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Mathematical modelling on diffusion and control of COVIDe19

Infectious Disease modelling 2020年第1期5卷 588-597页

作者： M.Veera Krishna Department of Mathematics Rayalaseema UniversityKurnoolAndhra Pradesh518007India

In this paper,we develop a mathematical model for the spread and control of the coronavirus disease.An outbreak of COVID-19 has led to more than one million confirmed cases as of April 3rd,2020.Understanding the early spread dynamics of the infection and evaluating the effectiveness of control measures is crucial for assessing the potential for sustained transmission to occur in new areas.Combining a mathematical model of severe COVID-19 spread with four datasets from within and outside of Wuhan,China;it is estimated how spread in Wuhan varied between January and February 2020.It is used these estimates to assess the potential for sustained human-to-human spread to occur in locations outside Wuhan if disease holders were introduced.It is combined SEIR framework model with data on cases of COVID-19 in China and International cases that originated in Wuhan to estimate how spread had varied over time during January and February 2020.Based on these estimates,it is calculated the probability that freshly introduced cases might produce outbreaks in other regions.Also,it is calculated approximately the median day by day basic reproduction number in Wuhan,refused from 2$45(95%CI:1.16-4.87)one week before travel restrictions were introduced on Jan 23rd,2020,to 1.05(0.42-2.40)one week after.Based on our estimates of,presumptuous SARS approximating disparity,it is computed that in locations with a similar spread potential to Wuhan in near the beginning of January,some time ago there are at least four independently set up cases,there is a more than fifty percent chance the infection will found within those inhabitants.COVID-19 spreading probably refused in Wuhan during delayed January 2020,corresponding with the prologue of voyage control channels.As more cases arrive in international locations with similar spread potential to Wuhan,before these organize measures,it is likely many chains of spread will fail to create initially but might lead to innovative outbreaks ultimately.

关键词： COVID-19 Coronavirus Mathematical modelling Diffusion Reproduction number

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The influence of tumour vasculature on fluid flow in solid tumours:a Mathematical modelling study

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Biophysics Reports 2021年第1期7卷 35-54页

作者： Moath Alamer Xiao Yun Xu Department of Chemical Engineering Imperial College London South Kensington Campus

Tumour vasculature is known to be aberrant, tortuous and erratic which can have significant implications for fluid flow. Fluid dynamics in tumour tissue plays an important part in tumour growth, metastasis and the delivery of therapeutics. mathematical models are increasingly employed to elucidate the complex interplay between various aspects of the tumour vasculature and fluid flow. Previous models usually assume a uniformly distributed vasculature without explicitly describing its architecture or incorporate the distribution of vasculature without accounting for real geometric features of the network. In this study, an integrated computational model is developed by resolving fluid flow at the single capillary level across the whole tumour vascular network. It consists of an angiogenesis model and a fluid flow model which resolves flow as a function of the explicit vasculature by coupling intravascular flow and interstitial flow in tumour tissue. The integrated model has been used to examine the influence of microvascular distribution, necrosis and vessel pruning on fluid flow, as well as the effect of heterogeneous vessel permeability. Our results reveal the level of nonuniformity in tumour interstitial fluid pressure(IFP), with large variations in IFP profile between necrotic and non-necrotic tumours. Changes in microscopic features of the vascular network can significantly influence fluid flow in the tumour where removal of vessel blind ends has been found to reduce IFP and promote interstitial fluid flow. Our results demonstrate the importance of incorporating microscopic properties of the tumour vasculature and intravascular flow when predicting fluid flow in tumour tissue.

关键词： Fluid flow Vasculature Tumour Mathematical modelling

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Mathematical modelling for Zoonotic Visceral Leishmaniasis dynamics:A new analysis considering updated parameters and notified human Brazilian data

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Infectious Disease modelling 2017年第2期2卷 143-160页

作者： Helio Junji Shimozako Jianhong Wu Eduardo Massad Faculty of Medicine University of S~ao Paulo and LIM 01-HCFMUSPAvenida Dr.Arnaldo 45501246-903Sao PauloSPBrazil Centre for Disease modelling York Institute for Health ResearchYork University4700Keele StreetTorontoONM3J 1P3Canada London School of Hygiene and Tropical Medicine University of LondonUK

Brazil is one of the highest endemic countries for Zoonotic Visceral Leishmaniasis:according to the Brazilian Ministry of Health,the annual number of new human cases and deaths due to this disease has been increasing for the last 20 years.In addition,regarding the Americas,the specific relationship between canine and human for Visceral Leishmaniasis dynamics is still not well understood.In this work we propose a new model for Zoonotic Visceral Leishmaniasis,based on the models previously published by Burattini et al.(1998)and Ribas et al.(2013).Herein,we modeled the disease dynamics using a modified set of differential equations from those two authors,considering the same assumptions(inclusion of human,dog and sandfly populations,all constants over time).From this set of equations we were able to calculate the basic reproduction number R 0 and to analyze the stability and sensitivity of the system to the parameters variability.As main result,when the stability of the system is reached,the normalized reporting human cases rate is estimated in 9.12E-08/day.This estimation is very close to the 2015 report from Araçatuba city,5.69E-08/day.We also observed from stability and sensitivity analysis that the activity of sandfly population is critical to introduction and maintenance of Zoonotic Visceral Leishmaniasis in the population.In addition,the importance of dog as source of infection concentrates on latent dog,since it does not show clinical symptoms and signs and,therefore,has a great contribution to disease dissemination.As conclusion,considering the presently ethical issues regarding to elimination of positive dog in Brazil and the highly sensitivity of disease dynamics on sandfly population,we recommend that the sandfly population control should be prioritized.

关键词： Zoonotic Visceral Leishmaniasis Disease dynamics Mathematical modelling Epidemiology

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mathematical and Numerical modelling of Copper Tube Extrusion after Optimizing Geometrical and Operating Parameters

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Journal of Minerals and Materials Characterization and Engineering 2022年第2期10卷 127-138页

作者： Ngoy Moïse Raphaël Moramess Mulaja Tshakatumba Constantin Tshipeshi Makina Héritier Ntambwe Sapu Aaron Tubadi Diamba José Mwema Mutamba Edouard Metallography and Materials Laboratory Department of Metallurgy and Materials Science Polytechnic Faculty of the University of Lubumbashi Lubumbashi Democratic Republic of Congo 2Electrical Engineering Laboratory Department of Electromechanics Polytechnic Faculty of the University of Lubumbashi Lubumbashi Democratic Republic of Congo Department of Civil Engineering Faculty of Industrial Engineer University of Likasi Likasi Democratic Republic of Congo

This study aimed to optimize cross-sectional area of the extruder and the flow rate of the material through the extruder. Extrusion process was first modelized using the continuum mechanics method before being simulated with the commercial software LS-DYNA using the Johnson-Cook model based on the finite element method after optimization of the factors with simplex algorithm. The study was carried out on a connecting rod: diameter of 145 mm, cross-section of 1.65 m2, length of 0.25 m, volume of 0.41 m3 and a mass of 37 kg. Optimum parameters obtained were temperature of 850℃, flow rate of 0.237 m/s, die diameter of 19.2 mm, pin diameter of 14 mm, extrusion strength of 565.6 kN and press pressure of 245 GPa. From these factors, a blank was obtained with external and internal diameters of 19.2 and 14 mm respectively over a length of 28 m with a thickness of 2.6 mm. Simulation using LS-DYNA software resulted in a difference in values of 7.4% between optimization and simulation when the difference of 2.4% was found between modelling and simulation. These values make the process optimal for industrial application to improve the extrusion requirements of copper tubes.

关键词： Copper Extrusion Mathematical modelling Numerical Simulation Simplex Algorithm LS-DYNA Software

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Mathematical modelling of gain-switched RF-excited CO2 waveguide laser

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Chinese Physics B 2004年第4期13卷 501-504页

作者：巴德田兆硕王骐 NationalKeyLaboratoryofTunableLaserTechnology HarbinInstituteofTechnologyHarbin150001China

The detailed mathematical models for the evolution of light pulses in RF-excited CO2 waveguide lasers are derived. Explicit expressions for the pulse characteristics in RF-excited CO2 waveguide lasers are obtained. Th... 详细信息

关键词： Mathematical modelling gain-switched RF excited CO2 waveguide lasers

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The calculation and optimal allocation of transmission capacity in natural gas networks with MINLP models

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中国化学工程学报:英文版 2023年第7期59卷 251-261页

作者： Yaran Bu Changchun Wu Lili Zuo Qian Chen National Engineering Laboratory for Pipeline Safety/Beijing Key Laboratory of Urban Oil and Gas Distribution Technology China University of Petroleum-BeijingBeijing 102249China

The transmission capacity of gas pipeline networks should be calculated and allocated to deal with the capacity booking with shippers. Technical capacities, which depend on the gas flow distribution at routes or interchange points, are calculated with a multiobjective optimization model and form a Pareto solution set in the entry/exit or point-to-point regime. Then, the commercial capacities, which can be directly applied in capacity booking, are calculated with single-objective optimization models that are transformed from the above multiobjective model based on three allocation rules and the demand of shippers.Next, peak-shaving capacities, which are daily oversupply or overdelivery amounts at inlets or deliveries,are calculated with two-stage transient optimization models. Considering the hydraulic process of a pipeline network and operating schemes of compressor stations, all the above models are mixed-integer nonlinear programming problems. Finally, a case study is made to demonstrate the ability of the models.

关键词： Mathematical modelling Natural gas Optimization Gas transmission capacity Gas network

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On determining the weight of edges in map-representing graphs-applications of heuristic methods in planning escape routes

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Journal of Traffic and Transportation Engineering(English Edition) 2022年第6期9卷 1027-1043页

作者： Marta Borowska-Stefańska MichałKowalski Filip Turoboś Szymon Wiśniewski Institute of the Built Environment and Spatial Policy Faculty of Geographical SciencesUniversity of LodzŁódź90–137Poland Institute of Mathematics Lodz University of TechnologyŁódź90–924Poland

In the paper we discuss and compare two commonly used methods of finding the shortest paths in networks,namely Dijkstra’s and A*algorithms.We compare their effectiveness in terms of traversing road network in circumstances that require swift decision making in the event of dynamically changing road conditions on the basis of studies conducted for evacuation plans.To build a proper model of such a network,a method of appropriate edge-weighting is introduced,based on empirical data collected by other researchers.Then,we use the basics of the theory of quasimetric spaces to introduce a heuristic to such graphs,which is easy to calculate metric.The heuristic we obtain is both admissible and consistent,which allows us to use it efficiently in A*search algorithms.The developed application can be used in studies into evacuation from hazardous areas.In this case,optimum calculative efficiency is achievable with a simultaneous reduction of calculation time(when compared to Dijkstra’s algorithm).Our application can be applied during the first stage,i.e.,prior to the occurrence of a disaster,since this is an appropriate time for preparation by planning,drilling,early warning,and designating the rescue services that are to participate in the following stages.

关键词： A*algorithm Dijkstra Heuristic methods Mathematical modelling Quasimetric spaces Planning escape routes

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Mathematical modelling OF FLOW PHENOMENA IN METAL BATH COVERED WITH MOLTEN SLAG

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Acta Metallurgica Sinica(English Letters) 1990年第12期3卷 370-376页

作者： QU Ying YANG Jian XU Baomei University of Science and Technology Beijing,Beijing,China

By use of the two-component LDA and high speed camera,the water model of the flow field in metal bath under molten slag layer has been tested.On the basis of experimental results,the flow boundary conditions of liquid metal at the slag-metal interface of a gas injecting bath were deduced.The flow field and the turbulent parameters of the metal bath covered with slag were solved by the vorticity-stream function method.The results reveal that the flow velocity, turbulent energy and circulating rate of the melt under slag are lower than that of without slagcover.Another one “dead zone” of the lowest turbulent energy is formed in the top layer under cover of slag near the ladle linning.

关键词： flow field metal bath injection metallurgy Mathematical modelling

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Leveraging mathematical models of disease dynamics and machine learning to improve development of novel malaria interventions

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Infectious Diseases of Poverty 2022年第3期11卷 37-53页

作者： Monica Golumbeanu Guo-Jing Yang Flavia Camponovo Erin M.Stuckey Nicholas Hamon Mathias Mondy Sarah Rees Nakul Chitnis Ewan Cameron Melissa A.Penny Swiss Tropical and Public Health Institute AllschwilSwitzerland Key Laboratory of Tropical Translational Medicine of Ministry of Education and School of Tropical Medicine and Laboratory Medicine The First and Second Affiliated Hospital of Hainan Medical UniversityHainan Medical UniversityHaikouHainanPeople’s Republic of China University of Basel BaselSwitzerland Center for Communicable Disease Dynamics Department of EpidemiologyHarvard T.H.Chan School of Public HealthBostonMA02115USA The Bill&Melinda Gates Foundation SeattleWAUSA Innovative Vector Control Consortium LiverpoolUK Malaria Atlas Project Big Data InstituteUniversity of OxfordOxfordUK Curtin University PerthAustralia Telethon Kids Institute Perth Children’s HospitalPerthAustralia

Background:Substantial research is underway to develop next-generation interventions that address current malaria control challenges.As there is limited testing in their early development,it is difficult to predefine intervention properties such as efficacy that achieve target health goals,and therefore challenging to prioritize selection of novel candidate interventions.Here,we present a quantitative approach to guide intervention development using mathematical models of malaria dynamics coupled with machine learning.Our analysis identifies requirements of efficacy,coverage,and duration of effect for five novel malaria interventions to achieve targeted reductions in malaria prevalence.Methods:A mathematical model of malaria transmission dynamics is used to simulate deployment and predict potential impact of new malaria interventions by considering operational,health-system,population,and disease characteristics.Our method relies on consultation with product development stakeholders to define the putative space of novel intervention specifications.We couple the disease model with machine learning to search this multi-dimensional space and efficiently identify optimal intervention properties that achieve specified health goals.Results:We apply our approach to five malaria interventions under development.Aiming for malaria prevalence reduction,we identify and quantify key determinants of intervention impact along with their minimal properties required to achieve the desired health goals.While coverage is generally identified as the largest driver of impact,higher efficacy,longer protection duration or multiple deployments per year are needed to increase prevalence reduction.We show that interventions on multiple parasite or vector targets,as well as combinations the new interventions with drug treatment,lead to significant burden reductions and lower efficacy or duration requirements.Conclusions:Our approach uses disease dynamic models and machine learning to support decision-making and resource investment,facilita

关键词： Infectious diseases Malaria Novel interventions Mathematical modelling Machine learning

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Seroprevalence and infection attack rate of COVID-19 in Indian cities

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Infectious Disease modelling 2022年第2期7卷 25-32页

作者： Yiming Fei Hainan Xu Xingyue Zhang Salihu S.Musa Shi Zhao Daihai He Department of Math and Stats The Hang Seng UniversityHong KongChina Department of Math and Stats McMaster UniversityCanada Department of Applied Mathematics The Hong Kong Polytechnic UniversityHong KongChina Department of Mathematics Kano University of Science and TechnologyWudilNigeria JC School of Public Health and Primary Care Chinese University of Hong KongHong KongChina CUHK Shenzhen Research Institute ShenzhenChina

Objectives:Serological surveys were used to infer the infection attack rate in different populations.The sensitivity of the testing assay,Abbott,drops fast over time since infection which makes the serological data difficult to interpret.In this work,we aim to solve this issue.Methods:We collect longitudinal serological data of Abbott to construct a sensitive decay function.We use the reported COVID-19 deaths to infer the infections,and use the decay function to simulate the seroprevalence and match to the reported seroprevalence in 12 Indian cities.Results:Our model simulated seroprevalence matchs the reported seroprevalence in most of the 12 Indian cities.We obtain reasonable infection attack rate and infection fatality rate for most of the 12 Indian cities.Conclusions:Using both reported COVID-19 deaths data and serological survey data,we infer the infection attack rate and infection fatality rate with increased confidence.

关键词： COVID-19 Pandemic Seroprevalence Attack rate Mathematical modelling

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