Mathematical Biosciences and Engineering最新文献

Microbiome data require statistical models that can simultaneously decode microbes' reaction to the environment and interactions among microbes. While a multiresponse linear regression model seems like a straight-forward solution, we argue that treating it as a graphical model is problematic given that the regression coefficient matrix does not encode the conditional dependence structure between response and predictor nodes. This observation is especially important in biological settings when we have prior knowledge on the edges from specific experimental interventions that can only be properly encoded under a conditional dependence model. Here, we propose a chain graph model with two sets of nodes (predictors and responses) whose solution yields a graph with edges that indeed represent conditional dependence, thus agreeing with the experimenter's intuition on the average behavior of nodes under treatment. The solution to our model is sparse via the Bayesian linear regression (LASSO). In addition, we propose an adaptive extension so that different shrinkages can be applied to different edges to incorporate edge-specific prior knowledge. Our model is computationally inexpensive through an efficient Gibbs sampling algorithm and can account for binary, counting, and compositional responses via an appropriate hierarchical structure. We test the performance of our model in a variety of simulated datasets, thereby showing superior performance to state-of-the-art approaches. We further apply our model to human gut and soil microbial compositional datasets, and we highlight that CG-LASSO can estimate biologically meaningful network structures in the data. Our software is available as an R package at https://github.com/YunyiShen/CAR-LASSO.

In this work, we propose a data augmentation strategy aimed at improving the training phase of neural networks and, consequently, the accuracy of their predictions. Our approach relies on generating synthetic data through a suitable compartmental model combined with the incorporation of uncertainty. Available data are used to calibrate the model, which is further integrated with deep learning techniques to produce additional synthetic data for training. The results show that neural networks trained on these augmented datasets exhibit significantly improved predictive performances. In particular, we focus on two different neural network architectures: Physics-Informed Neural Networks (PINNs) and Nonlinear Autoregressive (NAR) models. The NAR approach proves especially effective for short-term forecasting, thereby providing accurate quantitative estimates by directly learning the dynamics from data and avoiding the additional computational cost of embedding physical constraints into the training. In contrast, PINNs yield less accurate quantitative predictions but capture the qualitative long-term behavior of the system, thus making them more suitable to explore broader dynamical trends. Numerical simulations of the second phase of the COVID-19 pandemic in the Lombardy region (Italy) validate the effectiveness of the proposed approach.

The cardiovascular and ocular systems are intricately connected, with hemodynamic interactions playing a crucial role in both physiological regulation and pathological conditions. However, existing models often treat these systems separately, thus limiting the understanding of their interdependence. In this study, we present the Eye2Heart model, which is a novel closed-loop mathematical framework that integrates cardiovascular and ocular dynamics. Using an electrical-hydraulic analogy, the model describes the interactions between the heart and retinal circulation through a nonlinear system of ordinary differential equations. The model is tested against clinical and experimental data, thus demonstrating its ability to reproduce key cardiovascular parameters (e.g., stroke volume, cardiac output) and ocular hemodynamics (e.g., retinal blood flow). Additionally, we explore in silico the effects of intraocular pressure and left ventricular compliance on both local ocular and global systemic circulation, thus revealing critical dependencies between cardiovascular and ocular health. The results highlight the model's potential for studying cardiovascular diseases with ocular manifestations and support emerging research in oculomics by providing a mechanistic basis to interpret ocular biomarkers within a systemic context. This paves the way for patient-specific data integration and broader applications in personalized medicine.

Oncolytic viruses (OVs) are designed to selectively target and destroy cancer cells while sparing normal, healthy tissue. Several viruses for oncolytic virotherapy are currently developed. In this paper, we will use mathematical modeling to consider key strategies that can improve the efficacy of oncolytic virotherapy. These include the integration of immunotherapy approaches with virotherapy to amplify anti-tumor immune responses, as well as optimizing the timing, dosage, and sequencing of viral administrations. Specifically, we consider strategies that increase the burst size of the virus, immunostimulation and immunosuppression, we optimize for different weekly virus injection schedules, and we consider the combination of OV therapy with chimeric antigen receptor (CAR) T-cell therapy. A limiting factor is the availability of data. We parametrize the model using several different data sets. These, however, correspond to different cancers and experimental setups. Hence our model cannot be considered to be validated. Consequently, our results are qualitative. Our results highlight the critical importance of timing for virotherapy's efficacy and overall success. They outline strong evidence for promising treatment scenarios that needs to be further tested experimentally in the future.

This paper investigates the stochastic logistic difference equation, $ X_{n+1} = r X_n (1 - X_n)varepsilon_n $, where $ X_n $ is a random variable of population size, and $ {varepsilon_n} $ represents independent random perturbations with $ E[varepsilon_n] = 1 $ and $ E[varepsilon_n^2] = v > 1 $. Under the Gaussian moment-closure approximation, we derived a closed system of difference equations for the mean and variance of $ X_n $. The analysis of the system of difference equations identified two classes of equilibria: a trivial equilibrium $ (0, 0) $ representing extinction, and nontrivial equilibria corresponding to positive steady population levels. Explicit conditions for the existence and local stability of these equilibria were obtained, showing that the extinction state is stable when $ r^2v < 1 $, whereas nontrivial equilibria arise for $ r > 1 $ with stability dependent on the stochastic intensity $ v $. The saddle-node (fold) bifurcation induced by variations in the stochastic intensity $ v $ was explicitly formulated. Monte Carlo simulations confirmed the analytical analysis.

In recent years, numerous advances have been made in understanding how epidemic dynamics are affected by changes in individual behaviors. We propose a Susceptible-Infected-Susceptible (SIS) based compartmental model to tackle the simultaneous and coupled evolution of an outbreak and of the adoption by individuals of the isolation measure. The compliance with self-isolation is described with the help of the imitation dynamics framework. Individuals are incentivized to isolate based on the prevalence and the incidence rate of the outbreak, and are tempted to defy isolation recommendations depending on the duration of the isolation and on the cost of putting social interactions on hold. We are able to derive analytical results on the equilibria of the model under the homogeneous mean-field approximation. Simulating the compartmental model on empirical networks, we also perform a preliminary check of the impact of a network structure on our analytical predictions. We find that the dynamics collapse to surprisingly simple regimes where either the imitation dynamics no longer plays a role or the equilibrium prevalence depends on only two parameters of the model, namely the cost and the relative time spent in isolation. Whether individuals prioritize disease prevalence or incidence as an indicator of the state of the outbreak appears to play no role on the equilibria of the dynamics. However, it turns out that favoring incidence may help to flatten the curve in the transient phase of the dynamics. We also find a fair agreement between our analytical predictions and simulations run on an empirical multiplex network.

The triclustering method employed in this study integrates the $ delta $-Trimax approach with the fuzzy cuckoo search (FCS), thereby leveraging the Lévy flight and Gaussian distribution to analyze gene expression data in three dimensions. In this framework, the initial triclusters produced by $ delta $-Trimax are further optimized using FCS, where the Lévy flight enhances global exploration and the Gaussian distribution intensifies local exploitation, thus achieving a balanced search for optimal solutions. Each tricluster set is evaluated using the tricluster quality index (TQI) to ensure coherence across genes, conditions, and time points. The method was applied to gene expression datasets from primary fibroblast cells and heart disease samples. In the fibroblast dataset, the best tricluster set was obtained with $ delta = 0.015 $ and yielded the lowest average TQI value. For the heart disease dataset, the most optimal solution was achieved with $ delta = 0.026 $, which yielded the lowest average TQI, and the best tricluster showed large gene coverage across multiple time points. A functional analysis of the selected triclusters using gene ontology (GO) and Kyoto Encyclopedia of Genes and Genomes (KEGG) pathways uncovered significant enrichment in pathways such as the NF-$ kappa $B signaling pathway (hsa04064), TGF-$ beta $ signaling pathway (hsa04350), and calcium signaling pathway (hsa04020), all of which are mechanistically relevant to immune modulation, extracellular matrix organization, and cardiac muscle function. These findings highlight the utility of the proposed hybrid framework in uncovering biologically meaningful gene modules and provide valuable insights into the molecular mechanisms underlying fibrotic and cardiovascular diseases.

A wide variety of works exists on the dynamics of large populations, ranging from simple heuristic modeling to those based on advanced computer-supported methods. However, their interconnections remain mostly vague, which, in particular, limits the effectiveness of computer methods in this domain. In this work, we propose and justify the following concept. Typically, the description of the population dynamics is based on the sole use of low-order correlations. As we demonstrate here, in important cases, where the local population structure is shaped by strong interactions, higher-order correlations become essential. To verify when one can or cannot rely on studying low-order correlations only, we suggest to explicitly use probability measures as micro-states. Among such states may be those whose adequate characterization is based on their low-order correlation functions. In particular, this is the case for sub-Poissonian states where the large $ n $ asymptotics of the probability of finding $ n $ particles in a given vessel is similar to that for non-interacting entities, which can completely be described by the density of the particles. To illustrate this concept, a general individual-based model of an infinite population of interacting entities is analyzed. The evolution of this model preserves the sub-Poissonian states, which allows one to describe it through the correlation functions of such states for which a chain of evolution equations is obtained. The corresponding kinetic equation is derived, numerically solved, and analyzed.

Epidemic severity indices that incorporate disease information are essential tools for decision-makers, as these indices allow the design and evaluation of possible control strategies in advance of implementation in susceptible populations. In spatially structured settings, indices that consider human mobility provide valuable information on the spread of infectious diseases and the potential impact of mobility restrictions during outbreaks. In this context, the final epidemic size in metapopulation models serves as an effective measure of outbreak severity in geographical terms. However, the existence and uniqueness of the solution to the corresponding equation have only been established in particular cases. In this study, we derived conditions that guarantee the existence and uniqueness of the solution to the final epidemic size equation in a SIR-type metapopulation model. We also conducted a sensitivity analysis in a two-region, unidirectional infection scenario, which allowed us to examine the effects of mobility between an infected region and a susceptible one. Our results indicate that, under relatively simple conditions, restricting mobility can help contain outbreaks. However, we also identified situations in which mobility is not detrimental and may even be beneficial. These findings provide a preliminary framework for assessing the appropriateness of mobility restrictions during infectious disease outbreaks in spatially structured regions.

Mathematical models are valuable tools in the fight against infectious diseases such as dengue. However, their use to guide public health strategies in sub-Saharan Africa, particularly in Burkina Faso, remains limited due to the scarcity of locally calibrated models. Moreover, no study has yet applied the African vulture optimization algorithm (AVOA) for dengue parameters in this context. In this study, we develop a compartmental model to evaluate the impact of control strategies on the 2023 dengue epidemic in the Centre Region of Burkina Faso. The model combines a susceptible-infected (SI) structure for the mosquitoes aquatic phase, a susceptible-exposed-infected (SEI) structure for adult mosquitoes, and a susceptible-exposed-infected-recovered (SEIR) framework for the human population. It incorporates key features, including vertical transmission in mosquitoes and a distinction between clinically detected and undetected human cases. After mathematical analysis, key epidemiological parameters were estimated by calibrating the model against weekly reported case data from June to December 2023 using AVOA. The basic reproduction number ($ mathcal{R}_0 $) was estimated at 2.30, confirming the potential for sustained transmission. Sensitivity analysis identified the mosquito biting rate ($ b $), larval carrying capacity ($ k_A $), mosquito mortality ($ mu_V $), and the recovery rate of undetected cases as the most influential parameters. Finally, numerical simulations assessed the impact of control measures recommended by the Ministry of Health of Burkina Faso. The results show that the effectiveness of dengue control strategies depends critically on their intensity and, most importantly, their duration, highlighting the need for integrated, intensive, and sustained vector control measures combined with individual protective actions for effective and long-term management of dengue transmission.