Mathematical Biosciences and Engineering最新文献

Current research confirms abnormalities in resting-state electroencephalogram (EEG) power and functional connectivity (FC) patterns in specific brain regions of individuals with depression. To study changes in the flow of information between cortical regions of the brain in patients with depression, we used 64-channel EEG to record neural oscillatory activity in 68 relevant cortical regions in 22 depressed patients and 22 healthy adolescents using source-space EEG. The direction and strength of information flow between brain regions was investigated using directional phase transfer entropy (PTE). Compared to healthy controls, we observed an increased intensity of PTE information flow between the left and right hemispheres in the theta and alpha frequency bands in depressed subjects. The intensity of information flow between anterior and posterior regions within each hemisphere was reduced. Significant differences were found in the left supramarginal gyrus, right delta in the theta frequency band and bilateral lateral occipital lobe, and paracentral gyrus and parahippocampal gyrus in the alpha frequency band. The accuracy of cross-classification of directed PTE values with significant differences between groups was 91%. These findings suggest that altered information flow in the brains of depressed patients is related to the pathogenesis of depression, providing insights for patient identification and pathological studies.

Mathematical modeling plays a crucial role in understanding and combating infectious diseases, offering predictive insights into disease spread and the impact of vaccination strategies. This paper explored the significance of mathematical modeling in epidemic control efforts, focusing on the interplay between vaccination strategies, disease transmission rates, and population immunity. To facilitate meaningful comparisons of vaccination strategies, we maintained a consistent framework by fixing the vaccination capacity to vary from 10 to 100% of the total population. As an example, at a 50% vaccination capacity, the pulse strategy averted approximately 45.61% of deaths, while continuous and hybrid strategies averted around 45.18 and 45.69%, respectively. Sensitivity analysis further indicated that continuous vaccination has a more direct impact on reducing the basic reproduction number $ R_0 $ compared to pulse vaccination. By analyzing key parameters such as $ R_0 $, pulse vaccination coefficients, and continuous vaccination parameters, the study underscores the value of mathematical modeling in shaping public health policies and guiding decision-making during disease outbreaks.

Clusters of COVID-19 in high-risk settings, such as schools, have been deemed a critical driving force of the major epidemic waves at the societal level. In Japan, the vaccination coverage among students remained low up to early 2022, especially for 5-11-year-olds. The vaccination of the student population only started in February 2022. Given this background and considering that vaccine effectiveness against school transmission has not been intensively studied, this paper proposes a mathematical model that links the occurrence of clustering to the case count among populations aged 0-19, 20-59, and 60+ years of age. We first estimated the protected (immune) fraction of each age group either by infection or vaccination and then linked the case count in each age group to the number of clusters via a time series regression model that accounts for the time-varying hazard of clustering per infector. From January 3 to May 30, 2022, there were 4,722 reported clusters in school settings. Our model suggests that the immunity offered by vaccination averted 226 (95% credible interval: 219-232) school clusters. Counterfactual scenarios assuming elevated vaccination coverage with faster roll-out reveal that additional school clusters could have been averted. Our study indicates that even relatively low vaccination coverage among students could substantially lower the risk of clustering through vaccine-induced immunity. Our results also suggest that antigenically updated vaccines that are more effective against the variant responsible for the ongoing epidemic may greatly help decrease not only the incidence but also the unnecessary loss of learning opportunities among school-age students.

We considered a time-inhomogeneous diffusion process able to describe the dynamics of infected people in a susceptible-infectious (SI) epidemic model in which the transmission intensity function was time-dependent. Such a model was well suited to describe some classes of micro-parasitic infections in which individuals never acquired lasting immunity and over the course of the epidemic everyone eventually became infected. The stochastic process related to the deterministic model was transformable into a nonhomogeneous Wiener process so the probability distribution could be obtained. Here we focused on the inference for such a process, by providing an estimation procedure for the involved parameters. We pointed out that the time dependence in the infinitesimal moments of the diffusion process made classical inference methods inapplicable. The proposed procedure were based on the generalized method of moments in order to find a suitable estimate for the infinitesimal drift and variance of the transformed process. Several simulation studies are conduced to test the procedure, these include the time homogeneous case, for which a comparison with the results obtained by applying the maximum likelihood estimation was made, and cases in which the intensity function were time dependent with particular attention to periodic cases. Finally, we applied the estimation procedure to a real dataset.

The work presented a general discrete-time model of a population of trees affected by a parasite. The tree population was considered size-structured, and the parasite was represented by a single scalar variable. Parasite dynamics were assumed to act on a faster timescale than tree dynamics. The model was studied based on an associated nonlinear matrix model, in which the presence of the parasites was only reflected in the value of its parameters. For the model in all its generality, an explicit condition of viability/extinction of the parasite/tree community was found. In a simplified model with two size-classes of trees and particular forms of the vital rates, it was shown that the model undergoes a transcritical bifurcation and, likewise, a period-doubling bifurcation. It was found that, for any tree fertility rate that makes them viable without a parasite, if the parasite sufficiently reduces the survival of young trees, it can lead to the extinction of the entire community. The same cannot be assured if the parasite acts on adult trees. In situations where a high fertility rate coupled with a low survival rate of adult trees causes a non-parasitized population of trees to fluctuate, a parasite sufficiently damaging only young trees can stabilize the population. If, instead, the parasite acts on adult trees, we can find a destabilization condition on the tree population that brings them from a stable to an oscillating regime.

There are known methods to manage the population dynamics of wild and sterile mosquitoes by releasing genetically engineered sterile mosquitoes. Even if a two-dimensional system of ordinary differential equations is considered as a simple mathematical model for developing release strategies, fully understanding the global behavior of the solutions is challenging, due to the fact that the probability of mating is ratio-dependent. In this paper, we combine a geometric approach called the time-scale transformation and blow-up technique with the center manifold theorem to provide a complete understanding of dynamical systems near the origin. Then, the global behavior of the solution of the two-dimensional ordinary differential equation system is classified in a two-parameter plane represented by the natural death rate of mosquitoes and the sterile mosquito release rate. We also offer a discussion of the sterile mosquito release strategy. In addition, we obtain a better exposition of the previous results on the existence and local stability of positive equilibria. This paper provides a framework for the mathematical analysis of models with ratio-dependent terms, and we expect that it will theoretically withstand the complexity of improved models.

This work aims to study the role of sex disparities on the overall outcome of influenza A disease. Therefore, the classical Susceptible-Infected-Susceptible (SIS) endemic model was extended to include the impact of sex disparities on the overall dynamics of influenza A infection which spreads in an open population with a varying size, and took the potential lethality of the infection. The model was mathematically analyzed, where the equilibrium and bifurcation analyses were established. The model was shown to undergo a backward bifurcation at $ mathcal{R}_0 = 1 $, for certain range of the model parameters, where $ mathcal{R}_0 $ is the basic reproduction number of the model. The asymptotic stability of the equilibria was numerically investigated, and the effective threshold was determined. The differences in susceptibility, transmissibility and case fatality (of females with respect to males) are shown to remarkably affect the disease outcomes. Simulations were performed to illustrate the theoretical results.