Frontiers in Applied Mathematics and Statistics最新文献

Children are uniquely susceptible to severe influenza infection, with one million children experiencing severe life-threatening disease each year. However, there is little evidence that an underdeveloped immune system or differences in viral loads are responsible, implicating the host inflammatory response as responsible for increased lung injury in juveniles. Here, we used mechanism-based mathematical modeling, age-specific lung immune data from influenza-infected mice, Bayesian statistics, and rigorous Monte Carlo-based methods to identify immune mechanisms that may be differently regulated in juvenile animals. We hypothesized that the immunological mechanisms between juvenile and adult mice are primarily conserved, and that immune response differences arise due to a minimal set of parameter differences. First, we developed and identified parameter bounds for an ordinary differential equation (ODE) model of the innate immune response to influenza infection which capture the dynamic changes of select parameters. Using publicly available juvenile and adult murine data, we then conducted a computational screen of different age-specific model scenarios and evaluated the scenarios using the Akaike Information Criterion (AIC) and Bayesian Information Criterion (BIC) to select the optimal scenario. These results suggest that the rate of production of JAK-STAT pathway activators, like type I IFNs and IL-6, is age-specific. Preconditioned Monte Carlo (PMC) analysis revealed that JAK-STAT activator production is higher in juveniles than adults. Additional simulations suggest antiviral therapeutics may be more effective in juvenile populations. While not significantly suppressing virus replication, age-specific IFN or IL-6 production may be responsible for increased inflammation, lung injury, and mortality observed in juvenile influenza infection.

This paper investigates the volatility dynamics and underlying long memory features of four major cryptocurrencies-Bitcoin, Ethereum, Litecoin, and Ripple-which were selected due to their high liquidity, large trading volumes, and historical significance in the digital asset market. The long-range dependence exhibited in cryptocurrency markets is often overlooked. However, based on the strong evidence of persistent dependence in the return series, we adopt advanced volatility models that are capable of accommodating high volatility and heavy-tails, as well as the long memory properties of cryptocurrencies. Specifically, we employ long-memory extensions of the GAS (Long memory GAS) and GARCH (Fractionally Integrated Asymmetric Power ARCH) models, integrating heavy-tailed innovation distributions: the Generalized Hyperbolic Distribution (GHD) and Generalized Lambda Distribution (GLD). Standard GARCH and GAS models are included as benchmarks. The performance of the models are assessed using Value-at-Risk (VaR) estimation, backtesting (in-sample and out-of-sample) and volatility forecasting metrics. The results indicate that long memory models, particularly the FIAPARCH model, consistently outperforms the standard GAS and GARCH models in capturing tail risk and the volatility persistence. These findings emphasize the critical role of long memory in modeling the risk of cryptocurrencies, indicating that accounting for volatility persistence can significantly enhance the accuracy of risk estimates and strengthen risk management practices.