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.

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.

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.

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.

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.

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.

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.

TransCode:Uncovering COVID-19 transmission patterns via deep learning

Background The heterogeneity of COVID-19 spread dynamics is determined by complex spatiotemporal transmission patterns at a fine scale,especially in densely populated regions.In this study,we aim to discover such fine-scale transmission patterns via deep learning.Methods We introduce the notion of TransCode to characterize fine-scale spatiotemporal transmission patterns of COVID-19 caused by metapopulation mobility and contact behaviors.First,in Hong Kong,China,we construct the mobility trajectories of confirmed cases using their visiting records.Then we estimate the transmissibility of individual cases in different locations based on their temporal infectiousness distribution.Integrating the spatial and temporal information,we represent the TransCode via spatiotemporal transmission networks.Further,we propose a deep transfer learning model to adapt the TransCode of Hong Kong,China to achieve fine-scale transmission characterization and risk prediction in six densely populated metropolises:New York City,San Francisco,Toronto,London,Berlin,and Tokyo,where fine-scale data are limited.All the data used in this study are publicly available.Results The TransCode of Hong Kong,China derived from the spatial transmission information and temporal infectiousness distribution of individual cases reveals the transmission patterns(e.g.,the imported and exported transmission intensities)at the district and constituency levels during different COVID-19 outbreaks waves.By adapting the TransCode of Hong Kong,China to other data-limited densely populated metropolises,the proposed method outperforms other representative methods by more than 10%in terms of the prediction accuracy of the disease dynamics(i.e.,the trend of case numbers),and the fine-scale spatiotemporal transmission patterns in these metropolises could also be well captured due to some shared intrinsically common patterns of human mobility and contact behaviors at the metapopulation level.Conclusions The fine-scale transmission patterns due to the metapopulation level mobility(e.g.,travel across different districts)and contact behaviors(e.g.,gathering in social-economic centers)are one of the main contributors to the rapid spread of the virus.Characterization of the fine-scale transmission patterns using the TransCode will facilitate the development of tailor-made intervention strategies to effectively contain disease transmission in the targeted regions.

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.

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.

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.

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.

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.

EpiMix:A novel method to estimate effective reproduction number

Transmission potential of a pathogen,often quantified by the time-varying reproduction number R t,provides the current pace of infection for a disease and indicates whether an emerging epidemic is under control.In this study,we proposed a novel method,EpiMix,for R t estimation,wherein we incorporated the impacts of exogenous factors and random effects under a Bayesian regression framework.Using Integrated Nested Laplace Approx-imation,EpiMix is able to efficiently generate reliable,deterministic R t estimates.In the simulations and case studies performed,we further demonstrated the method's robust-ness in low-incidence scenarios,together with other merits,including its flexibility in selecting variables and tolerance of varying reporting rates.All these make EpiMix a potentially useful tool for real-time R t estimation provided that the serial interval distri-bution,time series of case counts and external influencing factors are available.

Cascading Failure Propagation Simulation in Integrated Electricity and Natural Gas Systems

The sharp increase in the total installed capacity of natural gas generators has intensified the dynamic interaction between the electricity and natural gas systems,which could induce cascading failure propagation across the two systems that deserves intensive research.Considering the distinct time response behaviors of the two systems,this paper discusses an integrated simulation approach to simulate the cascading failure propagation process of integrated electricity and natural gas systems(IEGSs).On one hand,considering instantaneous re-distribution of power flows after the occurrence of disturbance or failure,the steady-state AC power flow model is employed.On the other hand,gas transmission dynamics are represented by dynamic model to capture the details of its transition process.The interactions between the two systems,intensified by energy coupling components(such as gas-fired generator and electricity-driven gas compressor)as well as the switching among the operation modes of compressors during the cascading failure propagation process,are studied.An IEGS composed of the IEEE 30-bus electricity system and a 14-node 15-pipeline gas system is established to illustrate the effectiveness of the proposed simulation approach,in which two energy sub-systems are coupled by compressor and gas-fired generator.Numerical results clearly demonstrate that heterogeneous interactions between electricity and gas systems would trigger the cascading failure propagation between the two coupling systems.

Consumption Inequality in China： Theory and Evidence from the China Health and Nutrition Survey

We investigate consumption inequality in China both theoretically by constructing a theoretical model that delineates the transmission channels by which income shocks affect consumption and empirically through an Unequally Spaced Dynamic Panel Data model estimation. We find that China is experiencing consumption inequality with the full partial insurance of consumption against both permanent and transitory income shocks, although the impact of both types of shock are larger than the case of the United States. The results are due to precautionary savings motives of the Chinese. We further document how income becomes more dispersed in China and show how the family background of a child affects his outcome to a large extent. Policy implications based on our findings are proposed.

A Scalable Infrastructure for Online Performance Analysis on CFD Application

The fast-growing demand of computational fluid dynamics（CFD） application for computing resources stimulates the development of high performance computing（HPC） and meanwhile raises new requirements for the technology of parallel application performance monitor and analysis.In response to large-scale and long-time running for the application of CFD,online and scalable performance analysis technology is required to optimize the parallel programs as well as to improve their operational efficiency.As a result,this research implements a scalable infrastructure for online performance analysis on CFD application with homogeneous or heterogeneous system.The infrastructure is part of the parallel application performance monitor and analysis system（PAPMAS） and is composed of two modules which are scalable data transmission module and data storage module.The paper analyzes and elaborates this infrastructure in detail with respect to its design and implementation.Furthermore,some experiments are carried out to verify the rationality and high efficiency of this infrastructure that could be adopted to meet the practical needs.

Feasibility of controlling hepatitis E in Jiangsu Province, China: a modelling study

Background:Hepatitis E,an acute zoonotic disease caused by the hepatitis E virus(HEV),has a relatively high burden in developing countries.The current research model on hepatitis E mainly uses experimental animal models(such as pigs,chickens,and rabbits)to explain the transmission of HEV.Few studies have developed a multi-host and multiroute transmission dynamic model(MHMRTDM)to explore the transmission feature of HEV.Hence,this study aimed to explore its transmission and evaluate the effectiveness of intervention using the dataset of Jiangsu Province.