Mathematical Biosciences and Engineering最新文献

Uncertainty in parameter estimates from fitting within-host models to empirical data limits the model's ability to uncover mechanisms of infection, disease progression, and to guide pharmaceutical interventions. Understanding the effect of model structure and data availability on model predictions is important for informing model development and experimental design. To address sources of uncertainty in parameter estimation, we used four mathematical models of influenza A infection with increased degrees of biological realism. We tested the ability of each model to reveal its parameters in the presence of unlimited data by performing structural identifiability analyses. We then refined the results by predicting practical identifiability of parameters under daily influenza A virus titers alone or together with daily adaptive immune cell data. Using these approaches, we presented insight into the sources of uncertainty in parameter estimation and provided guidelines for the types of model assumptions, optimal experimental design, and biological information needed for improved predictions.

Super-resolution (SR) of magnetic resonance imaging (MRI) is gaining increasing attention for being able to provide detailed anatomical information. However, current SR methods often use the complex convolutional network for feature extraction, which is difficult to train and not suitable for limited computation resources in the medical scenario. To tackle these bottlenecks, we propose a multi-distillation residual network (MDRN) for more differential feature refinement, which has a superior trade-off between reconstruction accuracy and computation cost. Specifically, a novel feature multi-distillation residual block with a contrast-aware channel attention module was designed to make the residual features more focused on low-vision information, which maximizes the power of MDRN. Comprehensive experiments demonstrate the superiority of our MDRN over state-of-the-art methods in reconstruction quality and efficiency. Our method outperforms other existing methods in peak signal-noise ratio by up to 0.44-1.82 dB in 4× scale when GPU memory and runtime are lower than in other SR methods. The source code will be available at https://github.com/Jennieyy/MDRN.

Effector CD8⁺ cells lyse human immunodeficiency viruses (HIV)-infected CD4⁺ cells by recognizing a viral peptide presented by human leukocyte antigens (HLA) on the CD4⁺ cell surface, which plays an irreplaceable role in within-host HIV clearance. Using a semi-saturated lysing efficiency of a CD8⁺ cell, we discuss a model that captures HIV dynamics with different magnitudes of lysing rate induced by different HLA alleles. With the aid of local stability analysis and bifurcation plots, exponential interactions among CD4⁺ cells, HIV, and CD8⁺ cells were investigated. The system exhibited unexpectedly complex behaviors that were both mathematically and biologically interesting, for example monostability, periodic oscillations, and bistability. The CD8⁺ cell lysing rate, the CD8⁺ cell count, and the saturation effect were combined to determine the HIV kinetics. For a given CD8⁺ cell count, a low CD8⁺ cell lysing rate and a high saturation effect led to monostability to a high viral titre, and a low CD8⁺ cell lysing rate and a low saturation effect triggered periodic oscillations; this explained why patients with a non-protective HLA allele were always associated with a high viral titer and exhibited bad infection control. On the other hand, a high CD8⁺ cell lysing rate led to bistability and monostability to a low viral titer; this explained why protective HLA alleles are not always associated with good HIV infection outcomes. These mathematical results explain how differences in HLA alleles determine the variability in viral infection.

This study presented a novel approach for the precise ablation of breast tumors using focused ultrasound (FUS), leveraging a physics-informed neural network (PINN) integrated with a realistic breast model. FUS has shown significant promise in treating breast tumors by effectively targeting and ablating cancerous tissue. This technique employs concentrated ultrasonic waves to generate intense heat, effectively destroying cancerous tissue. In previous finite element method (FEM) models, the computational demands of handling extensive datasets, multiple dimensions, and discretization posed significant challenges. Our PINN-based solution operated efficiently in a mesh-free domain, achieving remarkable accuracy with significantly reduced computational demands, compared to conventional FEM techniques. Additionally, employing PINN for estimating partial differential equations (PDE) solutions can notably decrease the enormous number of discretized elements needed. The model employed a bowl-shaped acoustic transducer to focus ultrasound waves accurately on the tumor location. The simulation results offered detailed insights into each step of the FUS treatment process, including the generation of acoustic waves, the targeting of the tumor, and the subsequent heating and ablation of cancerous tissue. By applying a 3.8 nm displacement amplitude of transducer input pulse at a frequency of 1.1 MHz for 1 second, the temperature at the focal point elevated to 38.4 ℃, followed by another 90 seconds of cooling time, which resulted in significant necrosis of the tumor tissues. Validation of the PINN model's accuracy was conducted through FEM analysis, aligning closely with real-world FUS therapy scenarios. This innovative model provided physicians with a predictive tool to estimate the necrosis of tumor tissue, facilitating the customization of FUS treatment strategies for individual breast cancer patients.

Support vector machine (SVM) is an effective classification tool and maturely used in various fields. However, its performance is very sensitive to parameters. As a newly proposed swarm intelligence algorithm, snake optimizer algorithm (SO) can help to solve the parameter selection problem. Nevertheless, SO has the shortcomings of weak population initialization, slow convergence speed in the early stage, and being easy to fall into local optimization. To address these problems, an improved snake optimizer algorithm (ISO) was proposed. The mirror opposition-based learning mechanism (MOBL) improved the population quality to enhance the optimization speed. The novel evolutionary population dynamics model (NEPD) was beneficial for searching accurately. The differential evolution strategy (DES) helped to reduce the probability of falling into local optimal value. The experimental results of classical benchmark functions and CEC2022 showed that ISO had higher optimization precision and faster convergence rate. In addition, it was also applied to the parameter selection of SVM to demonstrate the effectiveness of the proposed ISO.

Traditional compartmental models of epidemic transmission often predict an initial phase of exponential growth, assuming uniform susceptibility and interaction within the population. However, empirical outbreak data frequently show early stages of sub-exponential growth in case incidences, challenging these assumptions and indicating that traditional models may not fully encompass the complexity of epidemic dynamics. This discrepancy has been addressed through models that incorporate early behavioral changes or spatial constraints within contact networks. In this paper, we propose the concept of "frailty", which represents the variability in individual susceptibility and transmission, as a more accurate approach to understanding epidemic growth. This concept shifts our understanding from a purely exponential model to a more nuanced, generalized model, depending on the level of heterogeneity captured by the frailty parameter. By incorporating this type of heterogeneity, often overlooked in traditional models, we present a novel mathematical framework. This framework enhances our understanding of how individual differences affect key epidemic metrics, including reproduction numbers, epidemic size, likelihood of stochastic extinction, impact of public health interventions, and accuracy of disease forecasts. By accounting for individual heterogeneity, our approach suggests that a more complex and detailed understanding of disease spread is necessary to accurately predict and manage outbreaks.

We present an individual-level probabilistic model to evaluate the effectiveness of two traditional control measures for infectious diseases: the isolation of symptomatic individuals and contact tracing (plus subsequent quarantine). The model allows us to calculate the reproduction number and the generation-time distribution under the two control measures. The model is related to the work of Fraser et al. on the same topic [1], which provides a population-level model using a combination of differential equations and probabilistic arguments. We show that our individual-level model has certain advantages. In particular, we are able to provide more precise results for a disease that has two classes of infected individuals - the individuals who will remain asymptomatic throughout and the individuals who will eventually become symptomatic. Using the properties of integral operators with positive kernels, we also resolve the important theoretical issue as to why the density function of the steady-state generation time is the eigenfunction associated with the largest eigenvalue of the underlying integral operator. Moreover, the same theoretical result shows why the simple algorithm of repeated integration can find numerical solutions for virtually all initial conditions. We discuss the model's implications, especially how it enhances our understanding about the impact of asymptomatic individuals. For instance, in the special case where the infectiousness of the two classes is proportional to each other, the effects of the asymptomatic individuals can be understood by supposing that all individuals will be symptomatic but with modified infectiousness and modified efficacy of the isolation measure. The numerical results show that, out of the two measures, isolation is the more decisive one, at least for the COVID-19 parameters used in the numerical experiments.

We considered predator-prey models which incorporated both an Allee effect and a new fear factor effect together, and where the predator predated the prey with a Holling type I functional response. We started off with a two-dimensional model where we found possible equilibria and examined their stabilities. By using the predator mortality rate as the bifurcation parameter, the model exhibited Hopf-bifurcation for the coexistence equilibrium. Furthermore, our numerical illustrations demonstrated the effect of fear and the Allee effect on the population densities, and we found that the level of fear had little impact on the long-term prey population level. The population of predators, however, declined as the fear intensity rose, indicating that the fear effect might result in a decline in the predator population. The dynamics of the delayed system were examined and Hopf-bifurcation was discussed. Finally, we looked at an eco-epidemiological model that took into account the same cost of fear and the Allee effect. In this model, the prey was afflicted with a disease. The prey was either susceptible or infected. Numerical simulations were carried out to show that as the Allee threshold rose, the uninfected prey and predator decreased, while the population of infected prey increased. When the Allee threshold hit a certain value, all populations became extinct. As fear intensity increased, the population of uninfected prey decreased, and beyond a certain level of fear, habituation prevented the uninfected prey from changing. After a certain level of fear, the predator population went extinct and, as a result, the only interaction left was between uninfected and infected prey which increased disease transmission, and so the infected prey increased. Hopf-bifurcation was studied by taking the time delay as the bifurcation parameter. We estimated the delay length to preserve stability.

Non-spatial models of competition between floating aquatic vegetation (FAV) and submersed aquatic vegetation (SAV) predict a stable state of pure SAV at low total available limiting nutrient level, N, a stable state of only FAV for high N, and alternative stable states for intermediate N, as described by an S-shaped bifurcation curve. Spatial models that include physical heterogeneity of the waterbody show that the sharp transitions between these states become smooth. We examined the effects of heterogeneous initial conditions of the vegetation types. We used a spatially explicit model to describe the competition between the vegetation types. In the model, the FAV, duckweed (L. gibba), competed with the SAV, Nuttall's waterweed (Elodea nuttallii). Differences in the initial establishment of the two macrophytes affected the possible stable equilibria. When initial biomasses of SAV and FAV differed but each had the same initial biomass in each spatial cell, the S-shaped bifurcation resulted, but the critical transitions on the N-axis are shifted, depending on FAV:SAV biomass ratio. When the initial biomasses of SAV and FAV were randomly heterogeneously distributed among cells, the vegetation pattern of the competing species self-organized spatially, such that many different stable states were possible in the intermediate N region. If N was gradually increased or decreased through time from a stable state, the abrupt transitions of non-spatial models were changed into smoother transitions through a series of stable states, which resembles the Busse balloon observed in other systems.

Multiscale modelling is a promising quantitative approach for studying infectious disease dynamics. This approach garners attention from both individuals who model diseases and those who plan for public health because it has great potential to contribute in expanding the understanding necessary for managing, reducing, and potentially exterminating infectious diseases. In this article, we developed a nested multiscale model of hepatitis B virus (HBV) that integrates the within-cell scale and the between-cell scale at cell level of organization of this disease system. The between-cell scale is linked to the within-cell scale by a once off inflow of initial viral infective inoculum dose from the between-cell scale to the within-cell scale through the process of infection; the within-cell scale is linked to the between-cell scale through the outflow of the virus from the within-cell scale to the between-cell scale through the process of viral shedding or excretion. The resulting multiple scales model is bidirectionally coupled in such a way that the within-cell scale and between-cell scale sub-models mutually affect each other, creating a reciprocal relationship. The computed reproductive number from the multiscale model confirms that the within-host scale and the between-host scale influence each other in a reciprocal manner. Numerical simulations are presented that also confirm the theoretical results and support the initial assumption that the within-cell scale and the between-cell scale influence each other in a reciprocal manner. This multiple scales modeling approach serves as a valuable tool for assessing the impact and success of health strategies aimed at controlling hepatitis B virus disease system.