Bulletin of Mathematical Biology最新文献

A central challenge in Human Immunodeficiency Virus (HIV) public health policy lies in determining whether to universally expand treatment access, despite the risk of sub-optimal adherence and consequent drug resistance, or to adopt a more strategic allocation of resources that balances treatment coverage with adherence support. This dilemma is further complicated by the need for timely switching to second-line therapy, which is critical for managing treatment failure but imposes additional burdens on limited healthcare resources. In this study, we develop and analyze a compartmental model of HIV transmission that incorporates both drug-sensitive and drug-resistant strains, diagnosis status, and treatment progression, including switching to second-line therapy upon detection of resistance. Basic reproduction numbers for both strains are derived, and equilibrium analysis reveals the existence of a disease-free state and two endemic states, where the drug-sensitive strain may be eliminated while the drug-resistant strain persists. Local and global sensitivity analyses are performed, using partial rank correlation coefficient (PRCC) and Sobol methods, to identify key parameters influencing different model outcomes. We extend the model using optimal control theory to assess multiple intervention strategies targeting diagnosis, treatment initiation, and adherence. A novel dynamic control framework is proposed to achieve the UNAIDS 95-95-95 targets through efficient resource allocation. Numerical simulations validate the analytical results and compare the effectiveness and cost-efficiency of control strategies. Our findings highlight that long-term HIV epidemic control depends critically on prioritizing adherence-focused interventions alongside efforts to expand first-line treatment coverage.

The application of non-steroidal anti-inflammatory drugs (NSAIDs) for Alzheimer's disease is considered to be a promising therapeutic approach. Epidemiological studies suggest potential benefits of NSAIDs; however, these findings are not consistently supported by clinical trials. This long-standing discrepancy has persisted for decades and remains a significant barrier to developing effective treatment strategies. To assess the efficacy of NSAIDs in Alzheimer's disease, we have developed a mathematical model based on a system of ordinary differential equations. The model captures the dynamics of key players in disease progression, including A $\beta$ -monomers, oligomers, pro-inflammatory mediators (M1 microglial cells and pro-inflammatory cytokines), and anti-inflammatory mediators (M2 microglial cells and anti-inflammatory cytokines). The effects of NSAIDs are modeled through a reduction in the production rate of inflammatory cytokines (IC). While a single NSAID administration temporarily reduces IC levels, their concentration eventually returns to baseline due to drug elimination. The return time depends on the drug dose, resulting in a patient-specific return time function. By analyzing this function, we propose an optimal treatment regimen and identify conditions under which NSAID treatment is most effective in reducing IC levels. Our results suggest that NSAID efficacy in Alzheimer's disease is influenced by the stage of the disease (with earlier intervention being more effective), patient-specific parameters, and the treatment regimen. The approach developed here can also be generalized to evaluate the efficacy of anti-inflammatory treatments for other diseases.

Although viral dynamics is typically modeled using ordinary differential equations, a natural way to address the phenomena of viral persistence and host cell survival is to use stochastic models of viral reproduction. Here we present a study of viral and substrate cell extinction and their dependence on viral production rate for two simple stochastic models of viral reproduction that differ in the method of viral release: one accounts for viral bursting, in which the release of viruses is instantaneous after cell lesion, the other for viral budding, in which new viral particles are released from infected cells gradually. We show that for both viral release mechanisms, simulation of continuous-time Markov chain versions of the stochastic models is the most accurate but also time-consuming way to obtain the results, and that traditional diffusion approximation methods lead to serious discrepancies in extinction probabilities and mean times. We then propose a modified stochastic differential equation approach that achieves a significant improvement in simulation speed while maintaining accuracy.

Understanding extinction probabilities in branching processes is pivotal for epidemiology and population dynamics. Traditional models often assume a fixed generation time, resulting in extinction probabilities determined solely by offspring distributions and remaining unchanged over time. By contrast, our study incorporates the generation time into the analysis, considering how the timing of each generation influences extinction dynamics. By focusing on the finite-time risk of extinction, our approach reveals that shorter generation times can lead to a temporary increase in the risk of population or epidemic die-out. We support our findings with precise fixed-point analyses and numerical integration techniques based on real data from various infectious diseases. Although the long-term probability of extinction does not change, the transient dynamics show that a faster-paced transmission process may elevate early extinction risk. The study highlights the crucial role of transmission timing in epidemic modeling and indicates that accounting for generation time can provide new perspectives for developing effective public health strategies and outbreak control measures.

The inference of phylogenetic networks, which model complex evolutionary processes including hybridization and gene flow, remains a central challenge in evolutionary biology. Until now, statistically consistent inference methods have been limited to phylogenetic level-1 networks, which allow no interdependence between reticulate events. In this work, we establish the theoretical foundations for a statistically consistent inference method for a much broader class: semi-directed level-2 networks that are outer-labeled planar and galled. We precisely characterize the features of these networks that are distinguishable from the topologies of their displayed quartet trees. Moreover, we prove that an inter-taxon distance derived from these quartets is circular decomposable, enabling future robust inference of these networks from quartet data, such as concordance factors obtained from gene tree distributions under the Network Multispecies Coalescent model. Our results also have novel identifiability implications across different data types and evolutionary models, applying to any setting in which displayed quartets can be distinguished.

Inference of phylogenetic networks is of increasing interest in the genomic era. However, the extent to which phylogenetic networks are identifiable from various types of data remains poorly understood, despite its crucial role in justifying methods. This work obtains strong identifiability results for large sub-classes of galled tree-child semidirected networks. Some of the conditions our proofs require, such as the identifiability of a network's tree of blobs or the circular order of 4 taxa around a cycle in a level-1 network, are already known to hold for many data types. We show that all these conditions hold for quartet concordance factor data under various gene tree models, yielding the strongest results from 2 or more samples per taxon. Although the network classes we consider have topological restrictions, they include non-planar networks of any level and are substantially more general than level-1 networks - the only class previously known to enjoy identifiability from many data types. Our work establishes a route for proving future identifiability results for tree-child galled networks from data types other than quartet concordance factors, by checking that explicit conditions are met.

Knowing gene regulatory networks (GRNs) is important for understanding various biological mechanisms. In this paper, we present a method, QWENDY, that uses single-cell gene expression data measured at four time points to infer GRNs. Based on a linear gene expression model, it solves the transformation of the covariance matrices. Unlike its predecessor WENDY, QWENDY avoids solving a non-convex optimization problem and produces a unique solution. We test the performance of QWENDY on three experimental data sets and two synthetic data sets. Compared to previously tested methods on the same data sets, QWENDY ranks the first on experimental data, although it does not perform well on synthetic data.

Virtual population (Vpop) generation is a central component of quantitative systems pharmacology (QSP), involving the sampling of parameter sets that represent physiologically plausible patients (PPs) and capture observed inter-individual variability in clinical outcomes. This approach poses challenges due to the high dimensionality and often non-identifiability nature of many QSP models. In this study, we evaluate the performance of the DREAM(ZS) algorithm, a multi-chain adaptive Markov chain Monte Carlo (MCMC) method for generating Vpop. Using the Van De Pas model of cholesterol metabolism as a case study, we compare DREAM(ZS) to the single-chain Metropolis-Hastings (MH) algorithm adopted by Rieger et al. Our comparison focuses on convergence behavior, parametric diversity, and posterior coverage, in relation to the ability of each method to explore complex parameter distributions and maintain outcomes correlations. DREAM(ZS) demonstrates superior exploration of the parameter space, reducing boundary accumulation effects common in traditional MH sampling, and restoring parameter correlation structures. These advantages are attributed in part to its adaptive proposal mechanism and the use of a bias-corrected likelihood formulation, which together contribute to a better parameters space sampling without compromising model fit. Our findings contribute to the ongoing development of efficient sampling methodologies for high-dimensional biological models, introducing a promising and easy to use alternative for Vpop generation in QSP, expanding the methodological approaches for in silico trial simulation.

The risk and intensity of mosquito-borne disease outbreaks are tightly linked to the frequency at which mosquitoes feed on blood, also known as the biting rate. However, standard models of mosquito-borne disease transmission inherently assume that mosquitoes bite only once per reproductive cycle-an assumption commonly violated in nature. Drivers of multiple biting, such as host defensive behaviors or climate factors, also affect the mosquito gonotrophic cycle duration (GCD), a quantity customarily used to estimate the biting rate. Here, we present a novel framework for incorporating more complex mosquito biting behaviors into transmission models. This framework can account for heterogeneity in and linkages between mosquito biting rates and multiple biting. We provide general formulas for the basic offspring number, $N_0$ , and basic reproduction number, $R_0$ , threshold measures for mosquito population and pathogen transmission persistence, respectively. To exhibit its flexibility, we expand on specific models derived from the framework that arise from empirical, phenomenological, or mechanistic modeling perspectives. Using the gonotrophic cycle duration as a standard quantity to make comparisons among the models, we show that assumptions about the biting process strongly affect the relationship between GCD and $R_0$ . While under the standard assumption of one bite per reproductive cycle, $R_0$ is an increasing linear function of the inverse of the GCD, alternative models of the biting process can exhibit saturating or concave relationships. Critically, from a mechanistic perspective, decreases in the GCD can lead to substantial decreases in $R_0$ . Through sensitivity analysis of the mechanistic model, we determine that parameters related to probing and ingesting success are the most important targets for disease control. This work highlights the importance of incorporating the behavioral dynamics of mosquitoes into transmission models and provides a method for evaluating how individual-level interventions against mosquito biting scale up to determine population-level mosquito-borne disease risk.

We develop and apply a learning framework for parameter estimation in initial value problems that are assessed only indirectly via aggregate data such as sample means and/or standard deviations. Our comprehensive framework follows Bayesian principles and consists of specialized Markov chain Monte Carlo computational schemes that rely on modified Hamiltonian Monte Carlo to align with constraints induced by summary statistics and a novel elliptical slice sampler adapted to the parameters of biological models. We benchmark our methods with synthetic data on microbial growth in batch culture and test them with real growth curve data from laboratory replication experiments on Prochlorococcus microbes. The results indicate that our learning framework can utilize experimental or historical data and lead to robust parameter estimation and data assimilation in ODE models that outperform least-squares fitting.