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Summary: Background: Drug overdose is an escalating public health crisis in the United States (U.S.). This study evaluated the temporal trend of drug overdose-related deaths in the U.S., with an emphasis on identifying disparities across subpopulations and the contributing drugs. Methods: Using the nationwide death dataset from the National Vital Statistics System (NVSS), we estimated the drug overdose-related age-standardized mortality rate (ASMR) and temporal trends for individuals aged 12 and older from 2012 to 2022. Excess mortality during the Coronavirus disease 2019 (COVID-19) pandemic was evaluated based on the pre-pandemic trends using predictive modeling analysis. Findings: Among 809,967 overdose-related deaths during 2012–2022, ASMR increased by 8.9% [95% confidence interval (CI): 6.0%–11.9%] per year from 2012 to 2019 and increased to 12.9% (95% CI: 2.1%–24.8%) from 2019 to 2022, with the excess ASMR of 16.9% in 2020, increased to 26.4% in 2021 and then decreased to 19.3% in 2022. Significant age, sex, racial/ethnic and geographic disparities were demonstrated, with adolescents (annual percentage change [APC]:21.6%) and males (APC:13.6%) having the most pronounced increase during the pandemic. Ethnic minorities especially the non-Hispanic American Indian/Alaska Native experienced the highest excess ASMR (33.1% in 2020). Illicit fentanyl and synthetics starting with the lowest ASMR in 2012 (1.0 per 100,000), marked the most dramatic increase and became the leading cause of overdose-related death since 2016 (7.5 per 100,000), leading to the highest ASMR by 2022 (27.4 per 100,000). All drug types except heroin experienced varying degrees of excess ASMRs, with prescription opioid pain relievers (23.5%–55.1%), benzodiazepines (27.4%–40.9%) and antidepressants (10.4%–17.8%) exhibiting consistent increases from 2020 to 2022, while the excess ASMRs for illicit fentanyl and synthetics (25.3%–10.0%), psychostimulants (32.8%–14.6%) and methadone (35.0%–33.3%) decreased between 2021 and 2022. Interpretation: Overdose-related mortality is increasing at an alarming rate, and the stark differences point to the need for targeted interventions to reduce the burden of drug overdose deaths. Funding: This research did not receive any specific grant from funding agencies in the public, commercial, or not-for-profit sectors.

Abstract Background During the pandemic, a notable increase in diabetic ketoacidosis (DKA) and hyperosmolar hyperglycemic state (HHS), conditions that warrant emergent management, was reported. We aimed to investigate the trend of DKA‐ and HHS‐related mortality and excess deaths during the pandemic. Methods Annual age‐standardized mortality rates related to DKA and HHS between 2006 and 2021 were estimated using a nationwide database. Forecast analyses based on prepandemic data were conducted to predict the mortality rates during the pandemic. Excess mortality rates were calculated by comparing the observed versus predicted mortality rates. Subgroup analyses of demographic factors were performed. Results There were 71 575 DKA‐related deaths and 8618 HHS‐related deaths documented during 2006–2021. DKA, which showed a steady increase before the pandemic, demonstrated a pronounced excess mortality during the pandemic (36.91% in 2020 and 46.58% in 2021) with an annual percentage change (APC) of 29.4% (95% CI: 16.0%–44.0%). Although HHS incurred a downward trend during 2006–2019, the excess deaths in 2020 (40.60%) and 2021 (56.64%) were profound. Pediatric decedents exhibited the highest excess mortality. More than half of the excess deaths due to DKA were coronavirus disease 2019 (COVID‐19) related (51.3% in 2020 and 63.4% in 2021), whereas only less than a quarter of excess deaths due to HHS were COVID‐19 related. A widened racial/ethnic disparity was observed, and females exhibited higher excess mortality than males. Conclusions The DKA‐ and HHS‐related excess mortality during the pandemic and relevant disparities emphasize the urgent need for targeted strategies to mitigate the escalated risk in these populations during public health crises.

Addressing the challenges posed by nonlinear lattice models, which are vital across diverse scientific disciplines, we present a new deep learning approach that harnesses the power of graph neural networks. By representing the lattice system as a graph and leveraging the graph structures to identify complex nonlinear relationships, we have developed a flexible solution that outperforms traditional techniques. Our model not only offers precise trajectory predictions and energy conservation properties by incorporating separable Hamiltonians but also proves superior to existing top-tier models when tested on classic nonlinear oscillator lattice problems: a mixed Fermi-Pasta-Ulam Klein-Gordon, a Klein-Gordon system with long-range interactions, and a two-dimensional Frenkel-Kontorova, highlighting its potential for wide-reaching applications.

Abstract Background Since December 14, 2020, New York City (NYC) has started the first batch of COVID-19 vaccines. However, the shortage of vaccines is currently an inevitable problem. Therefore, optimizing the age-specific COVID-19 vaccination is an important issue that needs to be addressed as a priority. Objective Combined with the reported COVID-19 data in NYC, this study aimed to construct a mathematical model with five age groups to estimate the impact of age-specific vaccination on reducing the prevalence of COVID-19. Methods We proposed an age-structured mathematical model and estimated the unknown parameters based on the method of Markov Chain Monte Carlo (MCMC). We also calibrated our model by using three different types of reported COVID-19 data in NYC. Moreover, we evaluated the reduced cumulative number of deaths and new infections with different vaccine allocation strategies. Results Compared with the current vaccination strategy in NYC, if we gradually increased the vaccination coverage rate for only one age groups from March 1, 2021 such that the vaccination coverage rate would reach to 40% by June 1, 2021, then as of June 1, 2021, the cumulative deaths in the 75–100 age group would be reduced the most, about 72 fewer deaths per increased 100,000 vaccinated individuals, and the cumulative new infections in the 0–17 age group would be reduced the most, about 21,591 fewer new infections per increased 100,000 vaccinated individuals. If we gradually increased the vaccination coverage rate for two age groups from March 1, 2021 such that the vaccination coverage rate would reach to 40% by June 1, 2021, then as of June 1, 2021, the cumulative deaths in the 65–100 age group would be reduced the most, about 36 fewer deaths per increased 100,000 vaccinated individuals, and the cumulative new infections in the 0–44 age group would be reduced the most, about 17,515 fewer new infections per increased 100,000 vaccinated individuals. In addition, if we had an additional 100,000 doses of vaccine for 0–17 and 75–100 age groups as of June 1, 2021, then the allocation of 80% to the 0–17 age group and 20% to the 75–100 age group would reduce the maximum numbers of new infections and deaths simultaneously in NYC. Conclusions The COVID-19 burden including deaths and new infections would decrease with increasing vaccination coverage rate. Priority vaccination to the elderly and adolescents would minimize both deaths and new infections.

Summary: Background: Diabetes mellitus (DM) is a critical risk factor for severe SARS-CoV-2 infection, and SARS-CoV-2 infection contributes to worsening glycemic control. The COVID-19 pandemic profoundly disrupted the delivery of care for patients with diabetes. We aimed to determine the trend of DM-related deaths during the pandemic. Methods: In this serial population-based study between January 1, 2006 and December 31, 2021, mortality data of decedents aged ≥25 years from the National Vital Statistics System dataset was analyzed. Decedents with DM as the underlying or contributing cause of death on the death certificate were defined as DM-related deaths. Excess deaths were estimated by comparing observed versus expected age-standardized mortality rates derived from mortality during 2006-2019 with linear and polynomial regression models. The trends of mortality were quantified with joinpoint regression analysis. Subgroup analyses were performed by age, sex, race/ethnicity, and state. Findings: Among 4·25 million DM-related deaths during 2006-2021, there was a significant surge of more than 30% in mortality during the pandemic, from 106·8 (per 100,000 persons) in 2019 to 144·1 in 2020 and 148·3 in 2021. Adults aged 25-44 years had the most pronounced rise in mortality. Widened racial/ethnic disparity was observed, with Hispanics demonstrating the highest excess deaths (67·5%; 95% CI 60·9-74·7%), almost three times that of non-Hispanic whites (23·9%; 95% CI 21·2-26·7%). Interpretation: The United States saw an increase in DM-related mortality during the pandemic. The disproportionate rise in young adults and the widened racial/ethnic disparity warrant urgent preventative interventions from diverse stakeholders. Funding: National Natural Science Foundation of China.

The topic of two-dimensional steady laminar MHD boundary layer flow across a wedge with non-Newtonian hybrid nanoliquid (CuO-TiO2/C2H6O2) with viscous dissipation and radiation is taken into consideration. The controlling partial differential equations have been converted to non-linear higher-order ordinary differential equations using the appropriate similarity transformations. It is demonstrated that a number of thermo-physical characteristics govern the transmuted model. The issue is then mathematically resolved. When the method’s accuracy is compared to results that have already been published, an excellent agreement is found. While the thermal distribution increases with an increase in Eckert number, radiation and porosity parameters, the velocity distribution decreases as porosity increases.

Abstract Background The long-term impact of sexual transmission on the hepatitis B virus (HBV) infection in China remains unclear. This study aims to estimate the independent influence of sexual transmission on HBV infection. Methods Based on the natural history of HBV infection and three national serosurvey data of hepatitis B in China, we developed an age- and sex-specific discrete model to describe the transmission dynamics of HBV. The initial conditions of the model were determined according to the age- and sex-specific national serosurvey data in 1992. Based on the national survey data of hepatitis B in 1992 and 2006, by using the Markov Chain Monte Carlo (MCMC) method, we estimated the age- and sex-specific seroclearance rates of hepatitis B surface antigen (HBsAg) and the horizontal transmission rates as well as their 95% confidence intervals (CI). Then we used the age- and sex-specific national serosurvey data of hepatitis B in 2014 to test the accuracy of our model-based estimation. Finally, we evaluated the independent impact of sexual transmission on HBV infection and discussed the long-term effect of promotion of condom use in China. Results We estimated that the annual rates of HBsAg seroclearance for males and females aged 1–59 years were respectively 1.04% (95% CI, 0.49–1.59%) and 1.92% (95% CI, 1.11–2.73%). Due to sexual transmission, in 2014, the total number of chronic HBV infections in people aged 0–100 years increased 292,581, of which males increased 189,200 and females increased 103,381. In 2006, the acute HBV infections due to sexual transmission accounted for 24.76% (male: 31.33%, female: 17.94%) and in 2014, which accounted for 34.59% (male: 42.93%, female: 25.73%). However, if the condom usage rate was increased by 10% annually starting in 2019, then compared with current practice, the total number of acute HBV infections from 2019 to 2035 would be reduced by 16.68% (male: 21.49%, female: 11.93%). The HBsAg prevalence in people aged 1–59 years in 2035 would be reduced to 2.01% (male: 2.40%, female: 1.58%). Conclusions Sexual transmission has become the predominant route of acute HBV infection in China, especially for men. The promotion of condom use plays a significant role in reducing the cases of acute HBV infection.

HIV is a topic that has been greatly discussed and researched due to its impact on human population. Many campaigns have been put into place, and people have been made aware of the various effects of the disease. This paper considers a fractional-order HIV epidemic model with the inclusion of prostitution in the population and its consequences on the disease transmission. The model describes the spread of HIV disease in a system consisting of a population of susceptible males and the female sex workers. The focus is on the spread of HIV by female sex workers through prostitution, because in the present world sexual transmission is the major cause of the HIV transmission. The fractional derivatives are taken in Caputo sense and the numerical solution of the model is obtained by L1 scheme which involves the memory trace that can capture and integrate all past activity. Positivity and boundedness of the solution and the stability conditions of the fractional-order system are determined. Moreover, model equilibria are determined, and their stability analysis are considered by using fractional Routh-Hurwitz stability criterion and fractional La-Salle's invariant principle. The threshold quantity namely basic reproduction number R0 is calculated and analyzed for the disease status. On the basis of R0, the disease progress can be determined i.e., the population is free from the disease if R01. Meanwhile, by using Lyapunov functional approach, the global dynamics of the endemic equilibrium point is discussed. Further, numerical simulations of the model and their graphical presentations are performed to visualize the effectiveness of our theoretical results and to observe the impact of the arbitrary order derivative. The results obtained show the effectiveness and strength of the applied L1 scheme.

Abstract Background The coronavirus disease 2019 (COVID-19) outbreak has seriously endangered the health and lives of Chinese people. In this study, we predicted the COVID-19 epidemic trend and estimated the efficacy of several intervention strategies in the mainland of China. Methods According to the COVID-19 epidemic status, we constructed a compartmental model. Based on reported data from the National Health Commission of People’s Republic of China during January 10–February 17, 2020, we estimated the model parameters. We then predicted the epidemic trend and transmission risk of COVID-19. Using a sensitivity analysis method, we estimated the efficacy of several intervention strategies. Results The cumulative number of confirmed cases in the mainland of China will be 86 763 (95% CI: 86 067–87 460) on May 2, 2020. Up until March 15, 2020, the case fatality rate increased to 6.42% (95% CI: 6.16–6.68%). On February 23, 2020, the existing confirmed cases reached its peak, with 60 890 cases (95% CI: 60 350–61 431). On January 23, 2020, the effective reproduction number was 2.620 (95% CI: 2.567–2.676) and had dropped below 1.0 since February 5, 2020. Due to governmental intervention, the total number of confirmed cases was reduced by 99.85% on May 2, 2020. Had the isolation been relaxed from February 24, 2020, there might have been a second peak of infection. However, relaxing the isolation after March 16, 2020 greatly reduced the number of existing confirmed cases and deaths. The total number of confirmed cases and deaths would increase by 8.72 and 9.44%, respectively, due to a 1-day delayed diagnosis in non-isolated infected patients. Moreover, if the coverage of close contact tracing was increased to 100%, the cumulative number of confirmed cases would be decreased by 88.26% on May 2, 2020. Conclusions The quarantine measures adopted by the Chinese government since January 23, 2020 were necessary and effective. Postponing the relaxation of isolation, early diagnosis, patient isolation, broad close-contact tracing, and strict monitoring of infected persons could effectively control the COVID-19 epidemic. April 1, 2020 would be a reasonable date to lift quarantine in Hubei and Wuhan.

COVID-19 is an infectious disease caused by the SARS-CoV-2 virus that caused an outbreak of typical pneumonia first in Wuhan and then globally. Although researchers focus on the human-to-human transmission of this virus but not much research is done on the dynamics of the virus in the environment and the role humans play by releasing the virus into the environment. In this paper, a novel nonlinear mathematical model of the COVID-19 epidemic is proposed and analyzed under the effects of the environmental virus on the transmission patterns. The model consists of seven population compartments with the inclusion of contaminated environments means there is a chance to get infected by the virus in the environment. We also calculated the threshold quantity R0to know the disease status and provide conditions that guarantee the local and global asymptotic stability of the equilibria using Volterra-type Lyapunov functions, LaSalle’s invariance principle, and the Routh–Hurwitz criterion. Furthermore, the sensitivity analysis is performed for the proposed model that determines the relative importance of the disease transmission parameters. Numerical experiments are performed to illustrate the effectiveness of the obtained theoretical results.

Background: In face of the continuing worldwide COVID-19 epidemic, how to reduce the transmission risk of COVID-19 more effectively is still a major public health challenge that needs to be addressed urgently.Objective: This study aimed to develop an age-structured compartment model to evaluate the impact of all diagnosed and all hospitalized on the epidemic trend of COVID-19, and explore innovative and effective releasing strategies for different age groups to prevent the second wave of COVID-19.Methods: Based on three types of COVID-19 data in New York City (NYC), we calibrated the model and estimated the unknown parameters using the Markov Chain Monte Carlo (MCMC) method.Results: Compared with the current practice in NYC, we estimated that if all infected people were diagnosed from March 26, April 5 to April 15, 2020, respectively, then the number of new infections on April 22 was reduced by 98.02, 93.88, and 74.08%. If all confirmed cases were hospitalized from March 26, April 5, and April 15, 2020, respectively, then as of June 7, 2020, the total number of deaths in NYC was reduced by 67.24, 63.43, and 51.79%. When only the 0–17 age group in NYC was released from June 8, if the contact rate in this age group remained below 61% of the pre-pandemic level, then a second wave of COVID-19 could be prevented in NYC. When both the 0–17 and 18–44 age groups in NYC were released from June 8, if the contact rates in these two age groups maintained below 36% of the pre-pandemic level, then a second wave of COVID-19 could be prevented in NYC.Conclusions: If all infected people were diagnosed in time, the daily number of new infections could be significantly reduced in NYC. If all confirmed cases were hospitalized in time, the total number of deaths could be significantly reduced in NYC. Keeping a social distance and relaxing lockdown restrictions for people between the ages of 0 and 44 could not lead to a second wave of COVID-19 in NYC.

Abstract Background Uncovering the evolutionary principles of gene coexpression network is important for our understanding of the network topological property of new genes. However, most existing evolutionary models only considered the evolution of duplication genes and only based on the degree of genes, ignoring the other key topological properties. The evolutionary mechanism by which how are new genes integrated into the ancestral networks are not yet to be comprehensively characterized. Herein, based on the human ribonucleic acid-sequencing (RNA-seq) data, we develop a new evolutionary model of gene coexpression network which considers the evolutionary process of both duplication genes and de novo genes. Results Based on the human RNA-seq data, we construct a gene coexpression network consisting of 8061 genes and 638624 links. We find that there are 1394 duplication genes and 126 de novo genes in the network. Then based on human gene age data, we reproduce the evolutionary process of this gene coexpression network and develop a new evolutionary model. We find that the generation rates of duplication genes and de novo genes are approximately 3.58/Myr (Myr=Million year) and 0.31/Myr, respectively. Based on the average degree and coreness of parent genes, we find that the gene duplication is a random process. Eventually duplication genes only inherit 12.89% connections from their parent genes and the retained connections have a smaller edge betweenness. Moreover, we find that both duplication genes and de novo genes prefer to develop new interactions with genes which have a large degree and a large coreness. Our proposed model can generate an evolutionary network when the number of newly added genes or the length of evolutionary time is known. Conclusions Gene duplication and de novo genes are two dominant evolutionary forces in shaping the coexpression network. Both duplication genes and de novo genes develop new interactions through a “rich-gets-richer" mechanism in terms of degree and coreness. This mechanism leads to the scale-free property and hierarchical architecture of biomolecular network. The proposed model is able to construct a gene coexpression network with comprehensive biological characteristics.

A mathematical model of the transmission dynamics of infectious disease is an important theoretical epidemiology method, which has been used to simulate the prevalence of hepatitis B and evaluate different immunization strategies. However, differences lie in the mathematical processes of modeling HBV transmission in published studies, not only in the model structure, but also in the estimation of certain parameters. This review reveals that the dynamics model of HBV transmission only simulates the spread of HBV in the population from the macroscopic point of view and highlights several main shortcomings in the model structure and parameter estimation. First, age-dependence is the most important characteristic in the transmission of HBV, but an age-structure model and related age-dependent parameters were not adopted in some of the compartmental models describing HBV transmission. In addition, the numerical estimation of the force of HBV infection did not give sufficient weight to the age and time factors and is not suitable using the incidence data. Lastly, the current mathematical models did not well reflect the details of the factors of HBV transmission, such as migration from high or intermediate HBV endemic areas to low endemic areas and the kind of HBV genotype. All of these shortcomings may lead to unreliable results. When the mathematical model closely reflects the fact of hepatitis B spread, the results of the model fit will provide valuable information for controlling the transmission of hepatitis B.

Abstract The age-specific seroclearance pattern of hepatitis B surface antigen (HBsAg) in chronic hepatitis B virus (HBV) infections of China remains unclear. In this study, based on three national serosurvey data of hepatitis B in China, we propose an age- and time-dependent discrete model and use the method of non-linear least squares to estimate the age-specific annual rate of HBsAg seroclearance. We found that the HBsAg seroclearance in chronic HBV infections of China aged 1–59 years occurred at an average annual rate of 1.80% (95% CI, 1.54–2.06%) from 1993 to 2006. The HBsAg seroclearance occurred predominantly in the early childhood, 20–24 and 35–39 year age groups. Moreover, our model estimated that HBsAg seroclearance resulted in 23.38% of the decrease of total HBsAg prevalence for population aged 1–59 years in 2006. It also prevented 9.30% of new HBV infections (about 7.43 million people) and 9.95% of HBV-related deaths (about 0.25 million people) from 1993 to 2006. This study develops a new and efficient method to estimate the age-specific incidence of HBsAg seroclearance at a population-level and evaluate its effect.

In this paper, we focus on high-order approximate solutions to two-level systems with quasi-resonant control. Firstly, we develop a high-order renormalization group (RG) method for Schrödinger equations. By this method, we get the high-order RG approximate solution in both resonance case and out of resonance case directly. Secondly, we introduce a time transformation to avoid the invalid expansion and get the high-order RG approximate solution in near resonance case. Finally, some numerical simulations are presented to illustrate the effectiveness of our RG method. We aim to provide a mathematically rigorous framework for mathematicians and physicists to analyze the high-order approximate solutions of quasi-resonant control problems.

This paper is devoted to studying the analytical series solutions for the differential equations with variable coefficients. By a general residual power series method, we construct the approximate analytical series solutions for differential equations with variable coefficients, including nonhomogeneous parabolic equations, fractional heat equations in 2D, and fractional wave equations in 3D. These applications show that residual power series method is a simple, effective, and powerful method for seeking analytical series solutions of differential equations (especially for fractional differential equations) with variable coefficients.

We investigate the influence of asymmetric interactions on coevolutionary dynamics of a predator-prey system by using the theory of adaptive dynamics. We assume that the defense ability of prey and the attack ability of predators all can adaptively evolve, either caused by phenotypic plasticity or by behavioral choice, but there are certain costs in terms of their growth rate or death rate. The coevolutionary model is constructed from a deterministic approximation of random mutation-selection process. To sum up, if prey's trade-off curve is globally weakly concave, then five outcomes of coevolution are demonstrated, which depend on the intensity and shape of asymmetric predator-prey interactions and predator's trade-off shape. Firstly, we find that if there is a weakly decelerating cost and a weakly accelerating benefit for predator species, then evolutionary branching in the predator species may occur, but after branching further coevolution may lead to extinction of the predator species with a larger trait value. However, if there is a weakly accelerating cost and a weakly accelerating benefit for predator species, then evolutionary branching in the predator species is also possible and after branching the dimorphic predator can evolutionarily stably coexist with a monomorphic prey species. Secondly, if the asymmetric interactions become a little strong, then prey and predators will evolve to an evolutionarily stable equilibrium, at which they can stably coexist on a long-term timescale of evolution. Thirdly, if there is a weakly accelerating cost and a relatively strongly accelerating benefit for prey species, then evolutionary branching in the prey species is possible and the finally coevolutionary outcome contains a dimorphic prey and a monomorphic predator species. Fourthly, if the asymmetric interactions become more stronger, then predator-prey coevolution may lead to cycles in both traits and equilibrium population densities. The Red Queen dynamic is a possible outcome under asymmetric predator-prey interactions.