Excitation Prediction by Dynamic Transmission Error under Sliding Friction in Helical Gear System

Monte Carlo method was adopted to calculate the meshing error considering the manufacture error and assembly error of the meshing point along the time-varying contact line for helical gear pair. The flexural-torsion-axis dynamic model coupled was established under the tooth friction force and solved by the perturbation method to compute real dynamic tooth load. The change laws of the friction force and friction torque were obtained in a meshing period. The transmission error formulation was analyzed to introduce meshing excitations. The maximum dynamic transmission error, the maximum meshing force and the maximum dynamic factor were calculated under different speeds, external loads and damping factors. The conclusions can provide theoretical basis for the gear design especially in tooth profile correction.

Transmission Dynamics and Optimal Control Strategies of a Hand-Foot-Mouth Disease Model with Treatment and Vaccination Interventions

In this article, the transmission dynamics of a Hand-Foot-Mouth disease model with treatment and vaccination interventions are studied. We calculated the basic reproduction number and proved the global stability of disease-free equilibrium when R0 R0 > 1. Meanwhile, we obtained the optimal control strategies minimizing the cost of intervention and minimizing the infected person. We also give some numerical simulations to verify our theoretical results.

A Probabilistic Description of the Impact of Vaccine-Induced Immunity in the Dynamics of COVID-19 Transmission

The recent outbreak of COVID-19 has caused millions of deaths worldwide and a huge societal and economic impact in virtually all countries. A large variety of mathematical models to describe the dynamics of COVID-19 transmission have been reported. Among them, Bayesian probabilistic models of COVID-19 transmission dynamics have been very efficient in the interpretation of early data from the beginning of the pandemic, helping to estimate the impact of non-pharmacological measures in each country, and forecasting the evolution of the pandemic in different potential scenarios. These models use probability distribution curves to describe key dynamic aspects of the transmission, like the probability for every infected person of infecting other individuals, dying or recovering, with parameters obtained from experimental epidemiological data. However, the impact of vaccine-induced immunity, which has been key for controlling the public health emergency caused by the pandemic, has been more challenging to describe in these models, due to the complexity of experimental data. Here we report different probability distribution curves to model the acquisition and decay of immunity after vaccination. We discuss the mathematical background and how these models can be integrated in existing Bayesian probabilistic models to provide a good estimation of the dynamics of COVID-19 transmission during the entire pandemic period.

Forecasting of COVID-19: spread with dynamic transmission rate

The COVID-19 was firstly reported in Wuhan,Hubei province,and it was brought to all over China by people travelling for Chinese New Year.The pandemic coronavirus with its catastrophic effects is now a global concern.Forecasting of COVID-19 spread has attracted a great attention for public health emergency.However,few re-searchers look into the relationship between dynamic transmission rate and preventable measures by authorities.In this paper,the SEIR(Susceptible Exposed Infectious Recovered)model is employed to investigate the spread of COVID-19.The epidemic spread is divided into two stages:before and after intervention.Before intervention,the transmission rate is assumed to be a constant since individual,community and government response has not taken into place.After intervention,the transmission rate is reduced dramatically due to the societal actions or measures to reduce and prevent the spread of disease.The transmission rate is assumed to follow an exponential function,and the removal rate is assumed to follow a power exponent function.The removal rate is increased with the evolution of the time.Using the real data,the model and parameters are optimized.The transmission rate without measure is calculated to be 0.033 and 0.030 for Hubei and outside Hubei province,respectively.After the model is established,the spread of COVID-19 in Hubei province,France and USA is predicted.From results,USA performs the worst according to the dynamic ratio.The model has provided a mathematical method to evaluate the effectiveness of the government response and can be used to forecast the spread of COVID-19 with better performance.

Effect analysis of friction and damping on anti-backlash gear based on dynamics model with time-varying mesh stiffness

A nonlinear model of anti-backlash gear with time-varying friction and mesh stiffness was proposed for the further study on dynamic characteristics of anti-backlash gear. In order to improve the model precision, applied force analysis was completed in detail, and single or double tooth meshing states of two gear pairs at any timing were determined according to the meshing characteristic of anti-backlash gear. The influences of friction and variations of damping ratio on dynamic transmission error were analyzed finally by numerical calculation and the results show that anti-backlash gear can increase the composite mesh stiffness comparing with the mesh stiffness of the normal gear pair. At the pitch points where the frictions change their signs, additional impulsive effects are observed. The width of impulsive in the same value of center frequency is wider than that without friction, and the amplitude is lower. When gear pairs mesh in and out, damping can reduce the vibration and impact.

SEIRS model for malaria transmission dynamics incorporating seasonality and awareness campaign

Malaria,a devastating disease caused by the Plasmodium parasite and transmitted through the bites of female Anopheles mosquitoes,remains a significant public health concern,claiming over 600,000 lives annually,predominantly among children.Novel tools,including the application of Wolbachia,are being developed to combat malaria-transmitting mosquitoes.This study presents a modified susceptible-exposed-infectious-recovered-susceptible(SEIRS)compartmental mathematical model to evaluate the impact of awareness-based control measures on malaria transmission dynamics,incorporating mosquito interactions and seasonality.Employing the next-generation matrix approach,we calculated a basic reproduction number(R0)of 2.4537,indicating that without robust control measures,the disease will persist in the human population.The model equations were solved numerically using fourth and fifth-order Runge-Kutta methods.The model was fitted to malaria incidence data from Kenya spanning 2000 to 2021 using least squares curve fitting.The fitting algorithm yielded a mean absolute error(MAE)of 2.6463 when comparing the actual data points to the simulated values of infectious human population(Ih).This finding indicates that the proposed mathematical model closely aligns with the recorded malaria incidence data.The optimal values of the model parameters were estimated from the fitting algorithm,and future malaria dynamics were projected for the next decade.The research findings suggest that social media-based awareness campaigns,coupled with specific optimization control measures and effective management methods,offer the most cost-effective approach to managing malaria.

Dynamic evolution of an SVEIR model with variants and non-pharmaceutical interventions for controlling COVID-19

The epidemiological characteristics and distributions of two epidemics in Fujian Province of Southeast China were attributed to the complex interactions among variant,host,and non-pharmaceutical interventions(NPIs).All reported cases in the Putian epidemic(September 8–October 2,2021,Delta variant B.1.617.2)and Fuzhou epidemic(October 22–November 18,2022,Omicron variant BA.5.2)were classified by sex,age group,occupation,and location in this study.Using surveillance data from the Fujian Provincial Center for Disease Control and Prevention,we established a virus-oriented SVEIR(Susceptible–Vaccinated–Exposed–Infected–Recovered)model to investigate the dynamic evolution features of these two variants and the effects of NPIs.The optimal simulations were carried out with variants and scenario investigations.The scenario investigations showed that NPIs significantly reduced the transmission risk and infection scales of COVID-19,and that the Omicron variant was more infectious than the Delta variant.Moreover,the dynamic investigations revealed the increasing tendencies from Delta to Omicron,such as the basic reproduction number,infection rate,percentage of high-risk cases,and the growth rate.Decreasing tendencies were also identified,such as the average recovery period,the awareness delay,and the percentage of symptomatic cases.This study highlighted that NPIs played critical roles in successfully containing the two epidemics.Such interventions are strongly recommended to public health policymakers.

应急状态下新冠流行曲线预测的方法学研究——基于北京市百度搜索和传统流感样病例监测

Surveillance is an essential work on infectious diseases prevention and control.When the pandemic occurred,the inadequacy of traditional surveillance was exposed,but it also provided a valuable opportunity to explore new surveillance methods.This study aimed to estimate the transmission dynamics and epidemic curve of severe acute respiratory syndrome coronavirus 2(SARS-Co V-2)Omicron BF.7 in Beijing under the emergent situation using Baidu index and influenza-like illness(ILI)surveillance.A novel hybrid model(multiattention bidirectional gated recurrent unit(MABG)-susceptible-exposed-infected-removed(SEIR))was developed,which leveraged a deep learning algorithm(MABG)to scrutinize the past records of ILI occurrences and the Baidu index of diverse symptoms such as fever,pyrexia,cough,sore throat,anti-fever medicine,and runny nose.By considering the current Baidu index and the correlation between ILI cases and coronavirus disease 2019(COVID-19)cases,a transmission dynamics model(SEIR)was formulated to estimate the transmission dynamics and epidemic curve of SARS-Co V-2.During the COVID-19 pandemic,when conventional surveillance measures have been suspended temporarily,cases of ILI can serve as a useful indicator for estimating the epidemiological trends of COVID-19.In the specific case of Beijing,it has been ascertained that cumulative infection attack rate surpass 80.25%(95%confidence interval(95%CI):77.51%-82.99%)since December 17,2022,with the apex of the outbreak projected to transpire on December 12.The culmination of existing patients is expected to occur three days subsequent to this peak.Effective reproduction number(Rt)represents the average number of secondary infections generated from a single infected individual at a specific point in time during an epidemic,remained below 1 since December 17,2022.The traditional disease surveillance systems should be complemented with information from modern surveillance data such as online data sources with advanced technical support.Modern surveillance channels should be used primarily in emerging infectious and disease outbreaks.Syndrome surveillance on COVID-19 should be established to following on the epidemic,clinical severity,and medical resource demand.

Mathematical modeling for Delta and Omicron variant of SARS-CoV-2 transmission dynamics in Greece

A compartmental,epidemiological,mathematical model was developed in order to analyze the transmission dynamics of Delta and Omicron variant,of SARS-CoV-2,in Greece.The model was parameterized twice during the 4th and 5th wave of the pandemic.The 4th wave refers to the period during which the Delta variant was dominant(approximately July to December of 2021)and the 5th wave to the period during which the Omicron variant was dominant(approximately January to May of 2022),in accordance with the official data from the National Public Health Organization(NPHO).Fitting methods were applied to evaluate important parameters in connection with the transmission of the variants,as well as the social behavior of population during these periods of interest.Mathematical models revealed higher numbers of contagiousness and cases of asymptomatic disease during the Omicron variant period,but a decreased rate of hospitalization compared to the Delta period.Also,parameters related to the behavior of the population in Greece were also assessed.More specifically,the use of protective masks and the abidance of social distancing measures.Simulations revealed that over 5,000 deaths could have been avoided,if mask usage and social distancing were 20%more efficient,during the short period of the Delta and Omicron outbreak.Furthermore,the spread of the variants was assessed using viral load data.The data were recorded from PCR tests at 417 Army Equity Fund Hospital(NIMTS),in Athens and the Ct values from 746 patients with COVID-19 were processed,to explain transmission phenomena and disease severity in patients.The period when the Delta variant prevailed in the country,the average Ct value was calculated as 25.19(range:12.32e39.29),whereas during the period when the Omicron variant prevailed,the average Ct value was calculated as 28(range:14.41e39.36).In conclusion,our experimental study showed that the higher viral load,which is related to the Delta variant,may interpret the severity of the disease.However,no correlation was confirmed regarding contagiousness phenomena.The results of the model,Ct analysis and official data from NPHO are consistent.

Modeling the transmission dynamics of a time-delayed epidemic model with saturated treatment rate

In this paper,an attempt has been made to explore a new delayed epidemiological model assuming that the disease is transmitted among the susceptible population and possessing nonlinear incidence function along with a saturated treatment rate.Due attention is paid to the positivity and boundedness of the solutions and the bifurcation of the dynamical system as well.Basic reproduction number is being calculated,and considering the latent period as a bifurcation parameter,it has been examined that a Hopf-bifurcation occurs near the endemic equilibrium point while the parameter attains critical values.We have also discussed the stability and direction of Hopf-bifurcation near the endemic equilibrium point,the global stability analysis and the optimal control theory.We conclude that the system reveals chaotic dynamics through a specific time-delay value.Numerical simulations are being performed in order to explain the accuracy and effectiveness of the acquired theoretical results.

The transmission mechanism theory of disease dynamics:Its aims,assumptions and limitations

Most of the progress in the development of single scale mathematical and computational models for the study of infectious disease dynamics which now span over a century is build on a body of knowledge that has been developed to address particular single scale descriptions of infectious disease dynamics based on understanding disease transmission process.Although this single scale understanding of infectious disease dynamics is now founded on a body of knowledge with a long history,dating back to over a century now,that knowledge has not yet been formalized into a scientific theory.In this article,we formalize this accumulated body of knowledge into a scientific theory called the transmission mechanism theory of disease dynamics which states that at every scale of organization of an infectious disease system,disease dynamics is determined by transmission as the main dynamic disease process.Therefore,the transmission mechanism theory of disease dynamics can be seen as formalizing knowledge that has been inherent in the study of infectious disease dynamics using single scale mathematical and computational models for over a century now.The objective of this article is to summarize this existing knowledge about single scale modelling of infectious dynamics by means of a scientific theory called the transmission mechanism theory of disease dynamics and highlight its aims,assumptions and limitations.

African swine fever and meat prices fluctuation:An empirical study in China based on TVP-VAR model

African swine fever(ASF),a fatal disease outbroken in China in August 2018,has widely attracted social concern especially in the information era.The occurrence of ASF led to an imbalance between supply and demand in pork and other meat markets.As a result,meat prices fluctuated greatly during the past year in 2019.To measure ASF quantitatively,the internet public concern index about ASF was created using web crawler methods.The relationships between ASF and meat prices were analyzed based on time-varying parameter vector auto-regressive(TVP-VAR)model.The results showed that there were some differences in the impact size,direction and duration of ASF on the prices of pork,chicken,beef and mutton,and the characteristics of time variability and heterogeneity were obvious.At the same time,the impact of ASF on meat prices is not consistent with the trend and degree of ASF.The impulse intensity is strongly correlated with the strength and duration of ASF,and it is generally weak in the early stage and much stronger in the middle and late periods.The results indicate that macro regulations,monitoring and early-warning system,standardizing production and circulation,and the public opinion monitoring and guidance about ASF should be given more attention in future to stabilize the market expectations and to promote a smooth functioning of the livestock markets.

A Scenario-Based Evaluation of COVID-19-Related Essential Clinical Resource Demands in China

The coronavirus disease 2019(COVID-19)pandemic is a global crisis,and medical systems in many countries are overwhelmed with supply shortages and increasing demands to treat patients due to the surge in cases and severe illnesses.This study aimed to assess COVID-19-related essential clinical resource demands in China,based on different scenarios involving COVID-19 spreads and interventions.We used a susceptible–exposed–infectious–hospitalized/isolated–removed(SEIHR)transmission dynamics model to estimate the number of COVID-19 infections and hospitalizations with corresponding essential healthcare resources needed.We found that,under strict non-pharmaceutical interventions(NPIs)or mass vaccination of the population,China would be able to contain community transmission and local outbreaks rapidly.However,under scenarios involving a low intensity of implemented NPIs and a small proportion of the population vaccinated,the use of a peacetime–wartime transition model would be needed for medical source stockpiles and preparations to ensure a normal functioning healthcare system.The implementation of COVID-19 vaccines and NPIs in different periods can influence the transmission of COVID-19 and subsequently affect the demand for clinical diagnosis and treatment.An increased proportion of asymptomatic infections in simulations will not reduce the demand for medical resources;however,attention must be paid to the increasing difficulty in containing COVID-19 transmission due to asymptomatic cases.This study provides evidence for emergency preparations and the adjustment of prevention and control strategies during the COVID-19 pandemic.It also provides guidance for essential healthcare investment and resource allocation.

Synchronization of three homodromy coupled exciters in a non-resonant vibrating system of plane motion

In this paper, the synchronization problem of three homodromy coupled exciters in a non-resonant vibrating system of plane motion is studied. By introducing the average method of modified small parameters, we deduced dimensionless coupling equation of three exciters, which converted the problem of synchronization into that of the existence and stability of zero solutions for the average differential equations of the small parameters. Based on the dimensionless coupling torques and characteristics of the cor- responding limited functions, the synchronization criterion for three exciters was derived as the absolute value of dimensionless residual torque difference between arbitrary two motors being less than the maximum of their dimensionless coupling torques. The stability criterion of its synchronous state lies in the double-condition that the inertia coupling matrix is positive definite and all its elements are positive as well. The synchronization determinants are the coefficients of synchronization ability, also called as the general dynamical symmetry coefficients. The double-equilibrium state of the vibrating system is manifested by numeric method, and the numeric and simulation results derived thereof indicate the indispensable and crucial role the structural parameters of the vibrating system play in the stability criterion of synchronous operation. Besides, by adjusting its structural parameters, the elliptical motion of the vibrating system successfully met the requirements in engineering applications.

Infer HIV transmission dynamics from gene sequences among young men who have sex with men in China

To investigate the transmission dynamics and temporal and spatial migration characteristics of HIV spread among men who have sex with men(MSM)in China,a total of 1012 HIV-1 partial pol sequences,including five subtypes,were studied.Bayesian analysis were applied for each subtype to infer its dynamic characters including the effective reproductive number(R_(e))and migration process.The mean curve of each R_(e) was almost always greater than 1(even the 95%highest posterior density(HPD)lower value)along with time,which supports the necessity for a comprehensive study about risk behaviors among young MSM group in China.We also should reappraise the free treatment strategy,especially the therapeutic effect during the free treatment policy.

COVID-19 transmission driven by age-group mathematical model in Shijiazhuang City of China

Background:A COVID-19 outbreak in the rural areas of Shijiazhuang City was attributed to the complex interactions among vaccination,host,and non-pharmaceutical interventions(NPIs).Herein,we investigated the epidemiological characteristics of all reported symptomatic cases by picking Shijiazhuang City,Hebei Province in Northern China as research objective.In addition,we established an age-group mathematical model to perform the optimal fitting and to investigate the dynamical profiles under three scenarios.Methods:All reported symptomatic cases of Shijiazhuang epidemic(January 2-February 3,2021)were investigated in our study.The cases were classified by gender,age group and location,the distributions were analyzed by epidemiological characteristics.Furthermore,the reported data from Health Commission of Hebei Province was also analyzed by using an age-group mathematical model by two phases and three scenarios.Results:Shijiazhuang epidemic caused by SARS-CoV-2 wild strain was recorded with the peak 84 cases out of 868 reported symptomatic cases on January 11,2021,which was implemented with strong NPIs by local government and referred as baseline situation in this study.The research results showed that R0 under baseline situation ranged from 4.47 to 7.72,and Rt of Gaocheng Distinct took 3.72 with 95%confidence interval from 3.23 to 4.35 on January 9,the declining tendencies of Rt under baseline situation were kept till February 3,the value of Rt reached below 1 on January 19 and remained low value up to February 3 for Gaocheng District and Shijiazhuang City during Shijiazhuang epidemic.This indicated Shijiazhuang epidemic was under control on January 19.However,if the strong NPIs were kept,but remote isolation operated on January 11 was not implemented as of February 9,then the scale of Shijiazhuang epidemic reached 9,482 cases from age group who were 60 years old and over out of 31,017 symptomatic cases.The investigation also revealed that Shijiazhuang epidemic reached 132,648 symptomatic cases for age group who were 60 years old and over(short for G2)under risk-based strategies(Scenario A),58,048 symptomatic cases for G2 under late quarantine strategies(Scenario B)and 207,124 symptomatic cases for G2 under late quarantine double risk strategies(Scenario C),and that the corresponding transmission tendencies of Rt for three scenarios were consistently controlled on Jan 29,2021.Compared with baseline situation,the dates for controlling Rt below 1 under three scenarios were delayed 10 days.Conclusions:Shijiazhuang epidemic was the first COVID-19 outbreak in the rural areas in Hebei Province of Northern China.The targeted interventions adopted in early 2021 were effective to halt the transmission due to the implementation of a strict and village-wide closure.However we found that age group profile and NPIs played critical rules to successfully contain Shijiazhuang epidemic,which should be considered by public health policies in rural areas of China's Mainland during the dynamic zero-COVID policy.

Modeling transmission dynamics of Ebola virus disease

Ebola virus disease （EVD） has emerged as a rapidly spreading potentially fatal disease. Several studies have been performed recently to investigate the dynamics of EVD. In this paper, we study the transmission dynamics of EVD by formulating an SEIR-type transmission model that includes isolated individuals as well as dead individuals that are not yet buried. Dynamical systems analysis of the model is performed, and it is consequently shown that the disease-free steady state is globally asymptotically stable when the basic reproduction number, R0 is less than unity. It is also shown that there exists a unique endemic equilibrium when R0 〉 1. Using optimal control theory, we propose control strategies, which will help to eliminate the Ebola disease. We use data fitting on models, with and without isolation, to estimate the basic reproductive numbers for the 2014 outbreak of EVD in Liberia and Sierra Leone.

An all-optical time-delay relay based on a bacteriorhodopsin film

Using a special property of dynamic complementary-suppression-modulated transmission （DCSMT） in the bacteriorhodopsin （bR） film, we have demonstrated an all-optical time-delay relay. To extend our work, the relationship between the delay time of the all-optical time-delay relay and parameters of a bR film is numerically studied. We show how the delay time changes with the product of concentration and thickness （PCT） of a bR film. Furthermore, the shortest and longest delay times are given for the relay of ＇switch off. The saturable delay time and maximum delaytime of ＇switch on＇ are also given. How the wavelengths （632.8, 568, 533 and 412 nm） and intensities of the illuminating light influence the delay time is also discussed. The simulation results are useful for optimizing the design of all-optical time-delay relays.

Transmission dynamics model and the coronavirus disease 2019 epidemic:applications and challenges

Since late 2019,the beginning of coronavirus disease 2019(COVID-19)pandemic,transmission dynamics models have achieved great development and were widely used in predicting and policymaking.Here,we provided an introduction to the history of disease transmission,summarized transmission dynamics models into three main types:compartment extension,parameter extension and population-stratified extension models,highlight the key contribution of transmission dynamics models in COVID-19 pandemic:estimating epidemiological parameters,predicting the future trend,evaluating the effectiveness of control measures and exploring different possibilities/scenarios.Finally,we pointed out the limitations and challenges lie ahead of transmission dynamics models.

A NOVEL APPLICATION OF A CLASSICAL METHOD FOR CALCULATING THE BASIC REPRODUCTIVE NUMBER, Ro FOR A GENDER AND RISK STRUCTURED TRANSMISSION DYNAMIC MODEL OF HUMAN PAPILLOMAVIRUS INFECTION

Mathematical models are increasingly being used in the evaluation of control strategies for infectious disease such as the vaccination program for the Human PapiUomavirus （HPV）. Here, an ordinary differential equation （ODE） transmission dynamic model for HPV is presented and analyzed. Parameter values for a gender and risk structured model are estimated by calibrating the model around the known prevalence of infection. The effect on gender and risk sub-group prevalence induced by varying the epidemiological parameters are investigated. Finally, the outcomes of this model are applied using a classical mathematical method for calculating R0 in a heterogeneous mixing population. Estimates for R0 under various gender and mixing scenarios are presented.