Bulletin of Mathematical Biology最新文献

The sterile insect technique (SIT) is a biological control technique based on mass-rearing, radiation-based sterilization that can induce fitness costs, and releases of the pest species targeted for population control. Sterile matings, between females and sterilized males, can reduce the overall population growth rate and cause a fall in population density. However, a proportion of irradiated males may escape sterilization, resulting in what is called residual fertility. Our aim in this study was to examine the impact of residual fertility on pest control employing a modeling approach. We modeled pest population dynamics with three generic differential equations representing sterilized males, wild males and wild females. We explored the impact of residual fertility, in the presence or absence of fitness costs, on potential pest control outcomes using a scenario with $100\%$ male sterilization as our standard of reference. We carried out a detailed mathematical analysis of the model's dynamics by calculating model equilibria and the latter's stability. Bifurcation analyses were performed with parameters for the Mediterranean fruit fly Ceratitis capitata. We showed that, when residual fertility is below a threshold value, wild populations can be eradicated by flooding the landscape with irradiated males. This threshold is higher when residual fertility is associated with fitness costs. Too high a level of residual fertility makes SIT less effective and hinders population eradication. That said, substantial decreases in population density can be achieved even when residual fertility is much larger than the above threshold.

The extracellular matrix (ECM) is a complex structure involved in many biological processes with collagen being the most abundant protein. Density of collagen fibers in the matrix is a factor influencing cell motility and migration speed. In cancer, this affects the ability of cells to migrate and invade distant tissues which is relevant for designing new therapies. Furthermore, increased cancer cell migration and invasion have been observed in hypoxic conditions. Interestingly, it has been revealed that the Hypoxia Inducible Factor (HIF) can not only impact the levels of metabolic genes but several collagen remodeling genes as well. The goal of this paper is to explore the impact of the HIF protein on both the tumour metabolism and the cancer cell migration with a focus on the Warburg effect and collagen remodelling processes. Therefore, we present an agent-based model (ABM) of tumour growth combining genetic regulations with metabolic and collagen-related processes involved in HIF pathways. Cancer cell migration is influenced by the extra-cellular collagen through a biphasic response dependant on collagen density. Results of the model showed that extra-cellular collagen within the tumour was mainly influenced by the local cellular density while collagen also influenced the shape of the tumour. In our simulations, proliferation was reduced with higher extra-cellular collagen levels or with lower oxygen levels but reached a maximum in the absence of cell-cell adhesion. Interestingly, combining lower levels of oxygen with higher levels of collagen further reduced the proliferation of the tumour. Since HIF impacts the metabolism and may affect the appearance of the Warburg Effect, we investigated whether different collagen conditions could lead to the adoption of the Warburg phenotype. We found that this was not the case, results suggested that adoption of the Warburg phenotype seemed mainly controlled by inhibition of oxidative metabolism by HIF combined with oscillations of oxygen.

Immune events such as infection, vaccination, and a combination of the two result in distinct time-dependent antibody responses in affected individuals. These responses and event prevalence combine non-trivially to govern antibody levels sampled from a population. Time-dependence and disease prevalence pose considerable modeling challenges that need to be addressed to provide a rigorous mathematical underpinning of the underlying biology. We propose a time-inhomogeneous Markov chain model for event-to-event transitions coupled with a probabilistic framework for antibody kinetics and demonstrate its use in a setting in which individuals can be infected or vaccinated but not both. We conduct prevalence estimation via transition probability matrices using synthetic data. This approach is ideal to model sequences of infections and vaccinations, or personal trajectories in a population, making it an important first step towards a mathematical characterization of reinfection, vaccination boosting, and cross-events of infection after vaccination or vice versa.

Quantitative population modelling is an invaluable tool for identifying the cascading effects of conservation on an ecosystem. When population data from monitoring programs is not available, deterministic ecosystem models have often been calibrated using the theoretical assumption that ecosystems have a stable, coexisting equilibrium. However, a growing body of literature suggests these theoretical assumptions are inappropriate for conservation contexts. Here, we develop an alternative for data-free population modelling that relies on expert-elicited knowledge of species populations. Our new Bayesian algorithm systematically removes model parameters that lead to impossible predictions, as defined by experts, without incurring excessive computational costs. We demonstrate our framework on an ordinary differential equation model by limiting predicted population sizes and their ability to change rapidly, utilising readily available knowledge from field observations and experts rather than relying on theoretical ecosystem properties. Our results show that using only coexistence and stability requirements can lead to unrealistic population dynamics, which can be avoided by switching to expert-derived information. We demonstrate how this change can dramatically impact population predictions, expected responses to management, conservation decision-making, and long-term ecosystem behaviour. Without data, we argue that field observations and expert knowledge are more trustworthy for representing ecosystems observed in nature, improving the precision and confidence in predictions.

Insects, especially forest pests, are frequently characterized by eruptive dynamics. These types of species can stay at low, endemic population densities for extended periods of time before erupting in large-scale outbreaks. We here present a mechanistic model of these dynamics for mountain pine beetle. This extends a recent model that describes key aspects of mountain pine beetle biology coupled with a forest growth model by additionally including a fraction of low-vigor trees. These low-vigor trees, which may represent hosts with weakened defenses from drought, disease, other bark beetles, or other stressors, give rise to an endemic equilibrium in biologically plausible parameter ranges. The mechanistic nature of the model allows us to study how each model parameter affects the existence and size of the endemic equilibrium. We then show that under certain parameter shifts that are more likely under climate change, the endemic equilibrium can disappear entirely, leading to an outbreak.

Partial Rank Correlation Coefficient (PRCC) is a powerful type of global sensitivity analysis. Usually performed following Latin Hypercube Sampling (LHS), this analysis can highlight the parameters in a mathematical model producing the observed results, a crucial step when using models to understand real-world phenomena and guide future experiments. Recently, Gasior et al. performed LHS and PRCC when modeling the influence of cell-cell contact and TGF- $\beta$ signaling on the epithelial mesenchymal transition (Gasior et al. in J Theor Biol 546:111160, 2022). Though their analysis provided insight into how these tumor-level factors can impact intracellular signaling during the transition, their results were potentially impacted by nondimensionalizing the model prior to performing sensitivity analysis. This work seeks to understand the true impact of nondimensionalization on sensitivity analysis by performing LHS and PRCC on both the original model that Gasior et al. proposed and seven different nondimensionalizations. Parameter ranges were kept small to capture shifts in the values that originally produced bistable behavior. By comparing these eight different iterations, this work shows that the issues from performing sensitivity analysis following nondimensionalization are two-fold: (1) nondimensionalization can obscure or exclude important parameters from in-depth analysis and (2) how a model is nondimensionalized can, potentially, change analysis results. Ultimately, this work cautions against using nondimensionalization prior to sensitivity analysis if the subsequent results are meant to guide future experiments.

Avian influenza virus type A causes an infectious disease that circulates among wild bird populations and regularly spills over into domesticated animals, such as poultry and swine. As the virus replicates in these intermediate hosts, mutations occur, increasing the likelihood of emergence of a new variant with greater transmission to humans and a potential threat to public health. Prior models for spread of avian influenza have included some combinations of the following components: multi-host populations, spillover into humans, environmental transmission, seasonality, and migration. We develop an ordinary differential equation (ODE) model for spread of a low pathogenic avian influenza virus that combines all of these factors, and we translate this into a stochastic continuous-time Markov chain model. Linearization of the ODE near the disease-free solution leads to the basic reproduction number $R_0$ , a threshold for disease extinction in both the ODE and Markov chain. The linearized Markov chain leads to a branching process approximation which provides an estimate for probability of disease extinction, i.e., probability no major disease outbreak in the multi-host system. The probability of disease extinction depends on the time and the population into which infection is introduced and reflects the seasonality inherent in the system. Some of the most sensitive parameters to model outcomes include wild bird recovery and environmental transmission. We find that migratory wild birds can drive infection numbers in other populations even when transmission parameters for those populations are low, and that environmental transmission can be a significant driver of infections.

We develop a convergent reaction-drift-diffusion master equation (CRDDME) to facilitate the study of reaction processes in which spatial transport is influenced by drift due to one-body potential fields within general domain geometries. The generalized CRDDME is obtained through two steps. We first derive an unstructured grid jump process approximation for reversible diffusions, enabling the simulation of drift-diffusion processes where the drift arises due to a conservative field that biases particle motion. Leveraging the Edge-Averaged Finite Element method, our approach preserves detailed balance of drift-diffusion fluxes at equilibrium, and preserves an equilibrium Gibbs-Boltzmann distribution for particles undergoing drift-diffusion on the unstructured mesh. We next formulate a spatially-continuous volume reactivity particle-based reaction-drift-diffusion model for reversible reactions of the form $\text{A}+\text{B}\leftrightarrow \text{C}$ . A finite volume discretization is used to generate jump process approximations to reaction terms in this model. The discretization is developed to ensure the combined reaction-drift-diffusion jump process approximation is consistent with detailed balance of reaction fluxes holding at equilibrium, along with supporting a discrete version of the continuous equilibrium state. The new CRDDME model represents a continuous-time discrete-space jump process approximation to the underlying volume reactivity model. We demonstrate the convergence and accuracy of the new CRDDME through a number of numerical examples, and illustrate its use on an idealized model for membrane protein receptor dynamics in T cell signaling.

The $\left[PS{I}^{+}\right]$ prion phenotype in yeast manifests as a white, pink, or red color pigment. Experimental manipulations destabilize prion phenotypes, and allow colonies to exhibit $\left[ps{i}^{-}\right]$ (red) sectored phenotypes within otherwise completely white colonies. Further investigation of the size and frequency of sectors that emerge as a result of experimental manipulation is capable of providing critical information on mechanisms of prion curing, but we lack a way to reliably extract this information. Images of experimental colonies exhibiting sectored phenotypes offer an abundance of data to help uncover molecular mechanisms of sectoring, yet the structure of sectored colonies is ignored in traditional biological pipelines. In this study, we present [PSI]-CIC, the first computational pipeline designed to identify and characterize features of sectored yeast colonies. To overcome the barrier of a lack of manually annotated data of colonies, we develop a neural network architecture that we train on synthetic images of colonies and apply to real images of $\left[PS{I}^{+}\right]$ , $\left[ps{i}^{-}\right]$ , and sectored colonies. In hand-annotated experimental images, our pipeline correctly predicts the state of approximately 95% of colonies detected and frequency of sectors in approximately 89.5% of colonies detected. The scope of our pipeline could be extended to categorizing colonies grown under different experimental conditions, allowing for more meaningful and detailed comparisons between experiments. Our approach streamlines the analysis of sectored yeast colonies providing a rich set of quantitative metrics and provides insight into mechanisms driving the curing of prion phenotypes.

Many biological and medical questions can be modeled using time-to-event data in finite-state Markov chains, with the phase-type distribution describing intervals between events. We solve the inverse problem: given a phase-type distribution, can we identify the transition rate parameters of the underlying Markov chain? For a specific class of solvable Markov models, we show this problem has a unique solution up to finite symmetry transformations, and we outline a recursive method for computing symbolic solutions for these models across any number of states. Using the Thomas decomposition technique from computer algebra, we further provide symbolic solutions for any model. Interestingly, different models with the same state count but distinct transition graphs can yield identical phase-type distributions. To distinguish among these, we propose additional properties beyond just the time to the next event. We demonstrate the method's applicability by inferring transcriptional regulation models from single-cell transcription imaging data.