Bulletin of Mathematical Biology最新文献

This paper illustrates a further application of topological data analysis to the study of self-organising models for chemical and biological systems. In particular, we investigate whether topological summaries can capture the parameter dependence of pattern topology in reaction diffusion systems, by examining the homology of sublevel sets of solutions to Turing reaction diffusion systems for a range of parameters. We demonstrate that a topological clustering algorithm can reveal how pattern topology depends on parameters, using the chlorite-iodide-malonic acid system, and the prototypical Schnakenberg system for illustration. In addition, we discuss the prospective application of such clustering, for instance in refining priors for detailed parameter estimation for self-organising systems.

Respiratory Syncytial Virus (RSV) can lead to severe bronchiolitis and pneumonia, especially in children under one year of age. The introduction of vaccines and immunoprophylaxis has highlighted the need for more representative models to evaluate their impact on public health strategies. In Spain, Nirsevimab, a recombinant human monoclonal antibody against RSV, was added to the 2023 immunization schedule for children, administered as a single intramuscular dose. We developed an agent-based model representing the population of the Valencian Community (CVA), Spain, to simulate RSV transmission and assess various immunization strategies. This model integrates demographic factors and incorporates random transitions between states. It also takes into account that the effectiveness of existing immunoprophylaxis decreases over time. Using this model, we systematically evaluated 133 contiguous-month immunization strategies and the non-immunization scenario. To determine the effectiveness of these strategies, we compared simulated outcomes related to hospitalizations in children aged 0-5 months and those under one year, as well as the incidence of infections in these age groups. Our findings show that several immunization strategies effectively reduce hospitalizations and infections in infants aged 0-5 months to a similar extent. Targeting newborns between October and March/April, along with immunizing children under one year of age born outside this period in October, consistently ranks among the best-performing approaches across multiple evaluation criteria. These strategies offer a strong balance between health impact and immunization effort, and are particularly effective in reducing hospitalizations among infants under one year.

Linear compartmental models are a widely used tool for analyzing systems arising in biology, medicine, and more. In such settings, it is essential to know whether model parameters can be recovered from experimental data. This is the identifiability problem. For a class of linear compartmental models with one input and one output, namely, those for which the underlying graph is a bidirected tree, Bortner et al. completely characterized which such models are structurally identifiability, which means that every parameter is generically locally identifiable. Here, we delve deeper, by examining which individual parameters are locally versus globally identifiable. Specifically, we analyze mammillary models, which consist of one central compartment which is connected to all other (peripheral) compartments. For these models, which fall into five infinite families, we determine which individual parameters are locally versus globally identifiable, and we give formulas for some of the globally identifiable parameters in terms of the coefficients of input-output equations. Our proofs rely on a combinatorial formula due to Bortner et al. for these coefficients.

Mathematical models are routinely applied to interpret biological data, with common goals that include both prediction and parameter estimation. A challenge in mathematical biology, in particular, is that models are often complex and non-identifiable, while data are limited. Rectifying identifiability through simplification can seemingly yield more precise parameter estimates, albeit, as we explore in this perspective, at the potentially catastrophic cost of introducing model misspecification and poor accuracy. We demonstrate how uncertainty in model structure can be propagated through to uncertainty in parameter estimates using a semi-parametric Gaussian process approach that delineates parameters of interest from uncertainty in model terms. Specifically, we study generalised logistic growth with an unknown crowding function, and a spatially resolved process described by a partial differential equation with a time-dependent diffusivity parameter. Allowing for structural model uncertainty yields more robust and accurate parameter estimates, and a better quantification of remaining uncertainty. We conclude our perspective by discussing the connections between identifiability and model misspecification, and alternative approaches to dealing with model misspecification in mathematical biology.

Aggregated Markov models provide a flexible framework for stochastic dynamics that develops on multiple timescales. For example, Markov models for ion channels often consist of multiple open and closed state to account for "slow" and "fast" openings and closings of the channel. The approach is a popular tool in the construction of mechanistic models of ion channels-instead of viewing model states as generators of sojourn times of a certain characteristic length, each individual model state is interpreted as a representation of a distinct biophysical state. We will review the properties of aggregated Markov models and discuss the implications for mechanistic modelling. First, we show how the aggregated Markov models with a given number of states can be calculated using Pólya enumeration. However, models with  [Formula: see text] open and  [Formula: see text] closed states that exceed the maximum number  [Formula: see text] of parameters are non-identifiable. We will present two derivations of this classical result and investigate non-identifiability further via a detailed analysis of the non-identifiable fully connected three-state model. Finally, we will discuss the implications of non-identifiability for mechanistic modelling of ion channels. We will argue that instead of designing models based on assumed transitions between distinct biophysical states which are modulated by ligand binding, it is preferable to build models based on additional sources of data that give more direct insight into the dynamics of conformational changes.

Exosomes are released by cancer cells to transport nucleic acids, proteins and lipids to neighboring or distant cells. They participate in various biological processes that promote tumor progression, including uncontrolled proliferation, angiogenesis, migration, local invasion, metastasis, immune evasion and treatment resistance. Experimental studies have reported that tumor acidity enhances the release of exosomes from cancer cells. In this study, we propose a novel mathematical model to investigate the interplay between tumor acidity and exosome secretion under in vivo and in vitro conditions. The model consists of a coupled system of reaction-diffusion equations describing the dynamics of oxygen, lactate, and exosomes, which we solve numerically using the finite difference method (FDM). Our predicted results show strong qualitative agreement with experimental observations. The simulations reveal that exosome levels are higher under oxygen-deprived conditions compared to oxygen-rich conditions. Moreover, in cyclic hypoxia-where oxygen levels fluctuate between normoxic and hypoxic states-lactate accumulation increases with longer hypoxia periods, whereas exosome levels rise under rapid oxygen fluctuations. Additionally, lactate levels reach a steady-state value in spatially heterogeneous oxygen environments. The results also highlight that the oxygen consumption rate has a range in which it is positively correlated with exosome levels.

Estimation of transmission and contact rate parameters among individuals in different age groups is a key point in the mathematical modeling of infectious disease transmission. Several approaches exist for this task, but given the complexity of the problem, it is not always clear which is the most appropriate in each case. Our goal is to contribute to this task in the event of an emerging disease. We propose a methodology to estimate the contact rate parameters from the fraction of the incidence reported in each age group at the beginning of the epidemic spread. Working with an age-structured SIR model, we obtain an equation that relates the contact parameters to various epidemiological quantities potentially available through different sources. We first explore, using an individual-based model, the appropriateness and limitations of our approach when strong restrictions on social activities are in place. We then apply the method to obtain information about the contact structure by age during the COVID-19 epidemic spread in Greater Buenos Aires (Argentina) in 2020. As we have the fractions of reported incidence by age but only rough estimations of other quantities involved in the method, we define several epidemiological scenarios based on various hypotheses. Using the different sets of contact parameters obtained, we evaluate control strategies and analyze the dependence of the results on our assumptions. Our method may also provide a useful framework for assessing how well contact matrices reproduce different aspects of the transmission process through comparison with individual-based model simulations of synthetic contact structures.

Chronic infection with hepatitis B virus (HBV) can lead to formation of abnormal nodular structures within the liver. To address how changes in liver anatomy affect overall virus-host dynamics, we developed within-host ordinary differential equation models of two-patch hepatitis B infection, one that assumes irreversible and one that assumes reversible movement between nodular structures. We investigated the models analytically and numerically, and determined the contribution of patch susceptibility, immune responses, and virus movement on within-patch and whole-liver virus dynamics. We explored the structural and practical identifiability of the models by implementing a differential algebra approach and the Monte Carlo approach for a specific HBV data set. We determined conditions for viral clearance, viral localization, and systemic viral infection. Our study suggests that cell susceptibility to infection within modular structures, the movement rate between patches, and the immune-mediated infected cell killing have the most influence on HBV dynamics. Our results can help inform intervention strategies.

Sclerotinia sclerotiorum, the causative agent of Sclerotinia stem rot (SR), is a significant yield-limiting disease affecting soybean crops in the temperate climates around the globe. Effective disease management practices rely on fungicides to mitigate the growth and spread of the disease. To infer optimal, profit-maximizing fungicide application rates, this study develops a mathematical model of SR and soybean growth with a requisite profit function. The optimal fungicide application rate was computed for variable profit parameters (fungicide cost and soybean bushel price), and model parameters (SR growth rate, maximal SR damage to crops and fungicide efficiency). Expectantly, higher soybean bushel prices, rates of SR growth, and maximal SR damage to crops return elevated optimal fungicide rates. In contrast, higher levels of fungicide efficiency motivate lower optimal fungicide rates. The model also reveals a discontinuity in the optimal fungicide application rates for elevated fungicide costs; in this economic context, it becomes more profitable to apply no fungicide rather than low, ineffectual amounts that still allow SR to reach near-maximal outbreak levels in a finite time period. Future refinements of the model will incorporate variable SR growth rates modeled on annual weather patterns, crop rotation practices, and further exploring the relationships that soybean densities and row spacing have on SR growth, in order to build a more robust system to analyze the long-term effect of disease behavior on soybean crop yield and profit.