Bulletin of Mathematical Biology最新文献

Mechanical ventilation is a life support system for patients with acute respiratory distress syndrome (ARDS). As part of strategies to protect the lung during ventilation, plateau pressure can be determined via an end-inspiratory pause; however, there is no agreed-upon pause duration in medical protocols. Mechanical ventilation can be modelled using the Viscoelastic model (VEM) for respiration. The identification of static compliance is of clinical interest, as it can be used to estimate plateau pressure. Practical identifiability analysis quantifies the confidence with which model parameters can be estimated from finite, noisy data. This paper evaluates the robustness of plateau pressure estimates in clinical data by analysing practical identifiability of the VEM identified in data with varying durations of end expiratory pauses. Profile likelihood and Hamiltonian Monte Carlo (HMC) simulations were used to determine estimation robustness. The methods were applied to mechanical ventilation data from a previous ARDS study. Profile likelihood and HMC showed strong agreement in both parameter estimates and identifiability results with similar confidence distributions. Both methods demonstrated a loss of parameter robustness that would preclude clinical utility when the end expiratory pause was reduced. By quantifying the confidence in parameter estimation and finding trade-offs in parameters that may be previously unknown when parameters are estimated, the methods give insight into the certainty of the estimate and parameter behaviours, even when the model fits the data well.

The higher-order network structure characterized by hypergraphs or simplicial complexes has become a research hotspot in network space. In this paper, a simplicial complex is used to describe the multivariate interaction between populations, and the reaction diffusion equation in higher-order organization is established. Under certain constraints, the Turing instability condition of the system is derived. Then, the advection mechanism is introduced to construct a reaction-diffusion model with directional migration mechanism, and the pattern dynamics of the reaction-diffusion-advection equation is systematically analyzed on two-dimensional torus and triangular lattice networks. In addition, in the numerical simulation part, it is found that the spatial density distribution in the stable patterns of the two populations is anti-phase. At the same time, we verify that the diffusion of the population depends on the topological structure and coupling, and conclude that the higher-order interaction on the triangular lattice network has a greater influence on the Turing instability than the higher-order Erdos-Renyi (ER) network. In the system process of simulating the existence of advection mechanism, the triangular lattice network will increase the spatial heterogeneity of the pattern due to the existence of directional migration mechanism. In the absence of diffusion, the increase of directional movement intensity will also cause Turing instability. Finally, the reaction-diffusion model in higher-order organization is applied to practice, and the validity of the model is verified.

Ecosystems are constantly exposed to newcoming strains or species. Which newcomer will be able to invade a resident multi-species community depends on the invader's relative fitness. Classical fitness differences between two growing strains are measured using the exponential model. Here we complement this approach, developing a more explicit framework to quantify fitness differences between two co-invading strains, based on the replicator equation. By assuming that the resident species' frequencies remain constant during the initial phase of invasion, we are able to determine the invasion fitness differential between the two strains, which drives growth rate differences post-invasion. We then apply our approach to a critical current global problem: invasion of the gut microbiota by antibiotic-resistant strains of the pathobiont Escherichia coli, using previously-published data. Our results underscore the context-dependent nature of fitness and demonstrate how species frequencies in a host environment can explicitly modulate the selection coefficient between two strains. This mechanistic framework can be augmented with machine-learning algorithms and multi-objective optimization to predict relative fitness in new environments, to steer selection, and design strategies to lower resistance levels in microbiomes.

Designing effective control strategies for managing epidemics in metapopulations, where human mobility plays a critical role, is essential for public health policies. In this paper, we propose a novel methodology for efficiently distributing control resources by considering both the epidemiological response of each region and the cost of implementing a control strategy to reduce contact rates within a given patch. Specifically, using the SEIR (Susceptible-Exposed-Infectious-Recovered) model to describe the epidemic process in each patch of the metapopulation, we derive a mathematical expression for the epidemic's final size in each patch, which measures the total number of individuals that become infected by the end of the epidemic. By solving this expression with an interactive approach, we guarantee computational efficiency even in large and highly connected metapopulations. Based on the final size of each patch, we propose an index to guide the control strategy efficiently. We compare this approach with other intuitive strategies, such as allocating all control resources to the most affected patch or distributing resources homogeneously. Our findings suggest that allocating control resources proportionally to the final size index best allocates resource returns across multiple zones. This strategy results in similar epidemic trajectories across regions, prevents resource concentration in a few areas, maintains lower local peaks, and ensures a more balanced epidemic impact across the metapopulation.

Despite the substantial success of combination antiretroviral therapy (ART) in suppressing HIV replication, achieving a complete cure remains challenging due to the persistence of viral reservoirs. The use of latency-reversing agents (LRAs) combined with natural killer (NK) cells in a "shock-and-kill" strategy has been experimentally confirmed as an effective approach to reducing reservoirs. Here, we utilized an HIV infection mathematical model that incorporates both 'virus-cell' and 'cell-cell' infection modes to assess the dynamic synergy of ART, LRAs, and NK cells. Model calibration was performed using experimental viral load data from HIV-1-infected humanized mice, employing Bayesian inference and an affine-invariant ensemble Markov Chain Monte Carlo (MCMC) sampling algorithm. Our findings validate the established understanding of HIV pathogenesis: post-treatment viral rebound is significantly influenced by the size of the viral reservoir, and 'cell-cell' transmission accounts for more than half of infections. Our findings also highlight the crucial role of natural killer (NK) cell-mediated immune responses in influencing interindividual variability in therapeutic responses to HIV. Comparative analysis of therapeutic strategies reveals that tripartite regimens combining ART with LRAs and NK cells demonstrate enhanced antiviral efficacy and accelerated treatment timelines. There is a key parameter region of the tripartite regimens therapy that will lead to an HIV cure. These insights collectively reinforce the immunotherapeutic potential of NK cells modulation and provide a mechanistic basis for optimizing combination therapies in eradication strategies.

We evaluate the risk of yellow fever outbreaks in a major trade event, with a case study of Canton Fair (Guangzhou, China), caused by case importation at different stages of the trade event. Our baseline model is a standard vector-borne disease transmission dynamics system, but we incorporate the division of a calendar year into favorable and unfavorable seasons based on impacts of different climatic conditions (temperature in particular) on mosquito population dynamics. We also incorporate square-waves to describe scenarios of case importation. We then use this periodic switching model to inform the potential of outbreaks and intensity of outbreaks due to case importation in different periods in relation to the two seasons. Our results show that importation of cases (even with a single case introduced) in the favorable season can induce a large outbreak in the local population in the host city, and the intensity of outbreak depends on the total number of imported cases (up to a level, when local transmission dominates). We also incorporate the public health interventions-isolation and emergency vaccination-to the model to provide quantitative information for the event organizer and public health decision makers for the preparedness and rapid response to the outbreak induced by case importation.

The accurate copying of nucleotides in DNA replication is arguably a digital computation. So are some cognitive capacities found in all organisms. In 2005 we proved that linking quantum calculations to evidence requires guesswork subject to revision (Madjid and Myers 2005). Based on this proof, we assume computations by living organisms undergo incessant unpredictable changes in their structure. This raises a question: how can changes in computations be made while preserving the integrity of the organism? We offer an answer expressed in the mathematics of marked graphs. Computations as networks of logical operations can be represented by marked graphs with live and safe markings. We represent a sequence of changes by a sequence of marked graphs. Then "Preserving the integrity of the organism" is expressed by preserving liveness and safety throughout the sequence of marked graphs. For example, we show how a single slime-mold amoeba inserts itself into a slime-mold filament without interrupting computation spread along the filament. Because interpretations of mathematics are mathematically undetermined, a quite different interpretation of the same sequence of marked graphs is possible. An alternative interpretation of the sequence of marked graphs is to see them as a cartoon of the insertion of a fragment of thought into a chain of human thoughts.

We propose a mathematical framework to systematically explore the propagation properties of a class of continuous in time nonlinear neural network models comprising a hierarchy of processing areas, mutually connected according to the principles of predictive coding. We precisely determine the conditions under which upward propagation, downward propagation or even propagation failure can occur in both bi-infinite and semi-infinite idealizations of the model. We also study the long-time behavior of the system when either a fixed external input is constantly presented at the first layer of the network or when this external input consists in the presentation of constant input with large amplitude for a fixed time window followed by a reset to a down state of the network for all later times. In both cases, we numerically demonstrate the existence of threshold behavior for the amplitude of the external input characterizing whether or not a full propagation within the network can occur. Our theoretical results are consistent with predictive coding theories and allow us to identify regions of parameters that could be associated with dysfunctional perceptions.

In this study, we establish a multi-population model that counting the number of reinfection and obtain the intrinsic relationship between the time-dependent transmission rates and reported case data. Using a Gaussian convolution-based approach on reported cases, we derive explicit expressions for first-infection and reinfection transmission rates and the compatibility conditions for parameters. Through computational analysis and numerical simulations, we compare the variations of these transmission rates over the same time period and explore the long-term transmissibility of COVID-19 in New York state. Our results indicate that the transmission pattern of COVID-19 is shifting from being primarily driven by initial infections to a "cyclical reinfection" pattern, a trend that became particularly evident after the spread of the Omicron variant. This study provides theoretical support for the estimation of time-dependent transmission rates and can contribute to long-term epidemic monitoring and control strategies.

Tumor cell heterogeneity poses a significant challenge in the treatment of colorectal cancer, with dedifferentiation being a key factor in the emergence and maintenance of such heterogeneity. Does dedifferentiation necessarily promote colorectal cancer growth? What are its regulatory mechanisms in treatment response? These critical questions remain insufficiently understood. To investigate this issue, we develop a cancer cell population dynamics model. Our findings reveal that dedifferentiation impacts cancer growth in complex and varied patterns. Specifically, dedifferentiation can either facilitate or hinder cancer growth, with the outcomes depending on the dedifferentiation probability and the growth rates of different types of tumor cells. Subsequently, we consider the implications of dedifferentiation for various treatment strategies. Chemotherapy, which simultaneously promotes cell death and induces dedifferentiation, shows variable efficacy, potentially leading to tumor shrinkage or growth. In contrast, the combination of chemotherapy and high-intensity immunotherapy significantly enhances therapeutic outcomes, achieving more stable tumor control. These findings underscore the importance of incorporating dedifferentiation dynamics into colorectal cancer growth models and treatment designs, highlighting the advantages of combination therapy in overcoming the limitations of monotherapy.