily number of spillovers, infections spread to NL community members from travellers and their close contacts, was higher than any time previously in the pandemic. By December 24, 2021, the expected number of spillovers was 44% higher than the previous high, which occurred in late July 2021 shortly after travel restrictions were first relaxed. We develop a method to assess the characteristics of potential future community outbreaks in regions that are implementing an elimination strategy. We apply this method to predict the effect of variant and vaccination coverage on the size of hypothetical community outbreaks in Mount Pearl, a suburb of the St. John's metropolitan area in NL. Our methodology can be used to evaluate alternative plans to relax public health restrictions when vaccine coverage is high in regions that have implemented an elimination strategy. This manuscript was submitted as part of a theme issue on "Modelling COVID-19 and Preparedness for Future Pandemics".

Previous work has shown how a minimal ecological structure consisting of patchily distributed resources and recurrent dispersal between patches can scaffold Darwinian properties onto collections of cells. When the timescale of dispersal is long compared with the time to consume resources, patch fitness increases but comes at a cost to cell growth rates. This creates conditions that initiate evolutionary transitions in individuality. A key feature of the scaffold is a bottleneck created during dispersal, causing patches to be founded by single cells. The bottleneck decreases competition within patches and, hence, creates a strong hereditary link at the level of patches. Here, we construct a fully stochastic model to investigate the effect of bottleneck size on the evolutionary dynamics of both cells and collectives. We show that larger bottlenecks simply slow the dynamics, but, at some point, which depends on the parameters of the within-patch model, the direction of evolution towards the equilibrium reverses. Introduction of random fluctuations in bottleneck sizes with some positive probability of smaller sizes counteracts this, even when the probability of smaller bottlenecks is minimal.

Computational models allow to explain phenomena that cannot be observed through an animal model, such as the strain and stress states which can highly influence regeneration of the tissue. For this purpose, we have developed a simulation tool to determine the mechanical conditions provided by the polymeric scaffold. The computational model considered the articular cartilage, the subchondral bone, and the scaffold. All materials were modeled as poroelastic, and the cartilage had linear-elastic oriented collagen fibers. This model was able to explain the remodeling process that subchondral bone goes through, and how the scaffold allowed the conditions for cartilage regeneration. These results suggest that the use of scaffolds might lead the cartilaginous tissue growth in vivo by providing a better mechanical environment. Moreover, the developed computational model demonstrated to be useful as a tool prior experimental in vivo studies, by predicting the possible outcome of newly proposed treatments allowing to discard approaches that might not bring good results.

We describe a novel mathematical model for blood flow, delivery of nanoparticles, and heat transport in vascularised tumour tissue. The model, which is derived via the asymptotic homogenisation technique, provides a link between the macroscale behaviour of the system and its underlying, tortuous micro-structure, as parametrised in Penta and Ambrosi (2015). It consists of a double Darcy's law, coupled with a double advection-diffusion-reaction system describing heat transport, and an advection-diffusion-reaction equation for transport and adhesion of particles. Particles are assumed sufficiently large and do not extravasate to the tumour interstitial space but blood and heat can be exchanged between the two compartments. Numerical simulations of the model are performed using a finite element method to investigate cancer hyperthermia induced by the application of magnetic field applied to injected iron oxide nanoparticles. Since tumour microvasculature is more tortuous than that of healthy tissue and thus suboptimal in terms of fluid and drug transport, we study the influence of the vessels' geometry on tumour temperature. Effective and safe hyperthermia treatment requires tumour temperature within certain target range, generally estimated between 42 °C and 46 °C, for a certain target duration, typically 0.5h to 2h. As temperature is difficult to measure in situ, we use our model to determine the ranges of tortuosity of the microvessels, magnetic intensity, injection time, wall shear stress rate, and concentration of nanoparticles required to achieve given target conditions.

Organisms have evolved different mechanisms in response to periods of environmental stress, including dormancy - a reversible state of reduced metabolic activity. Transitions to and from dormancy can be random or induced by changes in environmental conditions. Prior theoretical work has shown that stochastic transitioning between active and dormant states at the individual level can maximize fitness at the population level. However, such theories of 'bet-hedging' strategies typically neglect certain physiological features of transitions to dormancy, including time lags to gain protective benefits. Here, we construct and analyze a dynamic model that couples stochastic changes in environmental state with the population dynamics of organisms that can initiate dormancy after an explicit time delay. Stochastic environments are simulated using a multi-state Markov chain through which the mean and variance of environmental residence time can be adjusted. In the absence of time lags (or in the limit of very short lags), we find that bet-hedging strategy transition probabilities scale inversely with the mean environmental residence times, consistent with prior theory. We also find that increasing delays in dormancy decreases optimal transitioning probabilities, an effect that can be influenced by the correlations of environmental noise. When environmental residence times - either good or bad - are uncorrelated, the maximum population level fitness is obtained given low levels of transitioning between active and dormant states. However when environmental residence times are correlated, optimal dormancy initiation and termination probabilities increase insofar as the mean environmental persistent time is longer than the delay to reach dormancy. We also find that bet hedging is no longer advantageous when delays to enter dormancy exceed the mean environmental residence times. Altogether, these results show how physiological limits to dormancy and environmental dynamics shape the evolutionary benefits and even viability of bet hedging strategies at population scales.

Calcification in photosynthetic scleractinian corals is a complicated process that involves many different biological, chemical, and physical sub-processes that happen within and around the coral tissue. Identifying and quantifying the role of separate processes in vivo or in vitro is difficult or not possible. A computational model can facilitate this research by simulating the sub-processes independently. This study presents a spatio-temporal model of the calcification physiology, which is based on processes that are considered essential for calcification: respiration, photosynthesis, Ca2＋-ATPase, carbonic anhydrase. The model is used to test different hypotheses considering ion transport across the calicoblastic cells and Light Enhanced Calcification (LEC). It is also used to quantify the effect of ocean acidification (OA) on the Extracellular Calcifying Medium (ECM) and ATP-consumption of Ca2＋-ATPase. It was able to reproduce the experimental data of three separate studies and finds that paracellular transport plays a minor role compared to transcellular transport. In the model, LEC results from increased Ca2＋-ATPase activity in combination with increased metabolism. Implementing OA increases the concentration of CO2 throughout the entire tissue, thereby increasing the availability of CO3- in the ECM. As a result, the model finds that calcification becomes more energy-demanding and the calcification rate increases.

The coronavirus disease 2019 (COVID-19) pandemic that has been ongoing since 2019 is still ongoing and how to control it is one of the international issues to be addressed. Antiviral drugs that reduce the viral load in terms of reducing the risk of secondary infection are important. For the general control of emerging infectious diseases, establishing an efficient method to evaluate candidate therapeutic agents will lead to a rapid response. We evaluated clinical trial designs for viral entry inhibitors that have the potential to be effective pre-exposure prophylactic drugs in addition to reducing viral load after infection. We used a previously developed simulation of clinical trials based on a mathematical model of within-host viral infection dynamics to evaluate sample sizes in clinical trials of viral entry inhibitors against COVID-19. We assumed four measures as outcomes, namely change in log10-transformed viral load from symptom onset, PCR positive ratio, log10-transformed viral load, and cumulative viral load, and then sample sizes were calculated for drugs with 99 % and 95 % antiviral efficacy. Consistent with previous results, we found that sample sizes could be dramatically reduced for all outcomes used in an analysis by adopting inclusion/exclusion criteria such that only patients in the early post-infection period would be included in a clinical trial. A comparison of sample sizes across outcomes demonstrated an optimal measurement schedule associated with the nature of the outcome measured for the evaluation of drug efficacy. In particular, the sample sizes calculated from the change in viral load and from viral load tended to be small when measurements were taken at earlier time points after treatment initiation. For the cumulative viral load, the sample size was lower than that from the other outcomes when the stricter inclusion/exclusion criteria to include patients whose time since onset is earlier than 2 days was used. We concluded that the design of efficient clinical trials should consider the inclusion/exclusion criteria and measurement schedules, as well as outcome selection based on sample size, personnel and budget needed to conduct the trial, and the importance of the outcome regarding the medical and societal requirements. This study provides insights into clinical trial design for a variety of situations, especially addressing infectious disease prevalence and feasible trial sizes. This manuscript was submitted as part of a theme issue on "Modelling COVID-19 and Preparedness for Future Pandemics".

Segmentation is well known to digest the food rich in proteins, starch, and lipids; however, the mechanism leading to the digestion remains unclear. In this study, a theoretical model for segmental contractions of the small intestine is developed using lubrication method to explore the mechanisms involved. Here, the nonlinear partial differential equations governing the fluid flow were normalized in viscous regime and solved semi-analytically for a power law fluid under long wavelength approximation on a MatlabTM platform. Study indicates that shearing is highest at the 1st and 4th mid-occlusion in comparison to 2nd and 3rd mid-occlusion. Parametric study indicates that the flow is sensitive to - the span of segmentation or wavelength of the wave, occlusion of the wave and frequency of the contraction; with shearing being highest for dilatants. Shearing is more prominent at higher occlusion (>50 %) and frequency (>6Hz). Further, mixing is more prominent at the steep regions of the wave; having intensity of mixing highest for the outer waves in comparison to waves at mid-region of the segmentation. The power demand is found to be greater in segmentation and has the following precedence - frequency, wavelength, flow behavior index, and occlusion (up to 80 %). Further, multiplicity of the wave gives rise to multiple zones of mixing which increases the rate of mixing of the contents. Suggesting that, the segmentation primarily serves the purpose of mixing. The study will be useful to explore novel therapeutic strategies of managing patients suffering from various motility-associated disorders of the small intestine.

A mathematical model of infection, inflammation and immune response in an idealized bronchial tree is developed. This work is based on a model from the literature that is extended to account for the propagation dynamics of an infection between the airways. The inflammation affects the size of the airways, the air flows distribution in the airway tree, and, consequently, the oxygen transfers to blood. We test different infections outcomes and propagation speed. In the hypotheses of our model, the inflammation can reduce notably and sometimes drastically the oxygen flow to blood. Our model predicts how the air flows and oxygen exchanges reorganize in the tree during an infection. Our results highlight the links between the localization of the infection and the amplitude of the loss of oxygen flow to blood. We show that a compensation phenomena due to the reorganization of the flow exists, but that it remains marginal unless the power produced the ventilation muscles is increased. Our model forms a first step towards a better understanding of the dynamics of bronchial infections.