Mathematical Biosciences最新文献

More than 60% of individuals recovering from substance use disorder relapse within one year. Some will resume drug consumption even after decades of abstinence. The cognitive and psychological mechanisms that lead to relapse are not completely understood, but stressful life experiences and external stimuli that are associated with past drug-taking are known to play a primary role. Stressors and cues elicit memories of drug-induced euphoria and the expectation of relief from current anxiety, igniting an intense craving to use again; positive experiences and supportive environments may mitigate relapse. We present a mathematical model of relapse in drug addiction that draws on known psychiatric concepts such as the “positive activation; negative activation” paradigm and the “peak-end” rule to construct a relapse rate that depends on external factors (intensity and timing of life events) and individual traits (mental responses to these events). We analyze which combinations and ordering of stressors, cues, and positive events lead to the largest relapse probability and propose interventions to minimize the likelihood of relapse. We find that the best protective factor is exposure to a mild, yet continuous, source of contentment, rather than large, episodic jolts of happiness.

The mosquito-borne disease (malaria) imposes significant challenges on human health, healthcare systems, and economic growth/productivity in many countries. This study develops and analyzes a model to understand the interplay between malaria dynamics, economic growth, and transient events. It uncovers varied effects of malaria and economic parameters on model outcomes, highlighting the interdependence of the reproduction number ($R_0$) on both malaria and economic factors, and a reciprocal relationship where malaria diminishes economic productivity, while higher economic output is associated with reduced malaria prevalence. This emphasizes the intricate interplay between malaria dynamics and socio-economic factors. The study offers insights into malaria control and underscores the significance of optimizing external aid allocation, especially favoring an even distribution strategy, with the most significant reduction observed in an equal monthly distribution strategy compared to longer distribution intervals. Furthermore, the study shows that controlling malaria in high mosquito biting areas with limited aid, low technology, inadequate treatment, or low economic investment is challenging. The model exhibits a backward bifurcation implying that sustainability of control and mitigation measures is essential even when $R_0$ is slightly less than one. Additionally, there is a parameter regime for which long transients are feasible. Long transients are critical for predicting the behavior of dynamic systems and identifying factors influencing transitions; they reveal reservoirs of infection, vital for disease control. Policy recommendations for effective malaria control from the study include prioritizing sustained control measures, optimizing external aid allocation, and reducing mosquito biting.

Metronomic chemotherapy refers to the frequent administration of chemotherapeutic agents at a lower dose and presents an attractive alternative to conventional chemotherapy with encouraging response rates. However, the schedule of the therapy, including the dosage of the drug, is usually based on empiricism. The confounding effects of tumor-endothelial-immune interactions during metronomic administration of drugs have not yet been explored in detail, resulting in an incomplete assessment of drug dose and frequency evaluations. The present study aimed to gain a mechanistic understanding of different actions of metronomic chemotherapy using a mathematical model. We have established an analytical condition for determining the dosage and frequency of the drug depending on its clearance rate for complete tumor elimination. The model also brings forward the immune-mediated clearance of the tumor during the metronomic administration of the chemotherapeutic agent. The results from the global sensitivity analysis showed an increase in the sensitivity of drug and immune-mediated killing factors toward the tumor population during metronomic scheduling. Our results emphasize metronomic scheduling over the maximum tolerated dose (MTD) and define a model-based approach for approximating the optimal schedule of drug administration to eliminate tumors while minimizing harm to the immune cells and the patient’s body.

Understanding the conditions for maintaining cooperation in groups of unrelated individuals despite the presence of non-cooperative members is a major research topic in contemporary biological, sociological, and economic theory. The $N$-person snowdrift game models the type of social dilemma where cooperative actions are costly, but there is a reward for performing them. We study this game in a scenario where players move between play groups following the casual group dynamics, where groups grow by recruiting isolates and shrink by losing individuals who then become isolates. This describes the size distribution of spontaneous human groups and also the formation of sleeping groups in monkeys. We consider three scenarios according to the probability of isolates joining a group. We find that for appropriate choices of the cost-benefit ratio of cooperation and the aggregation–disaggregation ratio in the formation of casual groups, free-riders can be completely eliminated from the population. If individuals are more attracted to large groups, we find that cooperators persist in the population even when the mean group size diverges. We also point out the remarkable similarity between the replicator equation approach to public goods games and the trait group formulation of structured demes.

A basic mathematical model for IL-2-based cancer immunotherapy is proposed and studied. Our analysis shows that the outcome of therapy is mainly determined by three parameters, the relative death rate of CD$4^{+}$ T cells, the relative death rate of CD$8^{+}$ T cells, and the dose of IL-2 treatment. Minimal equilibrium tumor size can be reached with a large dose of IL-2 in the case that CD$4^{+}$ T cells die out. However, in cases where CD$4^{+}$ and CD$8^{+}$ T cells persist, the final tumor size is independent of the IL-2 dose and is given by the relative death rate of CD$4^{+}$ T cells. Two groups of in silico clinical trials show some short-term behaviors of IL-2 treatment. IL-2 administration can slow the proliferation of CD$4^{+}$ T cells, while high doses for a short period of time over several days transiently increase the population of CD$8^{+}$ T cells during treatment before it recedes to its equilibrium. IL-2 administration for a short period of time over many days suppresses the tumor population for a longer time before approaching its steady-state levels. This implies that intermittent administration of IL-2 may be a good strategy for controlling tumor size.

We have designed a stochastic model of embryonic neurogenesis in the mouse cerebral cortex, using the formalism of compound Poisson processes. The model accounts for the dynamics of different progenitor cell types and neurons. The expectation and variance of the cell number of each type are derived analytically and illustrated through numerical simulations. The effects of stochastic transition rates between cell types, and stochastic duration of the cell division cycle have been investigated sequentially. The model does not only predict the number of neurons, but also their spatial distribution into deeper and upper cortical layers. The model outputs are consistent with experimental data providing the number of neurons and intermediate progenitors according to embryonic age in control and mutant situations.

We propose a continuum model for pattern formation, based on the multiphase model framework, to explore in vitro cell patterning within an extracellular matrix (ECM). We demonstrate that, within this framework, chemotaxis-driven cell migration can lead to the formation of cell clusters and vascular-like structures in 1D and 2D respectively. The influence on pattern formation of additional mechanisms commonly included in multiphase tissue models, including cell-matrix traction, contact inhibition, and cell–cell aggregation, are also investigated. Using sensitivity analysis, the relative impact of each model parameter on the simulation outcomes is assessed to identify the key parameters involved. Chemoattractant–matrix binding is further included, motivated by previous experimental studies, and found to reduce the spatial scale of patterning to within a biologically plausible range for capillary structures. Key findings from the in-depth parameter analysis of the 1D models, both with and without chemoattractant–matrix binding, are demonstrated to translate well to the 2D model, obtaining vascular-like cell patterning for multiple parameter regimes. Overall, we demonstrate a biologically-motivated multiphase model capable of generating long-term pattern formation on a biologically plausible spatial scale both in 1D and 2D, with applications for modelling in vitro vascular network formation.

We use a compartmental model with a time-varying transmission parameter to describe county level COVID-19 transmission in the greater St. Louis area of Missouri and investigate the challenges in fitting such a model to time-varying processes. We fit this model to synthetic and real confirmed case and hospital discharge data from May to December 2020 and calculate uncertainties in the resulting parameter estimates. We also explore non-identifiability within the estimated parameter set. We find that the death rate of infectious non-hospitalized individuals, the testing parameter and the initial number of exposed individuals are not identifiable based on an investigation of correlation coefficients between pairs of parameter estimates. We also explore how this non-identifiability ties back into uncertainties in the estimated parameters and find that it inflates uncertainty in the estimates of our time-varying transmission parameter. However, we do find that $R_0$ is not highly affected by non-identifiability of its constituent components and the uncertainties associated with the quantity are smaller than those of the estimated parameters. Parameter values estimated from data will always be associated with some uncertainty and our work highlights the importance of conducting these analyses when fitting such models to real data. Exploring identifiability and uncertainty is crucial in revealing how much we can trust the parameter estimates.

The collective foraging behavior of ant colonies is a central focus in behavioral ecology. This paper enhances the classical model of foraging dynamics in harvester ant colonies by introducing a nonlinear recruitment rate and considering environmental variability. Initially, we analyze the existence and stability of steady states in the deterministic model. The results suggest that an increase in mean recruitment time can reduce the foraging threshold, leading to both forward and backward bifurcations. Furthermore, both average recruitment time and the interference intensity of recruiters impact the number of workers in each subgroup. Subsequently, we conduct an analysis of the long-term and transient dynamics of collective foraging in random environments, providing sufficient conditions for the colony to sustain foraging activity. The findings emphasize the scene-dependent impact of environmental stochasticity on foraging dynamics. When ant colonies deterministically cease foraging, environmental stochasticity may unexpectedly prolong the foraging state. Conversely, when colonies deterministically persist in foraging, environmental stochasticity may disrupt this continuity. Additionally, the effect of environmental stochasticity on foraging status varies with the initial worker size. Sizes near the boundary of the basin of attraction between non-foraging and foraging states exhibit greater sensitivity to environmental stochasticity, and sufficiently large stochasticity can impact foraging dynamics across a broader range of initial worker sizes. These findings underscore the intricate interplay between intrinsic factors (e.g., recruitment efficiency and interference intensity) and extrinsic factors (e.g., environmental stochasticity) in shaping the collective foraging dynamics of ant colonies.

Efficient and accurate large-scale networks are a fundamental tool in modeling brain areas, to advance our understanding of neuronal dynamics. However, their implementation faces two key issues: computational efficiency and heterogeneity. Computational efficiency is achieved using simplified neurons, whereas there are no practical solutions available to solve the problem of reproducing in a large-scale network the experimentally observed heterogeneity of the intrinsic properties of neurons. This is important, because the use of identical nodes in a network can generate artifacts which can hinder an adequate representation of the properties of a real network.

To this aim, we introduce a mathematical procedure to generate an arbitrary large number of copies of simplified hippocampal CA1 pyramidal neurons and interneurons models, which exhibit the full range of firing dynamics observed in these cells — including adapting, non-adapting and bursting. For this purpose, we rely on a recently published adaptive generalized leaky integrate-and-fire (A-GLIF) modeling approach, leveraging on its ability to reproduce the rich set of electrophysiological behaviors of these types of neurons under a variety of different stimulation currents.

The generation procedure is based on a perturbation of model’s parameters related to the initial data, firing block, and internal dynamics, and suitably validated against experimental data to ensure that the firing dynamics of any given cell copy remains within the experimental range. A classification procedure confirmed that the firing behavior of most of the pyramidal/interneuron copies was consistent with the experimental data. This approach allows to obtain heterogeneous copies with mathematically controlled firing properties. A full set of heterogeneous neurons composing the CA1 region of a rat hippocampus (approximately 1.2 million neurons), are provided in a database freely available in the live paper section of the EBRAINS platform.

By adapting the underlying A-GLIF framework, it will be possible to extend the numerical approach presented here to create, in a mathematically controlled manner, an arbitrarily large number of non-identical copies of cell populations with firing properties related to other brain areas.