Modeling Control, Lockdown & Exit Strategies for COVID-19 Pandemic in India
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Abstract
COVID-19–a viral infectious disease–has quickly emerged as a global pandemic infecting millions of people with a significant number of deaths across the globe. The symptoms of this disease vary widely. Depending on the symptoms an infected person is broadly classified into two categories namely, asymptomatic and symptomatic. Asymptomatic individuals display mild or no symptoms but continue to transmit the infection to other-wise healthy individuals. This particular aspect of asymptomatic infection poses a major obstacle in managing and controlling the transmission of the infectious disease. In this paper, we attempt to mathematically model the spread of COVID-19 in India under various intervention strategies. We consider SEIR type epidemiological models, incorporated with India specific social contact matrix representing contact structures among different age groups of the population. Impact of various factors such as presence of asymptotic individuals, lockdown strategies, social distancing practices, quarantine, and hospitalization on the disease transmission is extensively studied. Numerical simulation of our model is matched with the real COVID-19 data of India till May 15, 2020 for the purpose of estimating the model parameters. Our model with zone-wise lockdown is seen to give a decent prediction for July 20, 2020.
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SciScore for 10.1101/2020.07.25.20161992: (What is this?)
Please note, not all rigor criteria are appropriate for all manuscripts.
Table 1: Rigor
Institutional Review Board Statement not detected. Randomization not detected. Blinding not detected. Power Analysis not detected. Sex as a biological variable not detected. Table 2: Resources
No key resources detected.
Results from OddPub: We did not detect open data. We also did not detect open code. Researchers are encouraged to share open data when possible (see Nature blog).
Results from LimitationRecognizer: An explicit section about the limitations of the techniques employed in this study was not found. We encourage authors to address study limitations.Results from TrialIdentifier: No clinical trial numbers were referenced.
Results from Barzooka: We did not find any issues relating to the usage of bar …
SciScore for 10.1101/2020.07.25.20161992: (What is this?)
Please note, not all rigor criteria are appropriate for all manuscripts.
Table 1: Rigor
Institutional Review Board Statement not detected. Randomization not detected. Blinding not detected. Power Analysis not detected. Sex as a biological variable not detected. Table 2: Resources
No key resources detected.
Results from OddPub: We did not detect open data. We also did not detect open code. Researchers are encouraged to share open data when possible (see Nature blog).
Results from LimitationRecognizer: An explicit section about the limitations of the techniques employed in this study was not found. We encourage authors to address study limitations.Results from TrialIdentifier: No clinical trial numbers were referenced.
Results from Barzooka: We did not find any issues relating to the usage of bar graphs.
Results from JetFighter: We did not find any issues relating to colormaps.
Results from rtransparent:- Thank you for including a conflict of interest statement. Authors are encouraged to include this statement when submitting to a journal.
- Thank you for including a funding statement. Authors are encouraged to include this statement when submitting to a journal.
- No protocol registration statement was detected.
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SciScore for 10.1101/2020.07.25.20161992: (What is this?)
Please note, not all rigor criteria are appropriate for all manuscripts.
Table 1: Rigor
NIH rigor criteria are not applicable to paper type.Table 2: Resources
Experimental Models: Organisms/Strains Sentences Resources γsr + η + d3 )Ii (t), (3.1) Ṙi (t) = γar Ai (t) + γsr Ii (t) − d4 Ri (t), Ḋi (t) = ηIi (t), subject to the following initial conditions at time t = 0: Si = Si0 ≥ 0, Ei = Ei0 ≥ 0, Ai = Ai0 ≥ 0, Ii = Ii0 ≥ 0, Ri = Ri0 ≥ 0, Di = Di0 ≥ 0. γsr + η + d3 )Iisuggested: NoneLet tin g N ̂i( t ) = N i (t )− Di(t),iti s easytos eetha td N̂i ≤Λ−dN ̂i,whe re d = mind0, d1, d2,η+d 3, d4. d1 , d2 , η + d3…SciScore for 10.1101/2020.07.25.20161992: (What is this?)
Please note, not all rigor criteria are appropriate for all manuscripts.
Table 1: Rigor
NIH rigor criteria are not applicable to paper type.Table 2: Resources
Experimental Models: Organisms/Strains Sentences Resources γsr + η + d3 )Ii (t), (3.1) Ṙi (t) = γar Ai (t) + γsr Ii (t) − d4 Ri (t), Ḋi (t) = ηIi (t), subject to the following initial conditions at time t = 0: Si = Si0 ≥ 0, Ei = Ei0 ≥ 0, Ai = Ai0 ≥ 0, Ii = Ii0 ≥ 0, Ri = Ri0 ≥ 0, Di = Di0 ≥ 0. γsr + η + d3 )Iisuggested: NoneLet tin g N ̂i( t ) = N i (t )− Di(t),iti s easytos eetha td N̂i ≤Λ−dN ̂i,whe re d = mind0, d1, d2,η+d 3, d4. d1 , d2 , η + d3suggested: Noneγsr + η + d3 ) β(χ + d1 )( γsr + η + d3 ) β(χ + d1 )suggested: Noneγsr + η + d3 ) + β(χ + d1 )γas = , (χ + d1 )(γar + γas + d2 )( γsr + η + d3 ) + β(χ + d1suggested: Noneγsr + η + d3 ) β(χ + d1 )(γar + γas + d2 ) = . γsr + η + d3 ) β(χ + d1suggested: Noneγsr + η + d3 ) a11 = a12 a13 R0 is the maximum of the absolute eigenvalues of the next generation matrix F W −1 . γsr + η + d3 ) a11 = a12 a13 R0suggested: Noneγsr + η + d3 ) (3.3) If Λ = 0, dj = 0 (j = 0, 1, 2, 3, 4), then R0 = βα βγar (1 − α) + βγas γsr + η + d3suggested: NoneThe non-zero roots, also three in number, are obtained as roots of the cubic equation y 3 + a1 y 2 + a2 y + a3 = 0, (3.5) whose coefficients a1 , a2 , a3 are as follows: a1 = γar + γas + χ + y 3 + a1 y 2 + a2 y + a3suggested: Noneγsr + η − β > 0. γsr + η − β > 0suggested: None− d0 S ∗ , N β ∗ (A + I ∗ )S ∗ − (χ + d1 )E ∗ , N 0 = αχE ∗ − (γar + γas + d2 )A∗ , 0= ∗ ∗ (3.11) ∗ 0 = (1 − α)χE + γas A − (γsr + η + d3 )I , 0 = γar A∗ + γsr I ∗ − d4 R∗ . γsr + η + d3 )Isuggested: NoneβAN +βI N − (χ+ d 1 ) β S Nβ SN 0. AN + β IN − ( χ + d1suggested: NoneOth ere i g env a l u e s ar er ootsofthe e quation βχS∗( λ+ d0) λ+αm4 +(1−α) m3 + α γas=0λ +m1 (λ+m2) (λ +m3)(λ+m4)− N( 3.15 )whereβA∗βI∗ m1=++ d0> 0,m2=χ +d 1>0 ,NN(3 .16 )m3=γar+γa s+ d2> 0,m4=γ sr+η+d3> 0,Mo r e s u cc i nct ly,equation(3.1 5)mayb eexp re ssedasλ4 +a1λ3+a2λ2+a3 λ+ a4= 0 ,(3.17)w ithcoefficie nts a1=m1+m 2+ m3 + m 4 , βχ S ∗, Nβχ S∗a3=(m1+m2)m3m 4+(m3+ m4 )m1m 2− (αm4+(1−α )m3 +αγas+d0),Nβ χS∗(αm4 +(1−α)m3+α γas) .∗ ∗N(A +I )R0χαm4+(1−α) m3 +αγa s(3.1 9)Makinguseo f(3.19),expre ss i on sof a3,a4ma yberew ri tteninthefo llowingf or m establ ishingth eirpositiv ityβχS ∗βχ S∗ a3= m1(m3m 4+m2m3+m2m 4)−d0>d 0m 3 m4+m2m3+m2 m4−>0 ,N NβA∗βI∗a 4=m1m2m3m4−d 0m2 m3m4=+m2m3m4 >0. m1 ( λ + m2 ) ( λ + m3 ) ( λ + m4 ) − Nsuggested: NoneβI ∗ m1 = + + d0 > 0 , m2 = χ + d1 > 0suggested: Noneλ4 + a1 λ3 + a2 λ2 + a3 λ + a4 = 0suggested: Nonem1 + m2 + m3 + m4suggested: Nonem1 + m2 )m3 m4 + ( m3 + m4 )m1 m2 −suggested: NoneβχS ∗ a3 = m1 ( m3 m4 + m2 m3 + m2 m4 ) − d0 > d0 m3 m4 + m2 m3 + m2 m4 − > 0suggested: Nonem1 m2 m3 m4 − d0 m2 m3 m4 = + m2 m3 m4 > 0suggested: NoneFin all y , toe s t a b l is ht helastcon d itionin theRo ut h-H urwit zCrite ri o n (3.18) ,it isenou gh toverifythe fo llow ingtwoinequa litie s:a 1a2a3> 2a 23⇒ a1a2> 2a3 ,(3.20)a1a 2a 3>2 a21a4⇒ a2a3>2a1 a4.( 3 . 2 1 )T o pro veinequality(3. 20),we begi nw ithβχS∗a 1a2−2a3=(m1+m 2+ m3+ m 4)(m1+m2 )(m3+m4)+m1m 2+m 3m4−−N2 m1 m3 m 4 + ( m3 + m4 )m1 m2. a1 a2 a3 > 2a23 ⇒ a1 a2 > 2a3suggested: Nonea2 a3 > 2a21 a4 ⇒ a2 a3 > 2a1 a4suggested: NoneβχS ∗ a1 a2 − 2a3 = ( m1 + m2 + m3 + m4 ) ( m1 + m2 ) ( m3 + m4 ) + m1 m2 + m3 m4 − − N 2 m1 m3 m4 + ( m3 + m4 )m1 m2suggested: NoneFol low i n gso m e s i m pl ea lgebraicm a nipulat ions, we get 12a1a 2−2a3= m1 m 3 +m21m4 +m2 1m2+m1 m2 2+m1m23+m1m 24 +m3m 24+m23m4+P1m 1m3m4 +m2 m3m4(α m4 +(1 −α)m3 +αγ as)+C1,whe re P1= αm4+(1 −α)m3+αγ asan d C 1 = (m 2 2m3 a2 − 2a3 = m1 m3 + m21 m4 + m21 m2 + m1 m22 + m1 m23 + m1 m24 + m3 m24 + m23 m4 + P1 m1 m3 m4 + m2 m3 m4suggested: Nonem22 m3( 1 − α)m 3 + α γ a s+ m2 2m4(αm4+α γ as)+2m2 m3(1− α) m3+ αγas+ m2m3m4 (α m 4 +αγas) +m2 m24(αm 4+ αγas)+m2m3m 4( 1−α) m3+αγas>0. m22 m3 ( 1 − α)m3 + αγas + m22 m4suggested: NoneNex twe r e wri t e t h e ex pr essionfor a 2a3−2a1 a4βχS ∗m 1m3 m4+a2 a3−2a1 a4 = ( m1+m2) (m3 +m4)+m 1m 2+m3m4−N(m3 +m 4)m1 m2−2(m1+m2+m 3+m4) (m1 m2m3m4 −d 0m2 m3m4) . a2 a3 − 2a1 a4 βχS ∗ m1 m3 m4 + a2 a3 − 2a1 a4 = ( m1 + m2 ) ( m3 + m4 ) + m1 m2 + m3 m4 − N ( m3 + m4 )m1 m2 − 2 ( m1 + m2 + m3 + m4 ) ( m1 m2 m3 m4 − d0 m2 m3 m4suggested: NoneSoftware and Algorithms Sentences Resources Analysis based on real data In this subsection, we numerically simulate (using Python based solver) the SEAIRD control model (4.1) laced with the social distancing function (4.3) and match the computed results with real COVID-19 data of India till May 15, 2020. Pythonsuggested: (IPython, RRID:SCR_001658)Results from OddPub: We did not detect open data. We also did not detect open code. Researchers are encouraged to share open data when possible (see Nature blog).
Results from LimitationRecognizer: An explicit section about the limitations of the techniques employed in this study was not found. We encourage authors to address study limitations.
Results from Barzooka: We did not find any issues relating to the usage of bar graphs.
Results from JetFighter: We did not find any issues relating to colormaps.
About SciScore
SciScore is an automated tool that is designed to assist expert reviewers by finding and presenting formulaic information scattered throughout a paper in a standard, easy to digest format. SciScore is not a substitute for expert review. SciScore checks for the presence and correctness of RRIDs (research resource identifiers) in the manuscript, and detects sentences that appear to be missing RRIDs. SciScore also checks to make sure that rigor criteria are addressed by authors. It does this by detecting sentences that discuss criteria such as blinding or power analysis. SciScore does not guarantee that the rigor criteria that it detects are appropriate for the particular study. Instead it assists authors, editors, and reviewers by drawing attention to sections of the manuscript that contain or should contain various rigor criteria and key resources. For details on the results shown here, including references cited, please follow this link.
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SciScore for 10.1101/2020.07.25.20161992: (What is this?)
Please note, not all rigor criteria are appropriate for all manuscripts.
Table 1: Rigor
NIH rigor criteria are not applicable to paper type.Table 2: Resources
Software and Algorithms Sentences Resources Analysis based on real data In this subsection, we numerically simulate (using Python based solver) the SEAIRD control model (4.1) laced with the social distancing function (4.3) and match the computed results with real COVID-19 data of India till May 15, 2020. Pythonsuggested: (IPython, SCR_001658)Data from additional tools added to each annotation on a weekly basis.
About SciScore
SciScore is an automated tool that is designed to assist expert reviewers by finding and presenting formulaic information …
SciScore for 10.1101/2020.07.25.20161992: (What is this?)
Please note, not all rigor criteria are appropriate for all manuscripts.
Table 1: Rigor
NIH rigor criteria are not applicable to paper type.Table 2: Resources
Software and Algorithms Sentences Resources Analysis based on real data In this subsection, we numerically simulate (using Python based solver) the SEAIRD control model (4.1) laced with the social distancing function (4.3) and match the computed results with real COVID-19 data of India till May 15, 2020. Pythonsuggested: (IPython, SCR_001658)Data from additional tools added to each annotation on a weekly basis.
About SciScore
SciScore is an automated tool that is designed to assist expert reviewers by finding and presenting formulaic information scattered throughout a paper in a standard, easy to digest format. SciScore is not a substitute for expert review. SciScore checks for the presence and correctness of RRIDs (research resource identifiers) in the manuscript, and detects sentences that appear to be missing RRIDs. SciScore also checks to make sure that rigor criteria are addressed by authors. It does this by detecting sentences that discuss criteria such as blinding or power analysis. SciScore does not guarantee that the rigor criteria that it detects are appropriate for the particular study. Instead it assists authors, editors, and reviewers by drawing attention to sections of the manuscript that contain or should contain various rigor criteria and key resources. For details on the results shown here, including references cited, please follow this link.
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