Modeling the transmission dynamics of COVID-19 epidemic: a systematic review

The outbreak and rapid spread of COVID-19 has become a public health emergency of international concern.A number of studies have used modeling techniques and developed dynamic models to estimate the epidemiological parameters,explore and project the trends of the COVID-19,and assess the effects of intervention or control measures.We identified 63 studies and summarized the three aspects of these studies:epidemiological parameters estimation,trend prediction,and control measure evaluation.Despite the discrepancy between the predictions and the actuals,the dynamic model has made great contributions in the above three aspects.The most important role of dynamic models is exploring possibilities rather than making strong predictions about longer-term disease dynamics.

Simulation of Spread of Infectious Diseases and Population Mobility in a Deterministic Epidemic Patch Model

Computer simulation models are widely applied in various areas of the health care sector, including the spread of infectious diseases. Patch models involve explicit movements of people between distinct locations. The aim of the present work has been designed and explored a patch model with population mobility between different patches and between each patch and an external population. The authors considered a SIR （susceptible-infected-recovered） scheme. The model was explored by computer simulations. The results show how endemic levels are reached in all patches of the system. Furthermore, the performed explorations suggest that the people mobility between patches, the immigration from outside the system and the infection rate in each patch, are factors that may influence the dynamics of epidemics and should be considered in health policy planning.

Stochastic Epidemic Model of Covid-19 via the Reservoir-People Transmission Network

The novel Coronavirus COVID-19 emerged in Wuhan,China in December 2019.COVID-19 has rapidly spread among human populations and other mammals.The outbreak of COVID-19 has become a global challenge.Mathematical models of epidemiological systems enable studying and predicting the potential spread of disease.Modeling and predicting the evolution of COVID-19 epidemics in near real-time is a scientific challenge,this requires a deep understanding of the dynamics of pandemics and the possibility that the diffusion process can be completely random.In this paper,we develop and analyze a model to simulate the Coronavirus transmission dynamics based on Reservoir-People transmission network.When faced with a potential outbreak,decision-makers need to be able to trust mathematical models for their decision-making processes.One of the most considerable characteristics of COVID-19 is its different behaviors in various countries and regions,or even in different individuals,which can be a sign of uncertain and accidental behavior in the disease outbreak.This trait reflects the existence of the capacity of transmitting perturbations across its domains.We construct a stochastic environment because of parameters random essence and introduce a stochastic version of theReservoir-Peoplemodel.Then we prove the uniqueness and existence of the solution on the stochastic model.Moreover,the equilibria of the system are considered.Also,we establish the extinction of the disease under some suitable conditions.Finally,some numerical simulation and comparison are carried out to validate the theoretical results and the possibility of comparability of the stochastic model with the deterministic model.

Mathematical Analysis of the Transmission Dynamics of Tuberculosis

We develop a dynamical model to understand the underlying dynamics of TUBERCULOSIS infection at population level. The model, which integrates the treatment of individuals, the infections of latent and recovery individuals, is rigorously analyzed to acquire insight into its dynamical features. The phenomenon resulted due to the exogenous infection of TUBERCULOSIS disease. The mathematical analysis reveals that the model exhibits a backward bifurcation when TB treatment remains of infected class. It is shown that, in the absence of treatment, the model has a disease-free equilibrium (DEF) which is globally asymptotically stable (GAS) and the associated reproduction threshold is less than unity. Further, the model has a unique endemic equilibrium (EEP), for a special case, whenever the associated reproduction threshold quantity exceeds unity. For a special case, the EEP is GAS using the central manifold theorem of Castillo-Chavez.

基于lévy噪声的随机SIRS模型的拟最优控制

建立了一类基于lévy跳跃的不确定参数随机SIRS传染病模型.利用该模型研究了疫苗接种条件下的拟最优控制问题,使得治疗疾病过程中所花费的成本尽可能地小.根据伴随方程,给出了易感人群、感染人群和恢复人群的先验估计,并利用Hamiltonian函数和Gronwall不等式建立了拟最优控制的充分条件.

Markov切换下含疫苗接种和垂直感染的随机SIRS模型性质

该文研究了一类含Markov机制切换和疫苗接种及垂直感染的随机SIRS模型的动力学性质,通过构造带切换的Lyapunov函数,研究了模型具有平稳分布的判别条件,并研究了在模型中疾病趋于灭绝的阈值.最后通过举例来验证研究结果.结果表明:模型具有平稳分布和趋于灭绝的阈值是相同的.

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.

Big data technology in infectious diseases modeling,simulation,and prediction after the COVID-19 outbreak

After the outbreak of COVID-19,the interaction of infectious disease systems and social systems has challenged traditional infectious disease modeling methods.Starting from the research purpose and data,researchers im-proved the structure and data of the compartment model or used agents and artificial intelligence based models to solve epidemiological problems.In terms of modeling methods,the researchers use compartment subdivi-sion,dynamic parameters,agent-based model methods,and artificial intelligence related methods.In terms of factors studied,the researchers studied 6 categories:human mobility,nonpharmaceutical interventions(NPIs),ages,medical resources,human response,and vaccine.The researchers completed the study of factors through modeling methods to quantitatively analyze the impact of social systems and put forward their suggestions for the future transmission status of infectious diseases and prevention and control strategies.This review started with a research structure of research purpose,factor,data,model,and conclusion.Focusing on the post-COVID-19 infectious disease prediction simulation research,this study summarized various improvement methods and analyzes matching improvements for various specific research purposes.

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.

关于SIR和SIRS传染病数学模型历史研究

基于SIR和SIRS传染病数学模型内容的分析和讨论,通过以数学模型为工具来研究疾病传播,通过对相关文献内容的分析,为研究传染病数学模型提供文献支持。

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.

Dynamics of an SIRS model with age structure and two delays

ln this paper,we propose and investigate an SlRS model with age structure and twodelays.Both the infected and the recovered individuals have age structure,the infectionrate(from the infective to the susceptible)and the immune loss rate(from the recoveredto the susceptible)are related to two independent time delays,respectively.We provethat the proposed age structured SIRS model is well-posed by using the Co-semigrouptheory.The basic reproduction number Ro is given,and the unique endemic equilib-rium exists when R_(0)>1,while the disease-free equilibrium always exists.A rigorousmathematical analysis for the stability of two equilibria is provided.The disease-freeequilibrium is local asymptotically stable if R_(0)<1,and the endemic equilibrium is localasymptotically stable if R_(0)>1 and τl=0.Finally,we give numerical simulations toverify our results.

A discrete-time susceptible-infectious-recovered-susceptible model for the analysis of influenza data

We develop a discrete time compartmental model to describe the spread of seasonal influenza virus.As time and disease state variables are assumed to be discrete,this model is considered to be a discrete time,stochastic,Susceptible-Infectious-RecoveredSusceptible(DT-SIRS)model,where weekly counts of disease are assumed to follow a Poisson distribution.We allow the disease transmission rate to also vary over time,and the disease can only be reintroduced after extinction if there is a contact with infected individuals from other host populations.To capture the variability of influenza activities from one season to the next,we define the seasonality with a 4-week period effect that may change over years.We examine three different transmission rates and compare their performance to that of existing approaches.Even though there is limited information for susceptible and recovered individuals,we demonstrate that the simple models for transmission rates effectively capture the behaviour of the disease dynamics.We use a Bayesian approach for inference.The framework is applied in an analysis of the temporal spread of influenza in the province of Manitoba,Canada,2012e2015.

Improvement of the software for modeling the dynamics of epidemics and developing a user-friendly interface

The challenges humanity is facing due to the Covid-19 pandemic require timely and accurate forecasting of the dynamics of various epidemics to minimize the negative consequences for public health and the economy.One can use a variety of well-known and new mathematical models,taking into account a huge number of factors.However,complex models contain a large number of unknown parameters,the values of which must be determined using a limited number of observations,e.g.,the daily datasets for the accumulated number of cases.Successful experience in modeling the COVID-19 pandemic has shown that it is possible to apply the simplest SIR model,which contains 4 unknown parameters.Application of the original algo-rithm of the model parameter identification for the first waves of the COVID-19 pandemic in China,South Korea,Austria,Italy,Germany,France,Spain has shown its high accuracy in pre-dicting their duration and number of diseases.To simulate different epidemic waves and take into account the incompleteness of statistical data,the generalized SIR model and algorithms for determining the values of its parameters were proposed.The interference of the previous waves,changes in testing levels,quarantine or social behavior require constant monitoring of the epidemic dynamics and performing SIR simulations as often as possible with the use of a user-friendly interface.Such tool will allow predicting the dynamics of any epidemic using the data on the number of diseases over a limited period(e.g.,14 days).It will be possible to predict the daily number of new cases for the country as a whole or for its separate region,to estimate the number of carriers of the infection and the probability of facing such a carrier,as well as to estimate the number of deaths.Results of three SIR simulations of the COVID-19 epidemic wave in Japan in the summer of 2022 are presented and discussed.The predicted accumulated and daily numbers of cases agree with the results of observations,especially for the simulation based on the datasets corresponding to the period from July 3 to July 16,2022.A user-friendly interface also has to ensure an opportunity to compare the epidemic dynamics in different countries/regions and in different years in order to estimate the impact of vaccination levels,quarantine restrictions,social behavior,etc.on the numbers of new infections,death,and mortality rates.As example,the comparison of the COVID-19 pandemic dynamics in Japan in the summer of 2020,2021 and 2022 is presented.The high level of vaccinations achieved in the summer of 2022 did not save Japan from a powerful pandemic wave.The daily numbers of cases were about ten times higher than in the corresponding period of 2021.Nevertheless,the death per case ratio in 2022 was much lower than in 2020.

基于Matlab封闭系统中SIRS传染病模型的问题分析

在当下疫情多发需及时管控的背景下,对传染病进行定量研究其传播规律并建立传染病模型,可以为预测、控制、防范传染病大规模传播提供可靠的信息的研究显得尤为重要。文章利用微分方程理论针对假设的多种情境下建立传染病动力学SIRS模型来模拟传染病的传播过程及规律,并利用微分方程组针对多种不同情况使用MTALAB得出数值解。当初始潜伏者为密闭环境下工作人员及其它人员的情况下,分析得出其只对传染病传播期有影响,在传染病病情稳定后S、I、R三类人群的比率不变。在工作人员适当防护条件下改变了在公共场所内不同人群感染者的有效接触率,达到有效控制疫情传播方便及时管控的效果,因而得到了与实际贴切的模型,并且易于推广。

基于SEIR模型对新发传染病住院患者变化规律的预测研究

目的探求新发传染病发展规律,预测住院患者变化趋势,为今后应对突发公共卫生事件、评估医疗人力需求和制定疫情防控策略提供科学依据。方法基于SEIR模型理论,结合四川省新冠疫情防控政策,建立疫情传播过程中预警、暴发和恢复三个阶段的传染病动力学模型。根据四川省卫生健康委员会公布的新冠疫情实时数据,选取2020年1月21日-3月25日新冠病毒感染患者每日新增确诊病例数、累计确诊病例数、每日现有疑似病例数、累计出院病例数以及死亡病例数等,运用最小二乘优化问题算法,求解模型参数,输出模型拟合结果,从而评估模型可行性。结果模型拟合曲线与实际参考曲线的整体变化趋势基本一致;预警阶段的平均绝对百分比误差为30.06%,均方根误差为17.8404;暴发阶段的平均绝对百分比误差为10.14%,均方根误差为66.8452;恢复阶段的均方根误差为16.5082。结论该研究建立的多阶段SEIR模型整体拟合效果较好,可以用于预测新发传染病住院患者人数的变化趋势。

基于SIR的SNS网络舆情话题传播模型研究

舆情话题通常是由突发性的新闻事件所引发,社交网站(Social Network Sites,SNS)因其庞大的用户规模和开放性、即时性与互动性等特点,成为舆情话题传播的重要渠道。因此,研究SNS网络中的舆情话题传播机制,将有利于对舆情话题的传播过程进行分析与监控。然而传统的网络信息传播模型无法真实地描述SNS网络中的舆情话题传播过程。为了解决上述问题,分析了SNS网络中的信息互动模式及舆情话题的传播特点,基于无标度网络上的SIR模型,通过引入内部感染概率、外部感染概率、免疫概率以及直接免疫概率,构建了SNS网络中的舆情话题传播模型。仿真结果表明,基于SIR的舆情话题传播模型可以很好地描述SNS网络中的舆情话题演化规律。

一种改进的SIR网络谣言传播预警模型研究

网络舆情的传播规律与传染病模型的传播很相似,利用改进的传染病SIR模型分析网络谣言传播,通过节点的易感、感染、免疫3种状态反映谣言的传播特性,建立微分方程,根据伯努利微分方程的通解公式,得到预测函数形式。采用Matlab软件,根据案例真实值,使用非线性参数拟合进行建模仿真,得到谣言传播量随时间变化的预测函数表达式。结果表明,网络谣言传播在上升阶段时,遵循SI模型的传播规律;在下降阶段时,遵循改进的SIR模型的传播规律。该模型能够进行网络谣言传播潜伏期的高峰值预测、扩散周期预测及影响舆情传播的指标因素分析等,为网络谣言预警研究提供思路。

基于SIR传染病模型的印度新冠疫情波及影响分析

针对印度新型冠状病毒肺炎(COVID-19)疫情的传播,建立通过设定目标函数求最优解来确定模型未知参数的SIR传染病动力学模型。首先通过线性回归拟合参数范围,设定目标函数作为约束条件,结合龙格-库塔法,借助Matlab软件确定参数值最优解,进行SIR模型拟合和预测,发现印度疫情拐点将出现在2021年5月8日左右,结合预测数据推导未来每日新增及累计新增病例数,虽未来100 d内将持续出现新增病例,但疫情现期已经有消退趋势;其次考虑印度变种病毒B.1.617以及当下疫苗接种情况的影响,建立加入疫苗影响因素的SIR预测模型,通过进行疫苗接种灵敏度分析模拟出印度疫苗接种率大约需要达到75%,考虑有效保护率则接种率需要高达95%,才可以建立起群体免疫屏障;最后通过基本传染数验证了疫苗接种率,并对新冠波及影响做出了相应对策分析。

基于TE-SIS模型的突发事件网民情感博弈演化研究

社交网络的发展促进了对于突发事件网民的情感演化过程的研究,建立突发事件网民情感演化模型对于维持社会和谐稳定具有重要的意义。TE-SIS(two-dimensional emotional susceptible infectious susceptible)模型结合二维情感空间以及网民情感博弈进行演化分析。TE-SIS模型不仅考虑了网民对于突发事件持续关注的状态以及情绪反复感染的情况,同时突破传统传染病模型对于群体数量的限制,使网民个体间动态交互迭代出群体的情感演化方向,TE-SIS模型还能够仿真出真实突发事件发生后不同时期的情感演化情况。实验表明,提出的TE-SIS模型中情感输入率以及情感消解率极大影响对应情感状态的演化。同时根据模型中不同情感消解率所对应管控措施的强度来分析不同管控对于网民情感演化的影响。研究结果能够为分析突发事件网民情感演化机理提供新的思路和方法,对舆情的引导以及事件中网民情感调控具有重要意义。