Mathematical Biosciences and Engineering最新文献

The vascular tumor growth model proposed by Pinho et al. has gained attention in studies of the effect of anti-angiogenic therapy. In the present work, we extend Pinho's model to a reaction-diffusion model with different cell growth behaviors to evaluate the individual and combined effects of chemotherapy, anti-angiogenic therapy, and immunotherapy across different stages of vascular cancer. Analysis of the model includes the existence and stability of up to six different equilibria with bifurcations that define the transitions between them. By establishing conditions for the stability of the cancer-free equilibrium, we numerically explore different dynamics of cancer relapse. This includes examining the timing and frequency of relapse and identifying thresholds for critical treatment parameters. Furthermore, the numerical simulations of the extended model show that in the advanced stages of cancer, the integration of chemotherapy, immunotherapy, and anti-angiogenic therapy is essential for effective control of vascular cancer and reduces the overall duration of treatment.

The necessity of modeling the dynamics of infectious disease spread is driven by the imperative to accurately predict epidemics and assess the efficacy of control measures, such as isolation and quarantine. Conventional compartmental SIR and SEIR models have been widely used for predicting the course of epidemics, but they have limitations due to their inability to account for dynamic isolation. Research frequently recognizes the assumptions underlying these models but rarely provides justification for their validity within the specific contexts where they are applied. In this paper, we propose a novel approach based on the concept of a working set, which we utilize as a subset of agents actively involved in social contact and potential transmission. Our adapted working set model incorporates isolation states for susceptible and infected agents, enabling dynamic adjustment of the transmission rate according to the current size of the Working Set. The incorporation of a time window parameter enables the identification of current contacts and the identification of superspreaders, an important component for the optimization of epidemiological measures. Experimental results and comparative analysis showed that, compared to the SIR and SEIR models, the adapted working set model provides a more detailed and realistic tool for analyzing the spread of infection under dynamic control measures. Our model accounts for contact heterogeneity and allows a better assessment of the impact of isolation. The presented approach integrates resource management principles from computer systems with epidemiological models, providing a flexible and realistic tool for evaluating and optimizing infectious disease control measures. In addition, a practical analysis of established models reveals fundamental modeling principles that can be adapted to different scenarios.

This study presents an ordinary differential equation (ODE) based hybrid kinetic-metabolic model to predict the time evolution of biomass, glucose, hyaluronic acid (HA), and lactic acid during fermentation by Streptococcus equi subsp. zooepidemicus. The model incorporates simplified metabolic pathways and estimates the qualitative dynamics of internal, unmeasured metabolites involved in glycolysis, biomass synthesis, and HA production. Special emphasis is placed on the energetic molecules ATP/ADP, as well as the coenzymes NADH/NAD⁺, which are involved in redox reactions. These molecules have been shown to play regulatory roles in metabolism. The model predictions closely match the experimental data and provide insights into how varying glucose levels affect intracellular metabolic fluxes.

The combined effects of ecological and disease characteristics are examined in eco-epidemiological models, which incorporate infectious illnesses into interaction models. We assumed in this article that the prey population is somewhat infected, and the predator benefits more from eating susceptible prey than from feeding on infected prey. Infected and susceptible prey are equally competitive for resources, and the predator consumes both at the same rate. We employed polar blow-up and time-scale desingularization techniques to tackle the singularity caused by frequency-dependent disease transmission at the origin in our model. For simplicity, we considered the linear functional response for interactions between prey and predators. We aimed to determine the influence of fear of predation on the eco-epidemiological system. According to our findings, there are two ways in which predation fear might support the coexistence of three populations: stable coexistence and oscillatory coexistence. Furthermore, our finding remained unchanged if we eliminated two presumptions: that susceptible and infected prey compete equally for resources and that predators consume both prey at identical rates. We also compared the outcomes by taking into account the growth with positive density dependency (Allee effect) and arrived at the same conclusion.

Prior research has explored co-infections that involve two respiratory viruses, yet triple infections remain poorly elucidated. With the COVID-19 pandemic and seasonal epidemics of respiratory syncytial virus (RSV) and influenza, understanding the dynamics of triple infections is critical for public health preparedness. The simultaneous circulation of influenza A virus (IAV), RSV, and SARS-CoV-2 presents a significant public health burden, particularly among vulnerable populations such as children, the elderly, and immunocompromised individuals. Comprehending the interactions among these viruses is crucial to improve our capacity to forecast and curb disease outbreaks. This study addresses the escalating concern over the interaction of multiple respiratory viruses by introducing a simple mathematical model to analyze triple infection dynamics involving IAV, RSV, and SARS-CoV-2. The central question addressed in this study is how variations in infection rates influence each virus's duration and peak viral load in a triple-infection scenario. We find distinct regimes where each virus can dominate and suppress the viral load and duration of the remaining two viruses. We derive an analytical expression for the dependence of the critical infection rate of one virus on the infection rates of the other two viruses. While the model will need to be extended to realistically capture in vivo viral dynamics, this analysis helps provide insight into the complex dynamics of multiple virus infections.

In this article, we proposed a simplified mathematical model of primary tumor growth that involves four cell populations: Two types of cancer cells with different levels of immunogenicity, and the immune response in its two components, innate and adaptive. By varying the proliferation rate of non-immunogenic cancer cells and the innate immune stimulation parameter, and applying biparametric numerical continuation techniques, we identified distinct stability regions that revealed scenarios of tumor escape and latency. A closed curve of supercritical Hopf bifurcation points was also detected, delineating the parameter region in which limit cycles emerged. By examining the population maxima of each cell type at steady state, we identified parameter values at which both immunogenic and non-immunogenic tumor cell populations remain in stable equilibrium at modest levels, sustained by an immune response that does not escalate to intensities associated with immunological damage.

This study present a comparative modeling framework for COVID-19 dynamics using stationary and non-stationary transition probabilities within a Markov decision process (MDP). Stationary transitions assume constant rates, while non-stationary transitions capture time-dependent behaviors driven by policy interventions or behavioral changes. We develop a seven-compartmental epidemiological model, derive transition probabilities from binomial and multinomial processes, and implement time-dependent parameterizations to reflect real-world dynamics. Mathematical models for both stationary and non-stationary transition frameworks are developed and simulated over a 365-day period to emphasize dynamic variations in epidemic outcomes. Our findings highlight the significance of non-stationary modeling in accurately representing the dynamic characteristics of pandemic situations and provide recommendations for optimizing public health interventions under uncertainty. This comparative analysis offers useful information for epidemiological modeling and decision making in dynamic risk environments.

Adaptive immunity, performed by T and B lymphocytes, seeks total virus elimination through specific recognition of viral antigens. It has been shown that innate or adaptive immune response regulation variations are associated with an excessive immune response, leading to tissue damage with an increased risk of complications and death. This article is a novel contribution focused on models that represent pathogenic interactions with humans. In our case, the objective was to build and analyze a mathematical model for SARS-CoV-2 infection in the human host, including elements of respiratory cell dynamics, viral particles, and immune-responding cells. The methodology developed considered modeling by means of ordinary differential equations, validation by comparing referenced studies, and sensitivity analysis with respect to the variables considered. Finally, a comparison of simulation models was performed, verifying that an increase in viral particles increases the response of some adaptive immune system cells in the human host.

Boars, being one of the most widely spread ungulates worldwide, have a widely recognized important role in the balance of natural environment and forests. Since large boar populations severely damage crops and cause serious traffic accidents, they are widely hunted, thereby also representing a relevant economic resource. In the model presented here, the species is at times considered ravaging, enabling it to be kept in check, while on the other hand, it must be preserved from extinction as a protected species. We considered an idealized, relatively simple situation in which rangers of the park where the boars are hosted manage this animal population size when they extrude into the surrounding areas through the woods perimeter. Modeling this situation involves considering not the whole boar population, but only those that are involved in the spillover, i.e., those living in proximity of the woods edge. The theoretical investigation and the simulations revealed the existence of a transcritical bifurcation relating the two viable equilibria, coexistence, and the ranger-free point. Also, the possible onset of persistent oscillations via a Hopf bifurcation is shown, leading to periodic recalling of rangers to contain the spillovers. On the other hand, a better regime was obtained by reducing the environment's resources for the wild boars, which stabilized the the boar population at constant level, with a reduced presence of the rangers, reducing the costs of their periodic recalling.

Early warning signals are vital in predicting critical transitions in complex dynamical systems. For behavioral epidemiology systems in particular, this includes shifts in vaccine sentiments that may precede disease outbreaks. Conventional statistical indicators, such as variance and lag-1 autocorrelation, often struggle in noisy environments and may fail in real-world scenarios. In this study, we leveraged universal signals of critical slowing down to train deep learning classifiers, specifically using long short-term memory (LSTM) and residual neural network (ResNet) architectures, for detecting early warning signals in disease-related social media time series. These classifiers were trained on simulated data from a stochastic coupled behavior-disease model with additive Lévy noise, a non-Gaussian noise that better reflects the heavy-tailed nature of real-world fluctuations. Our results show that these classifiers consistently outperform conventional indicators in both sensitivity and specificity on theoretical data while delivering quantitatively clear results that are easier to interpret on empirical data. Integrating deep learning with real-time social media monitoring offers a powerful tool for preventing disease outbreaks through proactive public health interventions.