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On optimal control at the onset of a new viral outbreak

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Infectious Disease modelling 2024年第4期9卷 995-1006页

作者： Alexandra Smirnova Xiaojing Ye Department of Mathematics&Statistics Georgia State UniversityAtlantaUSA

We propose a versatile model with a flexible choice of control for an early-pandemic outbreak prevention when vaccine/drug is not yet *** that stage,control is often limited to non-medical interventions like social distancing and other behavioral *** the SIR optimal control problem,we show that the running cost of control satisfying mild,practically justified conditions generates an optimal strategy,u(t),t∈[0,T],that is sustainable up until some moment τ∈[0,T).However,for any t∈[τ,T],the function u(t)will decline as t approaches T,which may cause the number of newly infected people to ***,the window from 0 to τ is the time for public health officials to prepare alternative mitigation measures,such as vaccines,testing,antiviral medications,and *** addition to theoretical study,we develop a fast and stable computational method for solving the proposed optimal control *** efficiency of the new method is illustrated with numerical examples of optimal control trajectories for various cost functions and *** results provide a comprehensive demonstration of the effects of control on the epidemic spread and mitigation expenses,which can serve as invaluable references for public health officials.

关键词： Epidemiology compartmental model Transmission dynamic Optimal control

Mathematical modeling with optimal control analysis of social media addiction

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Infectious Disease modelling 2021年第1期6卷 405-419页

作者： Haileyesus Tessema Alemneh Negesse Yizengaw Alemu Department of Mathematics College of Natural and Computational SciencesUniversity of GondarGondarEthiopia

In this paper,we developed a deterministic mathematical model of social media addiction(SMA)with an optimal control *** qualitative analysis like the social media addiction free equilibrium point(E_(0)),endemic equilibrium point(E^(*)),basic reproduction number eR0T,were *** the stability analysis,we found that the social media addiction free equilibrium point(SMAFEP)is locally asymptotically stable if R_(0)1 the unique endemic equilibruim is locally assymptotically *** using Center Manifold theorem,the model exhabits a forward bifurcation at R_(0)=*** sensitivity of model parameters is done using the normalized forward sensitivity index ***,we introduced two time dependent controls on the basic model and formulated an optimal control ***,we used the Pontryagin’s maximum principle to find the optimal system of the *** simulations,on the optimal control problem using the fourth-order Range-Kutta forward-backward sweep method,on the suggested strategies for SMA is *** found that to effectively control SMA at a specified period of time,stakeholders and policymakers must apply the integrated control strategies C.

关键词： Social media addiction compartmental model Stablity analysis Optimal control Numerical simulation

Bayesian modeling of dynamic behavioral change during an epidemic

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Infectious Disease modelling 2023年第4期8卷 947-963页

作者： Caitlin Ward Rob Deardon Alexandra M.Schmidt Division of Biostatistics University of MinnesotaMinneapolisMNUSA Faculty of Veterinary Medicine University of CalgaryCalgaryABCanada Department of Mathematics and Statistics University of CalgaryCalgaryABCanada Department of Epidemiology Biostatisticsand Occupational HealthMontrealQCCanada

For many infectious disease outbreaks,the at-risk population changes their behavior in response to the outbreak severity,causing the transmission dynamics to change in *** change is often ignored in epidemic modeling efforts,making these models less useful than they could *** address this by introducing a novel class of datadriven epidemic models which characterize and accurately estimate behavioral *** proposed model allows time-varying transmission to be captured by the level of“alarm”in the population,with alarm specified as a function of the past epidemic *** investigate the estimability of the population alarm across a wide range of scenarios,applying both parametric functions and non-parametric functions using splines and Gaussian *** model is set in the data-augmented Bayesian framework to allow estimation on partially observed epidemic *** benefit and utility of the proposed approach is illustrated through applications to data from real epidemics.

关键词： Bayesian inference compartmental model SIR SEIR Transmission modeling

Reconstruction of incidence reporting rate for SARS-CoV-2 Delta variant of COVID-19 pandemic in the US

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Infectious Disease modelling 2024年第1期9卷 70-83页

作者： Alexandra Smirnova Mona Baroonian Department of Mathematics&Statistics Georgia State UniversityAtlantaUSA

In recent years,advanced regularization techniques have emerged as a powerful tool aimed at stable estimation of infectious disease parameters that are crucial for future projections,prevention,and *** other system parameters,i.e.,incubation and recovery rates,the case reporting rate,Ψ,and the time-dependent effective reproduction number,R_(e)t,are directly influenced by a large number of factors making it impossible to pre-estimate these parameters in any meaningful *** this study,we propose a novel iteratively-regularized trust-region optimization algorithm,combined with SuSvIuIvRD compartmental model,for stable reconstruction ofΨand R_(e)t from reported epidemic data on vaccination percentages,incidence cases,and daily *** innovative regularization procedure exploits(and takes full advantage of)a unique structure of the Jacobian and Hessian approximation for the nonlinear observation *** proposed inversion method is thoroughly tested with synthetic and real SARS-CoV-2 Delta variant data for different regions in the United States of America from July 9,2021,to November 25,*** study shows that case reporting rate during the Delta wave of COVID-19 pandemic in the US is between 12%and 37%,with most states being in the range from 15%to 25%.This confirms earlier accounts on considerable under-reporting of COVID-19 cases due to the impact of”silent spreaders”and the limitations of testing.

关键词： Epidemiology Incidence reporting rate compartmental model Transmission dynamic Regularization algorithm

modelling the COVID-19 epidemic and the vaccination campaign in Italy by the SUIHTER model

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Infectious Disease modelling 2022年第2期7卷 45-63页

作者： Nicola Parolini Luca Dede' Giovanni Ardenghi Alfio Quarteroni MOX Department of MathematicsPolitecnico di MilanoItaly Institute of Mathematics Ecole Polytechnique Federale de Lausanne(EPFL)Switzerland

Several epidemiological models have been proposed to study the evolution of COVID-19 *** this paper,we propose an extension of the SUIHTER model,to analyse the COVID-19 spreading in Italy,which accounts for the vaccination campaign and the presence of new variants when they become *** particular,the specific features of the variants(*** increased transmission rate)and vaccines(*** efficacy to prevent transmission,hospitalization and death)are modeled,based on clinical *** new model is validated comparing its near-future forecast capabilities with other epidemiological models and exploring different scenario analyses.

关键词： compartmental model COVID-19 Vaccination Virus variants Forecast Scenario analyses

COVID-19 epidemic prediction and the impact of public health interventions: A review of COVID-19 epidemic models

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Infectious Disease modelling 2021年第1期6卷 324-342页

作者： Yue Xiang Yonghong Jia Linlin Chen Lei Guo Bizhen Shu Enshen Long MOE Key Laboratory of Deep Earth Science and Engineering Institute of Disaster Management and ReconstructionSichuan UniversityChengduChina Chongqing Safety Engineering Institute Chongqing University of Science and TechnologyChongqingChina College of Architecture and Environment Sichuan UniversityChengduChina Key Laboratory of Birth Defects and Related Diseases of Women and Children West China Second Hospital of Sichuan UniversityChengduChina

The coronavirus disease outbreak of 2019(COVID-19)has been spreading rapidly to all corners of the word,in a very complex manner.A key research focus is in predicting the development trend of COVID-19 scientifically through mathematical *** conducted a systematic review of epidemic prediction models of COVID-19 and the public health intervention strategies by searching the Web of Science database.55 studies of the COVID-19 epidemic model were reviewed *** was found that the COVID-19 epidemic models were different in the model type,acquisition method,hypothesis and distribution of key input *** studies used the gamma distribution to describe the key time period of COVID-19 infection,and some studies used the lognormal distribution,the Erlang distribution,and theWeibull *** setting ranges of the incubation period,serial interval,infectious period and generation time were 4.9-7 days,4.41-8.4 days,2.3-10 days and 4.4-7.5 days,respectively,and more than half of the incubation periods were set to 5.1 or 5.2 *** models assumed that the latent period was consistent with the incubation *** models assumed that asymptomatic infections were infectious or pre-symptomatic transmission was possible,which overestimated the value of *** the prediction differences under different public health strategies,the most significant effect was in travel *** were different studies on the impact of contact tracking and social isolation,but it was considered that improving the quarantine rate and reporting rate,and the use of protective face mask were essential for epidemic prevention and *** input epidemiological parameters of the prediction models had significant differences in the prediction of the severity of the epidemic ***,prevention and control institutions should be cautious when formulating public health strategies by based on the prediction results of mathematical models.

关键词： COVID-19 Epidemic model Public health intervention compartmental model Reproduction number

SARS-COV-2 outbreak and control in Kenya - Mathematical model analysis

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Infectious Disease modelling 2021年第1期6卷 370-380页

作者： Rachel Waema Mbogo Titus Okello Orwa Institute of Mathematical Sciences Strathmore UniversityBox ***NairobiKenya

The coronavirus disease 2019(COVID-19)pandemic reached Kenya in March 2020 with the initial cases reported in the capital city Nairobi and in the coastal area *** reported by the World Health Organization,the outbreak of COVID-19 has spread across the world,killed many,collapsed economies and changed the way people live since it was first reported inWuhan,China,in the end of *** at the end of December 2020,it had led to over 2.8 million confirmed cases in Africa with over 67 thousand *** trend poses a huge threat to global public *** the early transmission dynamics of the infection and evaluating the effectiveness of control measures is crucial for assessing the potential for sustained transmission to occur in new *** employed a SEIHCRD mathematical transmission model with reported Kenyan data on cases of COVID-19 to estimate how transmission varies over *** model is concise in structure,and successfully captures the course of the COVID-19 outbreak,and thus sheds light on understanding the trends of the *** next generation matrix approach was adopted to calculate the basic reproduction number(R_(0))from the model to assess the factors driving the *** model illustrates the effect of mass testing on COVID-19 as well as individual self initiated behavioral *** results have significant impact on the management of COVID-19 and implementation of prevention *** results from the model analysis shows that aggressive and effective mass testing as well as individual self initiated behaviour change play a big role in getting rid of the COVID-19 epidemic otherwise the rate of infection will continue to increase despite the increased rate of recovery.

关键词： COVID-19 SEIHCRD-model Social distancing Mass testing compartmental model Basic reproduction number Simulations

A metapopulation network model for the spreading of SARSCoV-2: Case study for Ireland

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Infectious Disease modelling 2021年第1期6卷 420-437页

作者： Rory Humphries Mary Spillane Kieran Mulchrone Sebastian Wieczorek Micheal O’Riordain Philipp Hövel School of Mathematical Sciences University College CorkWestern RoadCorkT12XF64Ireland Department of Surgery Mercy University HospitalGrenville PlaceCorkT12WE28Ireland

We present preliminary results on an all-Ireland network modelling approach to simulate the spreading the Severe Acute Respiratory Syndrome CoronaVirus 2(SARS-CoV-2),commonly known as the *** the model,nodes correspond to locations or communities that are connected by links indicating travel and commuting between different *** this proposed modelling framework can be applied on all levels of spatial granularity and different countries,we consider Ireland as a case *** network comprises 3440 electoral divisions(EDs)of the Republic of Ireland and 890 superoutput areas(SOAs)for Northern Ireland,which corresponds to local administrative units below the NUTS 3 *** local dynamics within each node follows a phenomenological SIRX compartmental model including classes of Susceptibles,Infected,Recovered and Quarantined(X)inspired from Science 368,742(2020).For better comparison to empirical data,we extended that model by a class of *** consider various scenarios including the 5-phase roadmap for *** addition,as proof of concept,we investigate the effect of dynamic interventions that aim to keep the number of infected below a given *** is achieved by dynamically adjusting containment measures on a national scale,which could also be implemented at a regional(county)or local(ED/SOA)*** find that-in principle-dynamic interventions are capable to limit the impact of future waves of outbreaks,but on the downside,in the absence of a vaccine,such a strategy can last several years until herd immunity is reached.

关键词： compartmental model SARS-CoV-2 Coronavirus Non-pharmaceutical containment strategies Network model

Transmissibility of tuberculosis among students and non-students:an occupational-specific mathematical modelling

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Infectious Diseases of Poverty 2022年第6期11卷 5-26页

作者： Qiuping Chen Shanshan Yu Jia Rui Yichao Guo Shiting Yang Guzainuer Abudurusuli Zimei Yang Chan Liu Li Luo Mingzhai Wang Zhao Lei Qinglong Zhao Laurent Gavotte Yan Niu Roger Frutos Tianmu Chen State Key Laboratory of Molecular Vaccinology and Molecular Diagnostics School of Public HealthXiamen UniversityXiamenFujianPeople’s Republic of China CIRAD URM 17IntertrypMontpellierFrance Universitéde Montpellier MontpellierFrance Xiamen Center for Disease Control and Prevention XiamenFujianPeople’s Republic of China Jilin Provincial Center for Disease Control and Prevention ChangchunJilinPeople’s Republic of China Espace-Dev Universitéde MontpellierMontpellierFrance Chinese Center for Disease Control and Prevention 155 Changbai RoadChangping DistrictBeijingChina

Background: Recently, despite the steady decline in the tuberculosis (TB) epidemic globally, school TB outbreaks have been frequently reported in China. This study aimed to quantify the transmissibility ofMycobacterium tuberculosis (MTB) among students and non-students using a mathematical model to determine characteristics of TB ***: We constructed a dataset of reported TB cases from four regions (Jilin Province, Xiamen City, Chuxiong Prefecture, and Wuhan City) in China from 2005 to 2019. We classified the population and the reported cases under student and non-student groups, and developed two mathematical models [nonseasonal model (model A) and seasonal model (model B)] based on the natural history and transmission features of TB. The effective reproduction number (R(eff)) of TB between groups were calculated using the collected ***: During the study period, data on 456,423 TB cases were collected from four regions: students accounted for 6.1% of cases. The goodness-of-fit analysis showed that model A had a better fitting effect (P model A was 1.68 [interquartile range (IQR): 1.20–1.96] in Chuxiong Prefecture, 1.67 (IQR: 1.40–1.93) in Xiamen City, 1.75 (IQR: 1.37–2.02) in Jilin Province, and 1.79 (IQR: 1.56–2.02) in Wuhan City. The average R_(eff) of TB in the non-student population was 23.30 times (1.65/0.07) higher than that in the student ***: The transmissibility of MTB remains high in the non-student population of the areas studied, which is still dominant in the spread of TB. TB transmissibility from the non-student-to-student-population had a strong influence on students. Specific interventions, such as TB screening, should be applied rigorously to control and to prevent TB transmission among students.

关键词： Tuberculosis Transmission compartmental model Occupational-specific dynamics Student Nonstudent China