Daim Ntawv Ceeb Toom Txog Kev Hloov Pauv Hloov Pauv, Cov Tshuaj Tiv Thaiv Kab Mob thiab Kev Ua Qauv Ntawm Cov Kab Mob Sib Kis

Abstract

Kev nthuav tawm ntawm COVID-19 kev sib kis tau nyuaj heev rau kev kwv yees siv cov qauv lej rau cov kab mob sib kis. Thaum nws tau pom tias qhov kev hloov pauv ntawm qhov muaj feem cuam tshuam tau cuam tshuam rau cov khoom tseem ceeb xws li qhov tshwm sim siab tshaj plaws, kev tiv thaiv tsiaj txhu, thiab qhov loj kawg ntawm kev sib kis, qhov tshwm sim nyuaj no yuav luag tsis tuaj yeem ntsuas lossis ntsuas, thiab nws tseem tsis meej. yuav ua li cas koom nrog nws rau kev ua qauv thiab kev twv ua ntej. Hauv kev ua haujlwm no, peb qhia tau tias, los ntawm kev ua qauv kev xav, qhov sib txawv ntawm kev nkag siab ntawm tus kheej theem yog sib npaug rau ib feem θ ntawm cov pej xeem uas muaj kev tiv thaiv kab mob "artificial" sterilizing. Peb kuj muab cov qauv tshiab rau kev tiv thaiv tsiaj txhu thiab qhov kawg loj ntawm kev sib kis thiab qhia tau tias cov txiaj ntsig no tau qis dua li qhov kev kwv yees los ntawm cov qauv qub, thaum muaj qhov hloov pauv hloov tau. Hauv cov xwm txheej tshwj xeeb ntawm SARS-CoV-2, tam sim no muaj qhov tsis txaus ntseeg qhov hloov pauv tau yooj yim vim tias tsis muaj kev tiv thaiv los ntawm ob qho tshuaj tiv thaiv thiab kab mob yav dhau los, thiab peb qhov kev tshawb pom yuav raug siv los ua kom yooj yim rau cov qauv. Yog tias qhov kev hloov pauv no tseem tshwm sim ua ntej nthwv dej thawj zaug, raws li tau hais los ntawm ntau qhov kev tshawb fawb, cov kev tshawb pom no tuaj yeem pab piav qhia vim li cas qhov loj ntawm qhov pib nthwv dej ntawm SARS-CoV-2 kuj qis, piv rau qhov twg yuav muaj kev cia siab raws li tus qauv qauv.

cistanche tubulosa- txhim kho lub cev tiv thaiv kab mob

1 Kev Taw Qhia

Txij li cov kev ua haujlwm tseem ceeb ntawm Kermack thiab McKendrick [1–3] cov qauv kev ua lej suav nrog (xws li SIR, SEIR, thiab lwm yam) yog siv los ua qauv kev sib kis ntawm cov kab mob sib kis. Ntawm lwm yam, cov ntaub ntawv no tau qhia txog qhov tam sim no nto moo R0- tus nqi thiab pom tias qhov sib piv nrog tib neeg kev xav, kev kis kab mob yuav tsis kis mus rau tag nrho cov pej xeem, txawm tias kis tau li cas. Hloov chaw, qhov xwm txheej yuav pib lwj thaum feem ntawm qhov rov qab los txog qhov hu ua "Hard-Immunity Threshold", uas lawv tau txiav tawm cov qauv nto moo Txawm li cas los xij, ua ntej SARS-CoV-2 muaj kev sib kis, tsis muaj cov ntaub ntawv txhim khu kev qha los ntawm tus kab mob tshiab ( cuam tshuam rau tib neeg) uas qhov kev kwv yees no tuaj yeem kuaj tau. Hmoov tsis zoo, qhov no tseem yog qhov teeb meem loj, txij li piv txwv li kev kaw cia thiab kev yeem cais tawm (uas cov qauv tsis tuaj yeem kwv yees) tau muaj kev cuam tshuam loj rau kev sib kis. Txawm li cas los xij, cov ntaub ntawv los ntawm cov chaw xws li Sweden, uas tau ua tsawg tsawg los txwv kev sib kis hauv zej zog, qhia tias cov qauv lej muaj qhov nyiam tshaj qhov ntsuas qhov loj ntawm nthwv dej thaum muaj kev sib kis loj [4]. Ntau yam tseem ceeb tau paub tias muaj qhov cuam tshuam rau cov qauv nkhaus. Ib qho piv txwv zoo li no yog qhov hloov pauv hloov tau, saib xws li Ch. 1 thiab 3 hauv [5], thiab kab lus [6–9]. Los ntawm kev hloov pauv tau yooj yim, peb nyob ntawm no hais txog (lub sij hawm-invariant) qhov sib txawv ntawm cov tib neeg hauv qhov muaj feem yuav kis tau tus kab mob, muab qee yam kis tus kab mob, tsis zoo li tus neeg hloov pauv lub sijhawm. Cov txiaj ntsig zoo sib xws kuj tau tsim cov lej rau lwm yam kev hloov pauv, xws li hnub nyoog thiab kev ua haujlwm [10]. Xav paub ntau ntxiv, kev kis kab mob sib txawv (super-spreaders) tsis muaj kev cuam tshuam rau kev sib kis thaum muaj kev sib kis loj [11]. Txawm li cas los xij, cov lus xaus no tau muab los ntawm kev sib cav heuristic lossis tsuas yog sim cov qauv tsim nyog, thiab cov txheej txheem tom qab cov xwm txheej no tseem to taub tsis zoo. Tshwj xeeb, txij li qhov kev hloov pauv ntawm kev raug cuam tshuam yog qhov tsis tuaj yeem ua kom muaj nuj nqis, nws tsis paub meej tias yuav ua li cas koom nrog nws rau hauv cov qauv, yog li kev kwv yees ntawm yav tom ntej COVID{18}} nthwv dej, lossis kev kis tus kabmob kis mus ntxiv, tseem yog qhov kev sib tw loj.

cistanche tubulosa- txhim kho lub cev tiv thaiv kab mob

Raws li qhov tseeb, xav tias tus kab mob kis tau tshiab, uas nws qhov kev sib kis tau muaj feem cuam tshuam nrog kev sib txawv ntawm kev kis kab mob thiab / lossis kev cuam tshuam, tau qhia hauv kev sib txuas zoo xws li lub nroog loj, thiab xav tias muaj kev sib kis loj yuav tshwm sim. Ib qho yuav kwv yees R0, piv txwv li kev kwv yees kwv yees ntawm qhov nruab nrab ntawm cov kab mob tshiab uas ib tus neeg kis tau nce mus rau, los ntawm cov ntaub ntawv kab mob thaum ntxov, siv xws li EpiEstim [12] lossis [13]. Los ntawm kev tshawb nrhiav kev sib cuag, ib tus kuj tuaj yeem kwv yees lub sijhawm tiam Generation, uas yog lwm qhov kev ntsuas uas xav tau los khiav tus qauv SIR. Hauv qhov xwm txheej zoo li no, ib tus tuaj yeem nug cov lus nug yog tias qhov tso zis ntawm SIR simulation yooj yim yog qhov kev txiav txim zoo thawj zaug ntawm qhov yuav los, yog tias tsis muaj Cov Tshuaj Kho Mob. Cov qauv (1) puas yog qhov qhia tau zoo txog thaum twg peb yuav cia siab tias qhov tshwm sim yuav pib rov qab? Raws li cov ntaub ntawv los ntawm Sweden thaum lub sijhawm COVID-19 muaj thoob qhov txhia chaw, cov lus teb zoo li tsis muaj, saib [4] qhov uas nws tau pom tias qhov xwm txheej tau poob qis, tsis tau xav txog, ntawm qib seroprevalence qis dua qhov kwv yees los ntawm (1). Ntawm cov kev tshawb fawb theoretical ua ntej ntawm lub ncauj lus no, kab lus uas los ze tshaj los teb cov lus nug saum toj no yog Britton thiab. al. [10], qhov twg cov kws sau ntawv ua pov thawj tias kev hloov pauv hauv cov qauv kev ua ub no tuaj yeem txo qis ntawm kev tiv thaiv kab mob, piv nrog cov kev kwv yees classical raws li (1). Ib daim ntawv tshaj tawm qub nrog cov lus zoo sib xws yog [14]. Txawm li cas los xij, cov lus xaus no yog cov kev soj ntsuam empirical raws li cov qauv uas tau tsim los koom nrog cov pejxeem heterogeneity. Cov nyhuv damping no tsis tau tsim ua lej thiab nws tseem tsis paub meej tias yuav ua li cas, thiab qhov twg, qhov sib txawv heterogeneities tau tshwm sim. Tshwj xeeb, nws tseem tsis tau paub meej tias yuav ua li cas thiaj li twv tau qhov tseeb ntawm kev tiv thaiv tsiaj txhu. Peb tau hais tias, nyob rau hauv rooj plaub ntawm SARS-CoV-2, ntau yam xws li caj ces, kev tiv thaiv kab mob sib kis, thiab kev tiv thaiv hauv lub cev, tau pom tias muaj kev hloov pauv hauv kev raug mob [15–18].

cistanche tubulosa- txhim kho lub cev tiv thaiv kab mob

Nyem qhov no mus saib Cistanche Enhance Immunity khoom

【Nug ntxiv】 Email: cindy.xue@wecistanche.com / Whats App: 0086 18599088692 / Wechat: 18599088692

1.1 Novel contributions

Hauv kev ua haujlwm no, peb ua pov thawj hauv lej tias qhov kev hloov pauv ntawm qhov cuam tshuam muaj kev cuam tshuam rau cov qauv nkhaus, qhov kev hloov pauv hauv kev sib kis tsis yog (tsuas yog nws tsis cuam tshuam nrog yav dhau los, saib [7]). Qhov tseem ceeb tshaj, peb kuj pom tau tias qhov kev faib (feem ntau tsis paub) piav qhia txog qhov sib txawv li cas tsis xav tau rau kev ua qauv raug. Ntau precisely peb qhia tau hais tias ib tug susceptibility heterogeneous qauv yuav coj yuav luag zoo tib yam rau ib tug qauv (homogeneous) SIR qauv uas ib feem ntawm cov pejxeem muaj sterilizing tiv thaiv kab mob thiab hais tias tus meej zoo ntawm cov susceptibility distribution tsuas cuam tshuam rau theem ntawm sterilizing tiv thaiv. Nws yog ib qho tseem ceeb uas yuav tau piav qhia tias qhov kev tiv thaiv kab mob no tsuas yog muaj nyob rau hauv cov qauv lej yooj yim, thiab yuav tsum tsis txhob cuam tshuam nrog kev tiv thaiv kev tiv thaiv kab mob tiag tiag ntawm qee tus neeg. Hauv lwm lo lus, txawm tias txhua tus neeg raug tus kab mob no (rau qee qib), ntawm cov pej xeem theem nws yuav zoo li yog ib feem ntawm cov pej xeem muaj kev tiv thaiv tsis muaj menyuam. Peb yuav xa mus rau xws li kev tiv thaiv kab mob, xav tau rau kev ua lej kom raug, raws li "Artificial Sterilizing Immunity" (ASI), thiab cov feem ntawm cov pejxeem muaj nws li θ. Ntev npaum li θ tuaj yeem kwv yees los ntawm cov ntaub ntawv muaj, peb pom tias qhov kev tiv thaiv kab mob tiag tiag yog qis dua (1) kwv yees. Cov mis kom raug, nyob rau hauv lub xub ntiag ntawm qhov sib txawv susceptibility, yog muab los ntawm

thiab qhov kawg loj ntawm tus kab mob kis thoob qhov txhia chaw kuj raug txo los ntawm tib yam (1 − θ). Peb kuj yuav tsum ua kom pom tus lej tias lwm cov pejxeem heterogeneities, xws li cov uas suav nrog Britton thiab. al. [10], muaj cov txiaj ntsig zoo sib xws, thiab yog li cov kev tshawb pom hauv daim ntawv no tuaj yeem siv los txo tus naj npawb ntawm cov neeg tsis paub hauv cov qauv muaj tseeb ntau dua rau kev kis kab mob.

2 Cov lej ntawm kev kis kab mob kis tau zoo

Yuav kom piav qhia txog cov kev tshawb fawb txog lej, peb ua ntej muab cov ntsiab lus ntawm cov qauv yooj yim ua haujlwm li cas. SIR stands rau Susceptibles, Infectives, and Recovered, and is the simplest form of a "compartmental model" use in lej epidemiology (saib [19] for an introduction to this field). Hauv cov qauv, S, I, thiab R yog lub luag haujlwm ntawm lub sijhawm t, thiab los qhia seb cov no cuam tshuam li cas peb kuj tseem yuav qhia txog qhov ua haujlwm (redundant) ν piav qhia txog qhov xwm txheej, piv txwv li tus naj npawb ntawm cov kab mob tshiab txhua hnub (tsis txhob tsis meej pem. nrog kuv, uas piav qhia txog kev nthuav dav). Cov mis rau ν(t) yog nyob rau hauv lub plawv ntawm lub algorithm, thiab thaum pib, peb tsuas muaj ν(t)=I(t), qhov twg yog qhov tsis tu ncua uas txiav txim seb muaj pes tsawg tus mob tshiab qhov nruab nrab kis muab nce mus rau ib hnub. Yog tias a yog tus naj npawb nruab nrab ntawm txhua hnub uas muaj feem kis tau los ntawm tus neeg nruab nrab, thiab p yog qhov tshwm sim uas qhov kev sib cuag no ua rau kis tau tus mob, ces=ap. Raws li tus nqi ntawm susceptibles maj mam txo qis, peb yuav tsum tau hloov qhov no los ntawm kev sib faib nrog cov feem ntawm cov pejxeem uas tseem raug. Yog tias tag nrho cov pejxeem yog N qhov feem yog S (t) / N thiab cov qauv ua

Txhawm rau teeb tsa qhov sib npaug ntxiv peb kuj xav tau lub sijhawm tiam Tgeneration, piv txwv li lub sijhawm nruab nrab nws siv los ntawm kev kis mus rau kev rov zoo. Qhov seem sib npaug yog ces

qhov twg σ {{0}}/Tgeneration thiab 0 qhia qhov sib txawv. Cov kab zauv yog intuitively yooj yim to taub, qhov tshwm sim tsis tu ncua tau rho tawm los ntawm S thiab ntxiv rau kuv, thiab nyob rau tib lub sij hawm, muaj ib tug tam sim no ntawm recovering cov neeg uas tawm kuv ntawm tus nqi σI thiab tshwm nyob rau hauv R hloov.

Daim duab 1. Daim duab qhia txog kev rov qab los R thiab qhov muaj feem ntau I. (a) Cov duab pom zoo (raws li ib feem ntawm tag nrho cov pejxeem) rau ntau yam qauv SIR thiab tus nqi ruaj khov ntawm R0=1.66. Ua ntej, peb tso saib tus qauv SIR, tom qab ntawd S-SIR, thiab thaum kawg SIR nrog Artificial Sterilizing Immunity (ASI) nrog cov ntsuas ntawm (8). Nco ntsoov tias lawv pib tawm yuav luag zoo ib yam, tiam sis qhov kawg ob khoov downwards ntau dua li thawj zaug, uas dhau-shoos lub classical Herd-Immunity Threshold (HIT), qhov thib ob ob nyob ze ua ke thiab theem qis dua cov classical HIT. (b) Cov kab nkhaus sib thooj rau kev nthuav dav kuv (cov Sgraphs tau qhia nws tus kheej hauv daim duab 2).

SIR, thiab peb qhov txuas ntxiv ntawm no, yog qhov txiav txim siab hauv qhov kev txiav txim siab tias yog tias peb khiav nws ob zaug, cov zis yog tib yam. Cov qauv zoo li no tau ntseeg tias ua haujlwm zoo thaum muaj kev sib kis loj, qhov twg txoj cai ntawm cov neeg siv ntau [5, 11]. Tag nrho peb qhov kev tshawb pom muaj feem rau qhov xwm txheej no; rau kev ua qauv piv txwv, thawj theem lossis kev sib kis hauv tsev, lwm hom qauv siv. Qhov tshwm sim zoo tshaj plaws rau tus kab mob tshiab yog teem caij I(0)=n qhov twg n << N represents a small number of import cases arriving at time t = 0, and then set S(0) = N − n and R(0) = 0 (so everybody else is initially susceptible and no-one has yet recovered). The value of n is completely irrelevant to the shape of the curves that follow, a low value of n only gives the equation system a slower start so it takes a while longer for the outbreak to reach a certain value. Once this happens, the curves look the same independent of the value n. See the blue graphs in Fig 1 for some typical examples of R-curves and I-curves. In this model, R is always increasing and levels out on a number which is called "the final size of the pandemic" (see Fig 1a). S approximatively looks like N − R, since the prevalence I at any given time is small in comparison with the total population. The incidence ν typically looks just like I, albeit with a lower magnitude.

2.1 Cov qauv niaj hnub rau COVID-19

Cov qauv niaj hnub siv los ntawm pab pawg ua qauv kev tshaj lij feem ntau muaj ntau qhov chaw ntau dua li SIR, piv txwv li hais txog hnub nyoog stratification, qib kev ua haujlwm sib txawv, thaj chaw thaj chaw, cov chav tsev rau cov neeg xav tau ICU, thiab cov chav rau cov neeg tuag. Piv txwv li, tus qauv luam tawm los ntawm cov tswv cuab ntawm Imperial College COVID{{{0}}} pab neeg teb [20] muaj nyob rau hauv nws cov hauv paus ntsiab lus SIR (saib p. 9 as well as S2 Fig in the supplementary material of [ 20]), thiab tib yam mus rau tus qauv [21] siv los ntawm pab pawg ua qauv nrov Swedish, uas tau tswj kom haum rau ICU nyob thiab kev tuag nrog qhov tseeb siab thaum thawj nthwv dej hauv Sweden. Cov qauv tom kawg kuj tseem siv rau hauv ntau thaj tsam thiab cov qauv kev sib cuam tshuam ntawm cov no, tab sis qhov kev hloov pauv hauv cheeb tsam yog SEIR yooj yim. Nws kuj tseem yog ib qho ntxiv rau qhov chaw E rau "Tshwj xeeb", suav nrog lub sijhawm incubation, (raws li qhov tseeb yog ua tiav hauv ob qho piv txwv saum toj no). Txawm li cas los xij, raws li peb yuav tsum qhia hauv Tshooj 4, qhov no muaj kev txwv rau txhua tus cwj pwm. Los ntawm qhov no, peb txhais tau hais tias, rau txhua qhov teeb meem ntawm qhov tseem ceeb (R0, lub sijhawm incubation, thiab lwm yam) rau SEIR, nws yog ib qho ua tau kom tau txais ib qho yuav luag zoo tib yam nkhaus nrog SIR (thiab vice versa), yog tias peb tau tso cai hloov qhov parameter. nqi me ntsis. Txij li thaum tus nqi tseeb ntawm cov kev txwv no yeej tsis paub, qhov no txhais tau hais tias rau lub hom phiaj siv tau ib qho tuaj yeem cia siab rau SIR ib yam li ntawm SEIR, yam tsawg kawg rau kev nkag siab tag nrho cov qauv. Piv txwv li, hauv daim duab 3 peb qhia ib qho piv txwv ntawm SEIR thiab SIR nrog R0- tus nqi uas txawv ntawm 1%, thiab cov duab yuav luag zoo ib yam. Piv txwv li, qhov kawg ntawm tus kab mob sib kis sib txawv tsawg dua 1.5%. Tsis tas li ntawd, cov chav tsev hais txog kev mob hnyav thiab kev tuag kuj muaj qhov cuam tshuam tsis zoo rau tag nrho tus cwj pwm, tsuas yog vim tias tsuas yog ib feem me me ntawm cov kab mob yuav xaus rau hauv cov chav no. Raws li qhov no, peb sib cav hais tias kom nkag siab txog tus cwj pwm tag nrho, raws li peb xav tau ntawm no, nws txaus los kawm cov qauv SIR yooj yim dua. Rau lwm qhov kev sim ua piv txwv / qauv SARS-CoV-2 siv SIR/SEIR-type qauv saib piv txwv li [22, 23].

Nyob rau hauv sib piv, lwm hom heterogeneities xws li qib kev ua si sib txawv thiab txawv kev sib cuam tshuam cov qauv ntawm cov hnub nyoog pawg, muaj ib tug tseem ceeb damping nyhuv ntawm tus qauv nkhaus. Piv txwv li, lub hnub nyoog-kev ua si stratified SEIR los ntawm Britton thiab. al. [10] muaj qhov xwm txheej siab kawg ntawm li 35% qis dua tus qauv SIR, muab cov lus qhia sib piv. Qhov no yog raws li qhov kev tshawb pom nyob rau hauv [10], qhov twg ib tug poob rau hauv Herd-Immunity Threshold ntawm ib ncig ntawm 30% yog soj ntsuam rau lub hnub nyoog-kev ua qauv qauv, piv nrog rau cov kwv yees (1) raws li SIR. Qhov no yuav tau tham ntxiv hauv Tshooj 4.2. Tsis tas li ntawd, qhov kev hloov pauv hloov tau muaj qhov cuam tshuam loj, tab sis qhov no twb tau tham hauv qhov kev taw qhia thiab tau txheeb xyuas ntxiv hauv Tshooj 3.

2.2 Tus qauv piv rau kev muaj tiag tsis sib haum?

Txawm hais tias tus qauv siab dua puas tau piav qhia txog kev sib kis ntawm COVID-19 yog qhov nyuaj rau kev txiav txim siab, txij li ib tus neeg yuav ib txwm sib cav tias Non-Pharmaceutical Interventions (NPIs), nrog rau kev yeem hloov pauv tus cwj pwm, tau muaj kev cuam tshuam loj. Tsis tau thov kom muaj cov lus teb meej, rooj plaub ntawm Sweden yog qhov nthuav vim nws lub tswv yim so, uas ntxiv rau yuav luag tas mus li thaum 2020-2021. Tshwj xeeb, cov tsev kawm tau qhib, cov neeg tsis tuaj yeem ua haujlwm hauv tsev tau raug txhawb kom mus ua haujlwm, cov neeg hauv tsev neeg ntawm cov tsev neeg muaj kab mob yuav tsum ua haujlwm lossis mus kawm ntawv, thiab kev siv lub ntsej muag dav dav tsis tau siv, ua rau lub tebchaws zoo tagnrho. rau kev sib piv cov qauv nrog cov ntaub ntawv tiag tiag. Vim qhov kev sim tsis txaus, lub sijhawm ntawm cov xwm txheej tsis tshua muaj nqi, tab sis kev ntsuas ntawm seroprevalence los ntawm cov qauv ntshav muab cov ntaub ntawv tseem ceeb vim nws tau tsim tias feem ntau cov neeg uas tau txais COVID-19 kuj mus rau kev txhim kho lub cev tiv thaiv [ 24] thiab tias cov tshuaj tiv thaiv no tseem nyob tsawg kawg 9 lub hlis [25, 26]. Cov txiaj ntsig tau tshaj tawm los ntawm Swedish Public Health Agency [27] qhia tias kwv yees li 11% tau muaj COVID{13}} hauv thaj av Stockholm tom qab thawj nthwv dej ntawm 2020, uas tau nce mus txog 22% thaum Lub Ob Hlis 2021, tom qab nthwv dej thib ob. Tsis tas li ntawm cov neeg ua haujlwm hauv tsev kho mob hauv Sweden (tsis siv lub ntsej muag lub ntsej muag), feem ntau yog nyob ib ncig ntawm 20% [26] tom qab thawj nthwv dej, raws li kev soj ntsuam los ntawm cov tsev neeg muaj mob nyob rau lwm qhov [28].

cistanche tubulosa- txhim kho lub cev tiv thaiv kab mob

Txawm li cas los xij, tus qauv los ntawm Sjo¨din et. al., xa mus rau yav dhau los, kwv yees tus naj npawb ntawm cov neeg kis tus kab mob nyob ib ncig ntawm 30% tom qab thawj nthwv dej, txawm tias xav tias 56% txo qis hauv kev sib cuag ntawm cov neeg muaj hnub nyoog 0-59 thiab 98% txo ntawm cov hnub nyoog 60–79 (qhov no yog rau scenario d uas yog haum rau ICU-nyob thiab kev tuag, saib daim duab 2b, coj nyob rau hauv lub siab hais tias cheeb tsam Stockholm muaj 2.4 lab inhabitants). Raws li tib kab, Britton thiab. al. [10] kwv yees tias tus kab mob tuaj yeem tawm ntawm ib ncig ntawm 43% tag nrho cov kab mob, hauv ib hlis. Thaum cov kws sau ntawv tau hais tias qhov no tsis yog qhov kev kwv yees tiag tiag, nws yog raws li qhov tseeb tsis muaj tseeb rau COVID-19. Daim ntawv tshaj tawm nto moo 9 los ntawm Imperial College [29] tau kwv yees tag nrho cov naj npawb ntawm 81% kis tus kab mob hauv qhov "tsis muaj dab tsi" qhov xwm txheej, raws li qhov zoo tshaj plaws hu ua "tus qauv-raws li tus qauv" uas kuj kho cov neeg nyob hauv tsev sib cais. Raws li Table 3 nyob rau hauv tsab ntawv ceeb toom, tus naj npawb ntawm cov neeg tuag thiab lub siab tshaj plaws ICU muaj peev xwm raug txo los ntawm 50% thiab 81%, feem, nyob rau hauv qhov zoo tshaj plaws NPI scenario, uas yeej mus dhau qhov uas tau ua nyob rau hauv Sweden. Txawm li cas los xij, txij li Lub Ob Hlis 2021, thaum tus thawj Wuhan strain poob qis [30], cov kev kwv yees txo qis tshaj qhov tseeb ntawm tus lej los ntawm kwv yees li 4 (tuag) thiab 10 (ICU) (thaum txhais ncaj qha rau Stockholm County).

Daim duab 2. Cov duab ntawm cov kab mob S. S-curves sib raug rau 3 daim duab hauv daim duab 1. Raws li hauv daim duab 1, cov xiav dub, thiab paj yeeb tau normalized los ntawm kev faib los ntawm N. Qhov nkhaus dub yog li qhia qhov feem ntawm tag nrho cov pejxeem. raug tus kab mob no. Nco ntsoov tias thaum muaj kev sib kis thoob qhov txhia chaw, nyob ib ncig ntawm 68% tseem raug cuam tshuam, tsis zoo li qub SIR uas qib tawm ntawm thaj tsam 34%. Cov kab liab liab pib tawm tsam 57% muaj kev tiv thaiv kab mob tsis zoo, thiab yog li nws cov nqi pib yog 43% (tus lej no tau xaiv los ntawm cov qauv (8)). Nco ntsoov tias lub paj liab nkhaus zoo nkaus li cov xim dub tshwj tsis yog rau kev txhais lus ntsug, qhia txog qhov tseem ceeb ntawm qhov kev tshawb pom no. Tus qauv S-SIR muaj peb pawg S1, S2, thiab S3 sib raug rau p1=1 (labeled "super-susceptibles"), p2=0.1 (labeled "ib txwm"), thiab p{{ 17}}.02 (labeled "zoo-tiv thaiv"). Ntawm no peb tau normalized nrog tus nqi ntawm cov neeg nyob rau hauv txhua pab pawg neeg, yog li ntawd tag nrho cov curves pib ntawm 1. Nco ntsoov yuav ua li cas kev sib kis nyob rau hauv ob pawg sub-pawg tom qab theem tawm sai li sai tau thaum nws theem tawm nyob rau hauv lub super susceptible pab pawg neeg.

Lub ntsiab lus ntawm no tsis yog los thuam ib qho qauv tshwj xeeb, thiab kom meej meej, rooj plaub ntawm Sweden ib leeg tsis tuaj yeem ua pov thawj tias cov qauv yog qhov raug lossis tsis yog, raws li tau hais los ua ntej. Txawm li cas los xij, raws li qhov sib txawv loj ntawm qhov tseeb Swedish cov ntaub ntawv thiab ntau yam qauv tshwm sim tau piav qhia saum toj no, nws yog ib lo lus nug tseeb seb "cov qauv niaj hnub" puas muaj kev xav rau kev kwv yees ntau dhau ntawm lub zej zog sib kis thiab qhov kawg ntawm kev sib kis. Peb pom nws zoo li cov lus teb yog yog, thiab kev txhawb nqa ntxiv rau qhov kev xav no tau muab rau hauv [4]. Hauv daim ntawv no peb qhia tau hais tias kev hloov pauv hloov pauv yog ib yam uas ua rau muaj qhov tshwm sim no.

2.3 Pre-immunity, super-spreaders thiab lwm yam inhomogeneities

Yuav ua li cas peb hloov cov kab zauv (3) thiab (4) thiaj li yuav dampen cov nkhaus? Qhov kev xaiv yooj yim tshaj plaws yog xav tias qee feem θ ntawm cov pej xeem muaj qee hom kev tiv thaiv kab mob kom tsis txhob kis tus kab mob. Ua lej, qhov no yooj yim ua tiav los ntawm kev hloov kho thawj zaug rau

qhov twg ω {{0}} − θ yog ib feem ntawm qhov pib raug. Txawm li cas los xij, qhov no tsis yog qhov tseeb heev vim tias kev tiv thaiv kab mob feem ntau tsis yog binary, piv txwv li 0% lossis 100% (hu ua sterilizing immunity). Qhov kev xav tias qee tus neeg muaj kev cuam tshuam ntau dua li lwm tus yog qhov tseeb ntau dua li kev tiv thaiv binary. Hauv cov xwm txheej tshwj xeeb ntawm SARS-CoV-2, qhov kev xav tias qee tus neeg muaj qee yam kev tiv thaiv ua ntej tau tawm tswv yim hauv ntau cov ntawv tshaj tawm raws li kev piav qhia rau, tsawg kawg yog raws li qee qhov, tsis xav txog qhov pib kis mob me me, rau piv [31]. Daim ntawv no tseem sau ntau cov kev tshawb fawb qhia tias qee tus neeg muaj qee qhov kev tiv thaiv T-cell ua ntej. Txij thaum ntawd los, cov kab lus sib txawv tau pom ntau yam txheej txheem uas ua rau qee tus neeg muaj ntau dua lossis tsawg dua rau SARS-CoV-2, xws li [15–18]. Nws kuj tseem tsim tau zoo tias cov kab mob sib txawv heev, raws li tau hais ua ntej (saib piv txwv [32]). Tsis tas li ntawd, qhov no zoo li tsis cuam tshuam rau lawv mob npaum li cas; ntau tus neeg uas muaj kab mob hnyav heev txawm tias asymptomatic. Nyob rau hauv lub teeb ntawm qhov no, qhov xav tau tshaj plaws yog tias txoj hauv kev uas tus kab mob nkag mus rau tib neeg yog qhov muaj ntau yam sib txawv.

Txhawm rau ua tus qauv muaj tseeb dua rau kev sib kis ntawm COVID-19, lossis ib qho kab mob sib kis rau qhov teeb meem ntawd, nws yog qhov tsim nyog los faib cov chav S thiab kuv rau hauv ntau lub subcompartments S1, . . ., SJ and I1, . . ., IK qhov twg tib neeg nyob rau hauv txhua chav tsev muaj ib theem sib txawv ntawm susceptibility/infectivity. Txhawm rau saib yuav ua li cas teeb tsa qhov sib npaug sib npaug rau kev sib kis kab mob, nco qab tias yog tus naj npawb ntawm kev sib cuag txhua hnub los ntawm ib tus neeg. Peb tam sim no cia pjk yog qhov tshwm sim uas qhov kev sib cuag no ua rau kis tau tus mob thaum tus neeg hauv Sj ntsib ib qho hauv Ik. Qhov xwm txheej νj los ntawm pawg Sj ces dhau los

(cf (3)). Txij li thaum peb xav tias tsis muaj kev sib raug zoo ntawm kev kis kab mob thiab kev cuam tshuam, tag nrho cov kab mob tshiab ν 1 + . . . + νJ ces faib rau pawg I1, . . ., IK raws li lawv cov txheeb ze loj. Cov kev sib npaug ntxiv hauv (4) tau hloov kho yooj yim rau qhov teeb tsa vector tshiab, peb xa mus rau Sec. 1 hauv S1 Cov Ntaub Ntawv rau cov ntsiab lus. Hauv seem tom ntej no, peb txheeb xyuas tus cwj pwm ntawm cov kab ke sib npaug, thiab hauv Tshooj 4 peb kuj tham txog lwm qhov txuas ntxiv xws li SEIR thiab qib kev ua haujlwm sib txawv.

3 Cov txiaj ntsig tseem ceeb

Lub ntsiab lus tseem ceeb ntawm qhov kev tshawb fawb no yog qhov txuas ntxiv rau SIR thiab SEIR ntawm hom uas tau hais los saum toj no ua rau tag nrho cov nkhaus uas tsuas yog sib txawv ntawm SIR theem pib, muab cov qib ntawm Artificial Sterilizing Immunity (ASI) suav nrog. Ua ntej tshaj plaws, tom qab teeb tsa cov ntsiab lus hauv Tshooj 1 ntawm S1 Cov Ntaub Ntawv, peb ua pov thawj hauv Proposition 1.1 tias kev faib kuv mus rau hauv ntau lub sub-compartments tsis muaj txiaj ntsig, ntxiv txhawb cov lus xaus hauv [8, 9, 11]. Nyob rau hauv lwm yam lus, lub hav zoov ntawm "super-spreaders" tsis nyob rau hauv ib qho tseem ceeb txoj kev muaj feem xyuam rau lub zog ntawm tus kab mob kis. Tshem tawm txheej txheej ntawm qhov nyuaj, Eq (6) yooj yim rau

qhov twg pj yog qhov tshwm sim ntawm kev sib kis thaum muaj kev cuam tshuam hauv pab pawg Sj ntsib tus neeg kis tus kabmob "nruab nrab". Peb xa mus rau Eq (14)-(16) hauv S1 Cov Ntaub Ntawv rau tag nrho cov kab ke sib npaug, uas peb sau npe S-SIR rau "Susceptibility-Stratified SIR". Nws yog qhov xav paub heev uas qhov kev faib ntawm S rau hauv subcompartments tsis tuaj yeem, piv rau kuv, lej yuav raug txo kom tsawg dua rau qhov kev sib npaug yooj yim. Txawm li cas los xij, thiab qhov no yog qhov txiaj ntsig tseem ceeb ntawm daim ntawv no, peb tuaj yeem ua pov thawj hauv lej tias tag nrho tus cwj pwm ntawm S-SIR (nyob rau hauv cov nqe lus ntawm kev nthuav dav kuv thiab rov qab tau R) tsuas yog sib txawv ntawm qhov pib SIR (3) thiab (4) thaum suav nrog ASI rau qhov pib mob, raws li peb tau ua hauv (5). Qhov no yog lub ntsiab lus ntawm Theorem 2.1, uas muaj nyob rau hauv Tshooj 2 ntawm S1 Cov Ntaub Ntawv. Muab qhov tshwm sim p1, . . ., pJ, theorem kuj tseem muab cov qauv rau cov qauv tsim nyog ntawm kev sib kis coefficient (siv los xam qhov xwm txheej ν hauv (3)) thiab kev tiv thaiv kab mob sterilizing θ (siv hauv thawj zaug (5)), raws li hauv qab no:

qhov twg ω {{0}} − θ thiab wj yog feem ntawm cov pejxeem pib koom nrog Sj; wj=Sj({21}})/N. Ib qho piv txwv yooj yim ntawm cov txiaj ntsig no muaj nyob hauv Tshooj 1.3 hauv S1 Cov Ntaub Ntawv. Nws yog ib qho tseem ceeb uas yuav tsum tau ceev faj nrog kev txhais ntawm θ=1 − ω raws li ib feem ntawm cov neeg uas muaj kev tiv thaiv kab mob sterilizing, vim muaj, qhov tseeb, tsis muaj kev faib tawm ntawm θN tiv thaiv kab mob thiab ωN raug, uas yog vim li cas peb. tau xaiv lub ntsiab lus ASI; artificial sterilizing tiv thaiv kab mob. Cov txiaj ntsig no tau piav qhia hauv daim duab 1 thiab 2. Nco ntsoov tshwj xeeb tias, qhov xav tsis thoob, sai li sai tau thaum cov pab pawg muaj kev cuam tshuam loj tshaj plaws (labeled super-susceptibles hauv Fig 2) khiav tawm ntawm cov tib neeg tshiab kom kis tau, kev sib kis hauv txhua pab pawg yuav tsum tsis ua raws li. zoo. Tus cwj pwm no yog ib txwm, saib S1 Fig hauv S1 Cov Ntaub Ntawv rau qhov piv txwv zoo sib xws nrog cov nqi sib txawv. Peb tau pom tib qhov tshwm sim kuj thaum ua qauv nrog SEIR thiab thaum suav nrog xws li cov hnub nyoog sib txawv thiab qib kev ua haujlwm sib txawv, hauv qab no [10]; cov qauv nrog ntau cov khaubncaws sab nraud povtseg tsim cov khoom tsim tawm uas zoo li qhov sib txawv ntawm cov zis ntawm SIR nrog ASI, piv txwv li (3)–(5). Peb tawm raws li kev soj ntsuam tus lej uas peb tham ntxiv hauv Tshooj 4. Tshwj xeeb, muab qhov kwv yees theem ntawm ASI θ hauv ib lub zej zog, nws yog lej tsis tuaj yeem kos cov lus xaus txog ntau npaum li cas ntawm θ yog tshwm sim los ntawm inhomogeneities hauv hnub nyoog thiab tus cwj pwm, thiab ntau npaum li cas los ntawm kev hloov pauv hauv kev raug mob. Incidentally, thaum kawg ntawm txhua daim ntawv [1–3], Kermack thiab McKendrick tau ntxhov siab tias qhov tsis muaj zog hauv lawv cov qauv yog tias lawv xav tias muaj kev cuam tshuam tsis zoo, uas lawv xav tias tsis muaj tseeb hauv ntau qhov xwm txheej. Txawm li cas los xij, zoo li lawv yeej tsis tau los daws qhov teeb meem no, thiab peb tsis tau pom muaj kev tshawb xyuas lej nruj ntawm yuav ua li cas daws qhov teeb meem no nyob rau lwm qhov hauv cov ntaub ntawv ib yam nkaus. Tshwj xeeb, cov mis 1 − 1/R0 rau Herd-Immunity Threshold (HIT), uas yog los ntawm lawv cov ntaub ntawv hais lus, tej zaum yuav tsis raug, raws li tau hais hauv [10]. Hauv seem tom ntej, peb muab cov qauv ua kom zoo ntawm cov qauv no coj ASI rau hauv tus account.

3.1 Cov qauv rau R0 thiab cov tsiaj tiv thaiv kab mob

Nws yog ib qho yooj yim kom pom tias lub sij hawm tiam Tgeneration (qhia hauv qab no (3)) coincides nrog lub sij hawm nruab nrab tus neeg kis tus kab mob. Txij li yog tus kab mob kis tau tus mob, peb xaus lus tias R0=tiam rau tus qauv SIR (3) thiab (4), piv txwv li cov pej xeem raug cuam tshuam tag nrho. Txawm li cas los xij, nyob rau hauv lub xub ntiag ntawm ASI θ, tus nqi kis tau tus mob tsuas yog (1 − θ) thiab yog li tus qauv raug rau R0- tus nqi dhau los

Tus nqi saum toj no rau R{{0}} yog tus nqi uas yuav kwv yees los ntawm xws li EpiEstim [12] lossis [13] los ntawm lub sijhawm tiag tiag uas tsim los ntawm tus qauv (3) thiab (4) nrog pib cov ntaub ntawv (5). Kev ua lej, R0 txhais tau tias yog tus naj npawb ntawm cov kab mob tshiab uas ib tus neeg kis tau nce mus ua ntej kev tiv thaiv kab mob pib tsim. (Xav suav qhov no, ua ntej daws kuv 0 (t) {{10}} −σI(t), muab I(0)=1, nco qab tias σ {{13} }/Tgeneration, thiab tom qab ntawd ua ke qhov tshwm sim tshwm sim ν, raws li tau muab los ntawm (3), thaum khaws S(t) tsau ntawm S(0)=ωN.) Ib yam li ntawd, ib qho pom tias qhov zoo R-tus nqi, denoted Re(t), nyob rau hauv cov qauv saum toj no yog

Lo lus "herd-immunity" muaj ntau lub ntsiab lus [33]. Hauv kev kis tus lej lej, muab qee tus qauv thiab tus kab mob tshiab, Herd-Immunity Threshold tau txhais tias yog tag nrho cov kab mob kis tau thiab rov qab los xav tau kom ua tiav Re(t0)=1. Txij li thaum

(Nco qab (4)), peb pom tias qhov no coincides nrog lub ntsiab lus ntawm cov nthwv dej ntawm tus kab mob ib txwm pib rov qab. Dhau li ntawm qhov no, txhua qhov xwm txheej ntshuam yuav tsis ua rau muaj qhov tshwm sim tshiab. Peb qhia tus nqi no los ntawm HIT.

Nyob rau hauv tus qauv SIR, nws tau xav tias cov tib neeg sib xyaw ua ke thiab cov tib neeg rov qab tau muaj cov tshuaj tiv thaiv kab mob (piv txwv li kev tiv thaiv tsis muaj menyuam). Thaum nws paub tias cov tshuaj tiv thaiv kab mob ploj mus dhau sijhawm, tsawg kawg rau SARS-CoV-2, qhov kev poob qis no tshwm sim qeeb qeeb dua li lub sijhawm muaj kev sib kis [25], thiab yog li qhov kev xav tom kawg yog qhov tsim nyog rau kev sib tham ntawm cov herd-immunity pib nyob rau hauv lub sij hawm luv luv. Txawm li cas los xij, peb xav kom ntxhov siab tias qhov waning txhais tau hais tias kev tiv thaiv tsiaj txhu yeej tsis muaj kev ruaj ntseg, tab sis yuav ploj mus nrog lub sijhawm, thiab yog li qhov tseeb tias kev tiv thaiv tsiaj txhu tau mus txog thaum lub sijhawm nthwv dej tshwj xeeb tsis tiv thaiv cov nthwv dej yav tom ntej, uas yuav tshwm sim los ntawm waning antibodies los yog qhov tshwm sim ntawm cov hloov tshiab. Xav tias tam sim no tus qauv SIR nrog qee theem ntawm ASI piav qhia meej txog qhov tshwm sim. Lub Herd-Immunity Threshold HIT ces sib npaug S(0)/N − S(t0)/N qhov twg t0 yog lub sij hawm taw tes thaum lub herd-immunity pib mus txog, uas tuaj yeem pom los ntawm kev daws Re(t{{10}})=1. Hauv lwm lo lus, HIT yog qhov sib txawv ntawm feem S(t0)/N ntawm cov raug mob thaum lub sij hawm t0 thaum pab tsiaj tiv thaiv kab mob mus txog, thiab cov feem ntawm cov raug mob thaum xub thawj. Hauv SIR-qauv nrog ASI, daws Re(t{17}})=1 yields qhov sib npaug S(t0)/N=1/

Tgeneration, thiab yog li peb deduce

qhov twg peb siv cov qauv ua ntej (9) raws li lub ntsiab lus ntawm R0. Qhov no yog cov qauv rau kev tiv thaiv tsiaj txhu uas tau nthuav tawm hauv Eq (2) hauv kev taw qhia. Nws txhais tau hais tias cov qauv classical (1), muab qhov kwv yees ntawm R0 los ntawm xws li EpiEstim, yog qhov kwv yees dhau ntawm kev tiv thaiv tsiaj txhu. Qhov tseem ceeb tshaj, nws tso cai rau peb kwv yees HIT, muab qhov ASI parameter θ=1 − ω tuaj yeem kwv yees los ntawm cov ntaub ntawv muaj. Tias cov qauv ntawm classical tej zaum yuav ua yuam kev tau taw qhia ua ntej [14], thiab qhov kev pab cuam tsis ntev los no qhia tias HIT tuaj yeem qis dua tus nqi (1) yog [10]. Cov haujlwm no qhia txog qhov no los ntawm kev sim cov qauv yooj yim uas koom nrog kev sib raug zoo (feem ntau yog cov qauv kev sib raug zoo sib xyaw, tsis yog qhov sib txawv ntawm qhov kev nkag siab), thiab yog li nws muaj kev taw qhia me me rau kev kwv yees ntawm HIT. Formula (2) yog, rau peb txoj kev paub, thawj zaug cov nyhuv no tau muab cov qauv lej. Txhawm rau ua kom tiav, peb tau txiav tawm cov qauv tshiab rau kev tiv thaiv tsiaj txhu hauv cov qauv SIR nrog ASI. Txij li cov txiaj ntsig hauv Tshooj 3 txhais tau hais tias qhov no yog qhov kwv yees zoo rau Susceptibility-stratified SIR, nws ua raws li cov qauv saum toj no siv rau cov qauv no ib yam, nrog ω muab los ntawm (8). Hauv Tshooj 4 peb ua pov thawj tus lej tias tib qhov kev txiav txim siab zoo li muaj tseeb rau lwm yam kev sib txawv, thiab yog li cov qauv no yuav yog ib qho kev xaiv zoo dua rau kev kwv yees cov tsiaj tiv thaiv kab mob ntau dua (piv txwv tias tus nqi ntawm θ tuaj yeem suav tau los ntawm cov ntaub ntawv muaj. ). Nws yog ib qho tseem ceeb uas yuav tsum nco ntsoov tias (10) siv raws li qhov kev xav tias kev tiv thaiv kab mob ua tiav los ntawm kev sib kis ntawm ntuj. Lub hom phiaj tiv thaiv kab mob tiv thaiv kab mob yog tseem muab los ntawm cov qauv classical (1) (xav tias cov tshuaj tiv thaiv kab mob ua kom tsis muaj menyuam), uas tau qhia hauv Tshooj 1.2 ntawm S1 Cov Ntaub Ntawv. Qhov no qhia tau hais tias nws nyuaj dua kom ua tiav cov tsiaj tiv thaiv kab mob los ntawm kev txhaj tshuaj, tab sis xav tau kev ua haujlwm ntau ntxiv los tsim cov txiaj ntsig no hauv kev xyaum.

3.2 Damping thiab qhov kawg loj ntawm kev sib kis

Raws li tau hais ua ntej, ntau qhov haujlwm tau tsim tias qhov kev hloov pauv hloov tau muaj qhov cuam tshuam rau qhov tshwm sim. Los ntawm cov txiaj ntsig saum toj no, tam sim no tuaj yeem suav tau. Piv txwv tias ð~S; ~ kuv; ~ RÞ yog ib qho kev daws teeb meem rau SIR nyob rau hauv ib homogenous thiab tag nrho susceptible pejxeem (yog li ~Sð{{0}}Þ ¼ N), thiab cia ~ ib tug coj tus nqi sib kis. Muab tus nqi tas li ntawm ASI θ, nws yog qhov yooj yim kom pom tias ðS; Kuv; RÞ ¼ ðo~S; o~ kuv; o~ RÞ yog ib qho kev daws teeb meem rau (3)–(5), qhov twg ω=1 − θ thiab a ¼ ~a=o. Li no cov nyhuv ntawm ASI yog tiag tiag tsis muaj dab tsi tab sis ib tug rescaling ntawm tus qauv SIR nkhaus. Nco ntsoov tias rescaling tsis hloov tus nqi ntawm R0, uas vim yog formula (9) yog muab los ntawm tiam ¼ ~ aTgeneration nyob rau hauv ob qho tib si. Nws paub zoo tias qhov kawg loj ntawm kev sib kis ~p ¼ ~ Rð1Þ=N nyob rau hauv ib txwm SIR (zoo li SEIR) yog muab los ntawm kev daws 1

Li no, ua ke nrog peb cov txiaj ntsig tseem ceeb ntawm kev txo qis ntawm Susceptibility-Stratified SIR rau SIR nrog ASI, peb txiav txim siab tias cov kev daws teeb meem saum toj no π yog qhov kwv yees zoo rau qhov kawg loj ntawm kev sib kis rau S-SIR nrog ω muab los ntawm (8) .

4 Extension rau ntau yam qauv

Rau cov kab mob xws li COVID-19, nrog rau lub sijhawm luv luv ua raws li lub sijhawm sib kis luv dua, tsuas muaj qhov sib txawv ntawm kev ua qauv siv SIR thiab siv SEIR, thiab yog li peb ntseeg tias cov lus xaus tseem ceeb ntawm daim ntawv no txuas ntxiv mus. rau tus qauv no thiab. Ib yam li ntawd, peb tau pom cov lej uas ntau dua SEIR cov qauv siv cov hnub nyoog sib txawv thiab qib kev ua haujlwm rau hauv tus account, coj zoo li SIR yog tias peb suav nrog ASI. Peb tawm hauv kev txheeb xyuas qhov tseeb ntawm cov kev soj ntsuam no ua ib qho kev xav qhib thiab nthuav qhia peb tus kheej nrog qee qhov piv txwv.

4.1 TSI

SEIR muaj ob qhov tseem ceeb sib nrug ntawm R0, uas yog Tinfectious thiab Tincubation, qhov qub yog lub sijhawm nruab nrab uas tus neeg kis tau thiab lub sijhawm kawg yog lub sijhawm txij li thaum tus neeg kis mus txog thaum nws kis tau. Kev kwv yees rau qhov sib txawv, peb ntawm no ua raws Britton thiab. al. [10] thiab teeb Tincubation=4 thiab Tinfectious=3. Tom qab ntawd nws ua raws li lub sijhawm tiam sib npaug

qhov twg lub sij hawm tiam yog lub sij hawm nruab nrab ntawm ib tug neeg kis mus txog rau thaum tus neeg ntawd kis tau rau lwm tus (saib Eq (5) nyob rau hauv cov ntaub ntawv ntxiv rau [30] rau ib tug formal derivation). Nco ntsoov tias qhov no yog raws li qhov kev xaiv ntawm Tgeneration hauv ntu dhau los. Qhov laj thawj yog vim li cas SEIR thiab SIR muab cov txiaj ntsig zoo ib yam rau COVID-19 yog tias ob qho tib si feem ntau txiav txim siab los ntawm cov txiaj ntsig ntawm Generation thiab R0. Raws li kev txawj ntse, thaum muaj kev sib kis loj, nws tsis muaj teeb meem yog tias tus neeg mob tau 7 hnub thiab kis tau R0 cov neeg nyob rau hauv 7 hnub, lossis yog tias nws raug incubation rau 4 hnub thiab kis tau R{{11} } cov neeg nyob rau hauv 3 hnub ntxiv. Ua piv txwv, xav txog daim duab 3(a); peb pom tus cwj pwm zoo sib xws los ntawm kev xaiv cov kev txwv rau SIR thiab SEIR raws li cov qauv saum toj no (nrog R0 tsau). Ntxiv mus, los ntawm kev tso cai tsis pub dawb, SIR tuaj yeem ua kom coj tus cwj pwm yuav luag zoo ib yam li SEIR (txawm tias tsis koom nrog ASI). Txhawm rau txhawb qhov kev thov no, tsis yog qhov yuav luag zoo tag nrho sib tshooj ntawm xiav thiab dub nkhaus hauv daim duab 3, tau txais los ntawm kev ua kom Regeneration ruaj thiab hloov kho R0 los ntawm ib feem pua. Txij li tus nqi tiag tiag rau cov khoom nkag tsis paub tseeb hauv qhov tseeb, peb sib cav tias nws tsis cuam tshuam txawm tias ib tus siv SIR lossis SEIR, yam tsawg kawg rau kev ua qauv SARS-CoV-2 thiab cov kab mob uas muaj cov yam ntxwv zoo sib xws. Yog li ntawd, kev soj ntsuam ntawm daim ntawv no yuav tsum txuas mus rau SEIR ib yam nkaus, txawm tias peb tsis tuaj yeem tsim cov lej no.

4.2 Heterogeneous qauv

Kev hloov pauv tsis zoo tsis yog tib hom ntawm cov pej xeem heterogeneity uas tuaj yeem pom nws tus kheej li ASI ntawm qib macro. Hauv [10] cov kws sau ntawv tsim cov qauv SEIR heterogeneous coj cov qauv sib txawv ntawm cov pab pawg hnub nyoog sib txawv rau hauv tus account, nrog rau qhov tseeb tias tib neeg hauv txhua pab pawg hnub nyoog muaj ntau qhov sib txawv. Peb tau siv lawv cov qauv thiab tom qab ntawd nrhiav cov kev txwv rau SIR nrog ASI uas yuav ua rau muaj txiaj ntsig zoo sib xws. Cov txiaj ntsig tau pom hauv daim duab 3(b). Ntxiv dua thiab, qhov sib txawv yog qhov zoo uas nws yuav tsis tuaj yeem pom hauv kev xyaum. Txij ntawm no mus, dab tsi yuav tshwm sim raws li qee theem ntawm cov pej xeem (pre-) kev tiv thaiv hauv cov qauv lej yuav, qhov tseeb, yog kev sib xyaw ntawm ntau haiv neeg sib txawv, nyob rau hauv qhov sib txawv ntawm qhov kev raug mob tsuas yog ib qho khoom xyaw xwb.

Fig 3. Kev kwv yees siv SIR nrog ASI. (a) SEIR nrog R0=1.66 thiab Tinfectious + Tinfective=7 (xiav), SIR nrog tib R0 thiab Tgeneration=7 (liab), thiab thaum kawg SIR nrog 1% qis R0, tib Tgeneration (dub). (b) Hnub nyoog-kev ua si stratified SEIR nrog R{{10}}.66 thiab Tinfectious + Tinfective=7 (xiav); SIR siv tib Tgeneration tab sis ASI ntawm 25% thiab txawv me ntsis R0 (dub).

5 Kev sib tham

Tej zaum yuav muaj ntau yam laj thawj vim li cas qee tus neeg muaj kev pheej hmoo ntau dua li lwm tus kis los ntawm tus kab mob tshiab, xws li kev tiv thaiv kab mob hauv lub cev thiab hloov mus rau kev tiv thaiv kab mob sib kis los ntawm lwm cov kab mob uas paub txog thiab kev sib txawv ntawm caj ces. Rau ib tus kab mob tshiab, ua kom tsis muaj kab mob ua ntej, piv txwv li cov tib neeg uas tiv thaiv kab mob tsis tau muaj tus kab mob, feem ntau yuav tsis muaj nyob. Lub ntsiab lus tseem ceeb ntawm txoj kev tshawb no yog tias kev ua kom tsis muaj menyuam tiv thaiv ib tus neeg tsis xav tau txhawm rau txhawm rau soj ntsuam qhov zoo li kev tiv thaiv kab mob tsis zoo ntawm cov pej xeem, uas peb tau tsim ASI; artificial sterilizing tiv thaiv kab mob. Peb qhia lej tias, txhawm rau kom muaj ASI, peb tsuas yog xav tau kev hloov pauv me ntsis hauv kev raug mob. Tsis tas li ntawd, peb pom cov lej uas lwm hom pejxeem heterogeneities, xws li cov qauv sib txawv ntawm kev sib raug zoo, kuj qhia lawv tus kheej li ASI.

cistanche cog-nce kev tiv thaiv kab mob

Cov kev tshawb pom hauv daim ntawv no tsis txwv lawv tus kheej rau SARS-CoV-2 tab sis qhov tseem ceeb qhia tau tias cov qauv qub rau kev tiv thaiv tsiaj txhu thiab cov qauv rau kev sib kis ntawm cov kab mob nrog cov hauv paus hniav hauv cov ntawv nto moo los ntawm Kermack thiab McKendrick [1 ] tsis muaj peev xwm ua qauv ntawm cov kab mob sib kis uas ua rau muaj kev hloov pauv loj hauv kev cuam tshuam, thiab yuav tsum tau hloov kho raws li tau piav qhia hauv Tshooj 3.1. Kev kwv yees ntawm kev tiv thaiv kab mob HIT yog qhov tseem ceeb rau kev tswj xyuas kab mob kom zoo thiab kev npaj. Piv txwv li, yog tias ib lub zej zog txiav txim siab kaw ua ntej HIT mus txog, nws yuav luag paub tseeb tias tus kab mob yuav rov tshwm sim tshwj tsis yog NPIs raug tswj xyuas tas li. Cov mis mos classical (1) tseem siv ntau heev, txawm tias qhov tseeb tias nws paub tias vam khom ntau qhov kev xav uas yuav ua rau muaj qhov tsis raug. Peb tau tsim ib qho qauv tshiab uas peb ua pov thawj siv tau thaum muaj kev hloov pauv hloov tau. Txij li thaum peb qhia tias peb tus qauv yooj yim, SIR nrog ASI, kuj zoo li yog qhov zoo hloov pauv rau cov qauv uas muaj cov qauv sib txawv sib txawv, nws muaj peev xwm hais tias (2) feem ntau siv ntau tshaj qhov peb muaj peev xwm ua pov thawj lej.

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