Analysis of Infectious Disease Problems (Covid-19) and Their Global Impact PDF
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Infosys Science Foundation Series in Mathematical Sciences Praveen Agarwal Juan J. Nieto Michael Ruzhansky Delfim F. M. Torres Editors Analysis of Infectious Disease Problems (Covid-19) and Their Global Impact Infosys Science Foundation Series Infosys Science Foundation Series in Mathematical Sciences SeriesEditors GopalPrasad,UniversityofMichigan,AnnArbor,USA IreneFonseca,CarnegieMellonUniversity,Pittsburgh,PA,USA EditorialBoard ChandrashekharKhare,UniversityofCalifornia,LosAngeles,USA MahanMj,TataInstituteofFundamentalResearch,Mumbai,India ManindraAgrawal,IndianInstituteofTechnologyKanpur,Kanpur,India RitabrataMunshi,TataInstituteofFundamentalResearch,Mumbai,India S.R.S.Varadhan,NewYorkUniversity,NewYork,USA WeinanE,PrincetonUniversity,Princeton,USA TheInfosysScienceFoundationSeriesinMathematicalSciences,aScopus-indexed book series, is a sub-series of the Infosys Science Foundation Series. This sub- seriesfocusesonhigh-qualitycontentinthedomainofmathematicalsciencesand various disciplines of mathematics, statistics, bio-mathematics, financial mathe- matics, applied mathematics, operations research, applied statistics and computer science. With this series, Springer and the Infosys Science Foundation hope to provide readers with monographs, handbooks, professional books and textbooks ofthehighestacademicqualityoncurrenttopicsinrelevantdisciplines.Literature inthissub-serieswillappealtoawideaudienceofresearchers,students,educators, andprofessionalsacrossmathematics,appliedmathematics,statisticsandcomputer sciencedisciplines. Moreinformationaboutthissubseriesathttp://www.springer.com/series/13817 · · Praveen Agarwal Juan J. Nieto · Michael Ruzhansky Delfim F. M. Torres Editors Analysis of Infectious Disease Problems (Covid-19) and Their Global Impact Editors PraveenAgarwal JuanJ.Nieto AnandInternationalCollegeofEngineering InstituteofMathematics Jaipur,Rajasthan,India UniversityofSantiagodeCompostela Santiago,Spain MichaelRuzhansky DepartmentofMathematics:Analysis, DelfimF.M.Torres LogicandDiscreteMathematics DepartmentofMathematics GhentUniversity UniversityofAveiro Ghent,Belgium Aveiro,Portugal MathematicalSciences QueenMaryUniversityofLondon London,UK ISSN2363-6149 ISSN2363-6157 (electronic) InfosysScienceFoundationSeries ISSN2364-4036 ISSN2364-4044 (electronic) InfosysScienceFoundationSeriesinMathematicalSciences ISBN978-981-16-2449-0 ISBN978-981-16-2450-6 (eBook) https://doi.org/10.1007/978-981-16-2450-6 MathematicsSubjectClassification(2010):26A33,42A38,42B10,46F12,65R10,65F35,65J05,26A18 ©TheEditor(s)(ifapplicable)andTheAuthor(s),underexclusivelicensetoSpringerNature SingaporePteLtd.2021 Thisworkissubjecttocopyright.AllrightsaresolelyandexclusivelylicensedbythePublisher,whether thewholeorpartofthematerialisconcerned,specificallytherightsoftranslation,reprinting,reuse ofillustrations,recitation,broadcasting,reproductiononmicrofilmsorinanyotherphysicalway,and transmissionorinformationstorageandretrieval,electronicadaptation,computersoftware,orbysimilar ordissimilarmethodologynowknownorhereafterdeveloped. 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The registered company address is: 152 Beach Road, #21-01/04 Gateway East, Singapore 189721, Singapore Preface Anyconditionwhichinterfereswiththenormalfunctioningofthebodyandwhich causes discomfortordisabilityorimpairmentofthehealthofalivingorganism is calledadisease.Thediseaseagent isafactor(substanceorforce)whichcausesa diseasebyitsexcessordeficiencyorabsence.Theimpactofseverediseasesonpeople isarealconcernintermsofsufferingaswellassocialandeconomicimplications. Inrecentera,thereareseveralcommunicablediseases,namelyCovid-19,malaria, dengue fever, HIV/AIDS, tuberculosis, cholera, Zika virus,chickenpox, influenza, pneumonia, and so on, which impair the health of the human population around the globe. Some of these communicable diseases carry from person to person by viral diseases and their pathogens, which impact the human body through sexual intercourse. Inrecentyears,thecontroloftheseacutediseaseshasbeenagreatconcernfor bio-mathematiciansandmedicalexperts.Ithasbeenapprovedthattheseinfectious diseasesarefataltobillionsofpeopleandalsocausethelossoftheirworth.Mathe- maticalmodelingplaysacrucialroleinthestudyoftheseadversetypesofdiseases. The basic ambition to evaluate and eradicate these diseases through mathematical modelsistominimizetheireffectsbyunderstandingtheirmechanismandtheagents that cause the spread of these diseases, so that it gives a better chance to predict thesediseasesandtheirimpactsandalsogiveawaytocontrolthem.Mathematical modelsallowustoextrapolatefromcurrentinformationaboutthestateandprogress ofanoutbreaktopredictthefutureand,mostimportantly,toquantifytheuncertainty inthesepredictions.Mostofthesemathematicalmodelscontainordinaryorpartial differential equations. In some cases, instead of integer order, fractional order can beusedtoanalyzetherealphenomenabehindtheproblems.Inonewayoranother, researchers encounter different kinds of nonlinear ordinary or partial differential equations. Theaimofthiseditedvolumeistocollectoriginalresearcharticlesthatfocuson recentresults,whichcanbeobtainedfromthenovelmethodsconstructedbymany researchers, for all types of infection diseases, as well as developments in recent methodswithnewoperatorsornewapproximations.Itisalsoinvolvingthereview articlesdiscussingthecurrentstateoftheart. v vi Preface In this book, we are happy to have 30 chapters in two parts. Part I is based on“general analysis,”and PartIIcontains papers on“country-specific analysison Covid-19.”Allchaptersarecontributedfromeminentresearchersaroundtheglobe who are internationally known experts in their fields. Throughout this book, the analysis of infectious disease problems (Covid-19) and their global impact have been explained very carefully in the simplest possible terms and illustrated by a number of complete workout examples. This book contains some useful theorems andtheirproofs. Thebookisorganizedasfollows. In Part I, chapter “Continued and Serious Lockdown Could Have Minimized Many Newly Transmitted Cases of Covid-19 in the U.S.: Wavelets, Deterministic Models,andData”discussesmodel-basedestimatesofCovid-19intheUSAduring April–June2020.Model-basedpredictionsofCovid-19forthelowandhighrange oftransmissionratesandwithvaryingdegreesofpreventivemeasuresincludingthe lockdownshavebeenprovided.Itisshownhow10casesthatdonotadheretoproper careanddonotcomplywiththelockdownonApril30,2020,result,attheendof May and at the end of June, in 50,000 and 55,000 new cases, respectively. These valuesforthemonthsofMayandJunewouldbe251,000and511,000,respectively, in the case of a worse adherence rate of 50 infected (but unidentified) individuals. Continuedandseriouslockdownmeasuresbringtheaveragedailyrateofnewcases tolowerfigures,witharangeof4,300perdayto8,000perdayinMay. In chapter “Dynamical Analysis of a Caputo Fractional Order SIR Epidemic ModelwithaGeneralTreatmentFunction,”afractional-orderSIRepidemicmodel isproposed.Wefirstprovetheexistence,uniqueness,non-negativity,andbounded- nessofsolutionstotheconsideredmodel.Wealsostudytheexistenceofequilibrium points.Somesufficientconditionsarederivedtoensure,intermsofthebasicrepro- ductionnumber,theglobalasymptoticstabilityofthedisease-freeequilibriumpoint andendemicequilibriumpoint.Finally,numericalsimulationsareillustratedtoverify thevalidityofourtheoreticalresults. Inchapter“ProtectiveFaceShieldEffectiveness:MathematicalModelling,”a3D mathematicalmodeloftheairflowdistributionnearthecylindricalsurfaceofaface shield was explored. The model is based on a numerical solution of the Navier– Stokesgasdynamicsequations.Thesimulationresultsarecomparedwithfull-scale experiments. A probability model is also considered. Quantitative conclusions are madeabouttheeffectivenessoftheprotectivefaceshields. Chapter“OntheEvolutionEquationforModellingtheCovid-19Pandemic”intro- ducesanddiscussestheevolutionequationand,basedexclusivelyonthisequation, considersrandomwalkmodelsforthetimeseriesavailableonthedailyconfirmed Covid-19casesfordifferentcountries.Itisshownthataconventionalrandomwalk model is not consistent with the current global pandemic time series data, which exhibits non-ergodic properties. We therefore consider a self-affine random walk field model which provides the non-ergodic fields that are evident in the available data.Thisisbasedonusingaspectralscalingrelationshipofthetype1/ωα,whereωis theangularfrequencyandα∈(0,1)conformstoazero-meanGaussiandistribution. Itisthenshownthatαisaprimaryparameterforevaluatingtheglobalstatusofthe Preface vii pandemicinthesensethatthepandemicwillbecomeextinguishedasα→0forall countries.Forthisreason,and,basedonthedatacurrentlyavailable,astudyismade ofthevariationsfor100randomlyselectedcountries.Finally,inthecontextofthe bio-dynamichypothesis,aparametricmodelisconsideredforsimulatingthethree- dimensionalstructureofaspikeproteinwhichmaybeofvalueinthedevelopment ofavaccine. Chapter“ModellingtheDynamicsofFakeNewsSpreadingTransmissionDuring Covid-19ThroughSocialMedia”discussesthetransmissionoffakenewstounder- standtherateofspreading.Therefore,theobjectiveofthispaperistoproposeamath- ematicalmodelthatcandescribethedynamicsofthespreadoffakenewsthrough social media along the period of MCO through different social media platforms. Thisstudyalsosuggestssomemeasuresthatcanbetakenbydifferentparties,such asindividuals,society,andgovernmenttosolvetheissueoffakenewstransmission. Inchapter“GeneralizedLogisticEquationsinCovid-RelatedEpidemicModels,” we discuss how to develop a simple computable model for infection propagation, based on vicinity and interaction time conditions, between healthy and infectious persons.Thissimpleandrobustmodelcanbeadaptedforrealisticsimulations.The threeusecasesstudiedindetailareasfollows: (1) Anelderlycarehome,wherecontaminationatjointmealsisconsidered, (2) A household in lockdown, stay at home, with contamination at joint meals considered,and (3) A large venue event with lots of interaction between participants and crowd effects. Each use case is presented in its phenomenology, with some illustrative refer- ences, facts, and data, of interest for practical simulation and model adaptation, scenarios, and corresponding interpretations. Then, the agent-based model condi- tionaltovicinityandinteractiontimebetweenhealthyandinfectedpersonswithin thisusecaseisestablished,withitshypotheses.Anactivestochasticcontagionprop- agationmodelisdeveloped,derivingtheprobabilityofinfectionfromthepresence ofinfectiouspersonsinthevicinityofahealthyperson,duringaninteractiontime. Numericalexamplesarediscussed.Boundsandlimitsareestablishedinsomespecific casesofinterest. Chapter “A Transition of Shared Mobility in Metro Cities—A Challenge Post-LockdownCovid-19”bringsacontributiontothefoundationalbasicresearch onthelogisticequationanditsgeneralizationswhichhopefullyhaverepercussions forepidemiologicapplications. Inchapter“AnalysisofCovid-19VirusSpreadingStatisticsbytheUseofaNew Modified Weibull Distribution,” we use a Bureau of Public Road (BPR) model to combat this issue endangering the environment and public health. We exploit the BPR function to relate average travel time to the estimated number of commuters traveling by car. We collect mode share data from the NITI Aayog, state resource centres,whichgiveuniquefiguresoftheimpactofsharedmobilityinIndiaandhow, in its absence, various sectors will be affected. Using the given data and the BPR, weevaluateincreasedvehiclevolumesontheroadifdifferentportionsoftransitand viii Preface carpool users switch to single-occupancy vehicles and its effect on multiple other factors.Basedonthisstudy,wepredictthatcitieswithsignificanttransitridership are at risk for extreme traffic and pollution unless transit systems can resume safe witheffectiveprotocols. In chapter “Lifting Lockdown Control Measure Assessment: From Finite- toInfinite-DimensionalEpidemicModelsforCovid-19,”inanticipationofsubstan- tialfataleffectsonthehealthofpeoplefollowingthishuman-to-humanspread,we aim to propose a new six-parameter modified Weibull distribution to analyze the spreadofCovid-19.Weapplythismodeltostudythecumulativecasesinfectedin somecountries,wegiveaglobalanalysisofthestatisticaldataofthepandemic,and weprovethatournewdistributionefficientlygeneralizessomeexistingmodelsand fitscorrectlysomedataregisteredfromFebruarytoJune2020.Weusetheseresults toassessthepotentialforhuman-to-humanspreadtooccuraroundtheglobe. The main focus of chapter “Introduction to the Grey Systems Theory and Its Application in Mathematical Modeling and Pandemic Prediction of Covid-19” is onpublichealthcontrolstrategies,whicharecurrentlythemainwaytomitigatethe Covid-19pandemic.Weintroduceandcomparecompartmentalmodelsofincreasing complexityforCovid-19transmissiontodescribethedynamicsofthediseasespread. WebeginbyconsideringanSEAIRmodelincludingbasiccharacteristicsrelatedto Covid-19.Next,weshallpayattentiontoagestructuremodelingtoemphasizethe roleofage-groupindividualsonthediseasespread.Amodelwithconstantdelayis alsoformulatedtoshowtheimpactofthelatencyperiodontheseverityofCovid- 19.SincethereisevidencethatforCovid-19disease,importantrelationshipsexist betweenwhatishappeninginthehostandwhatisoccurringatthepopulationlevel, weshalllinkthebasicmodeltoin-hostdynamicsthroughtheso-calledthreshold- typedelaymodels.Finally,wewillincludedemographiceffectstothemostcomplex modelsandwewillconductrigorousbifurcationanalysistoquantifypossiblefactors responsiblefordiseaseprogression. Chapter“MathematicalAnalysisofDiagnosisRateEffectsinCovid-19Transmis- sionDynamicswithOptimalControl”isdevotedtopresentthescientificbackground for the appearance of gray systems in the 1980s. Then, the history of astonishing development, along with the main components and fundamental principles of the graysystems,isalsointroduced.Currently,agraysystemisanemergingresearch areawithstrongpossibilitiestotransectacrossandapplytoawiderangeofscien- tificareas,includingindustry,agriculture,geology,ecology,medicine,education,etc. However,mostapplicationsofthesystemsarefromChinese-speakingresearchers, while the theory itself is still uncommon in uncertainty mathematics. Finally, the representative models with high accuracy are put into practice by predicting and handlingtheoutbreakoftheCovid-19pandemic.Notonlycanthesystemspredict the total number of positive cases, but they can also be applied in various other medicalpractices,includingtelecareanddatamanagement.Theirperformancesare also compared with other uncertainty models, including machine learning, which hasproventhatgraysystemmodelshavetheabilitytoperformequallywell,oreven better,especiallyinthecontextoflimiteddata. Preface ix Many countries around the world are trying to fight Covid-19, and their main methodsarelockdown,quarantine,isolation,andawarenessprogramstoencourage people toadopt socialdistancingandmaintainpersonalhygiene. Thelockdown is aimedtorestrictthemovementofhumansfromortocertainplaces.Quarantineis aimedtowardseparatingthesusceptiblehumansfrominfectedorexposedhumansas muchaspossible,whereasisolationisaimedtowardkeepingtheconfirmedcasesof infectedhumansawayfromtherestofthepopulation.Theconfirmedcasesaremainly identifiedthroughthediagnosisofindividualswhoshowedsymptomsofCovid-19 and sometimes through random checking of individuals hoping to identify either asymptomatic or pre-symptomatic cases, which is generally an expensive method. Inthischapter,wedevelopamathematicalmodeltoinvestigatetheroleofdiagnosis rateinthetransmissiondynamicsofCovid-19togetherwiththecombinedeffectsof quarantineandisolation. Chapter “Development of Epidemiological Modeling RD-Covid-19 of Coron- avirusInfectiousDiseaseandItsNumericalSimulation”discussesamodelwhichis fullyanalyzedbothqualitativelyandquantitativelyinordertogaininsightaboutthe roleofdifferentmodelparametersinthediseasetransmissiondynamics,especially thoserelatedtodiagnosisandquarantine.Theanalysiswillincludetheestimationof boththebasicandthecontrolreproductionnumbersandsensitivityanalysisofthe reproductionnumberstothecorrespondingmodelparameters.Theoptimalcontrol theorywillbealsoappliedtothemodeltoexaminetheroleofsomeotheroptimal control strategies and to study the effect of diagnosis and quarantine rates in the effectivenessofthesecontrols. In chapter “Mediterranean Diet—A Healthy Dietary Pattern and Lifestyle forStrongImmunity,”wehavedevelopedanewepidemiologicaldynamicalmodel named RD-Covid-19 (version 1.0) model. The traditional epidemiological model of an infectious disease known as susceptible–exposed–infected–recovered–dead (SEIRD) is modified to develop this new model. RD-Covid-19 is a networked epidemiologicalmodelinwhichadata-drivenlogisticmodelandtraditionalmodels suchassusceptible,infected,andrecovered(SIR),SEIR,andSEIQRDPareinter- linked. The completer model forecasts the spread of the Covid-19. For the model, the parameters are estimated by fitting the model with real data.1 The Levenberg– Marquardtnonlinearleast-squaresoptimizationtechniqueisappliedfortheestima- tionoftheparametersandforthefittingofthemodel.Numericalsimulationofthe model carried out with the estimated values of the parameters and outcome of the model generates the temporal profile of infected, recovered, and death cases. The severityofthemodelismeasuredbycomputingthebasicreproductionnumber(R0). Data(real-timedata)usedinthemodelRD-Covid-19relatedtothepublicarecatego- rizedasconfirmed,recovered,anddeathcases.Themodelisexecutedtoexplorethe coronaoutbreakinChina,India,Brazil,andRussia.Theestimatedvalueofthebasic reproductionnumber,R0,iswellinagreementwiththatobtainedfromtheoutcome oftraditionalmodelsSIRandSEIR.Implementationoflockdownimpactsthemodel and its innovation, showing the advantage to make decisions on risk management 1Source:JohnHopkinsUniversityandWHOdashboard.
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