COVID Transmission Modeling: An Insight into Infectious Diseases Mechanism

385 Pages·2022·16.723 MB·English

by  B. Narasimha Murthy, DM Basavarajaiah

COVID Transmission
Modeling

COVID Transmission
Modeling
An Insight into Infectious Diseases
Mechanism
DM Basavarajaiah
B Narasimha Murthy
First edition published 2022
by CRC Press
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and by CRC Press
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CRC Press is an imprint of Taylor & Francis Group, LLC
© 2022 DM Basavarajaiah and B Narasimha Murthy
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Library of Congress Cataloging‑in‑Publication Data
Names: Basavarajaiah, DM, author. | Murthy, B. Narasimha, author.
Title: COVID transmission modeling : an insight into infectious diseases mechanism /
DM Basavarajaiah, B. Narasimha Murthy.
Description: First edition. | Boca Raton : Chapman & Hall\CRC Press, 2022. |
Includes bibliographical references and index. |
Summary: “This book will explore and formulate new mathematical/statistical and epidemiological modelling based
on the research findings. It covers all the aspects of mitigation, estimation of transmission rate, control measures,
economic impact assessment, genetic complexity of COVID and herd immunity”—Provided by publisher.
Identifiers: LCCN 2021058806 (print) | LCCN 2021058807 (ebook) |
ISBN 9781032069708 (hardback) | ISBN 9781032069746 (paperback) | ISBN 9781003204794 (ebook)
Subjects: LCSH: COVID-19 (Disease)—Transmission. | Coronavirus infections—Prevention. |
COVID-19 (Disease)—Economic aspects.
Classification: LCC RA644.C67 B365 2022 (print) | LCC RA644.C67 (ebook) |
DDC 362.1962/414—dc23/eng/20220121
LC record available at https://lccn.loc.gov/2021058806
LC ebook record available at https://lccn.loc.gov/2021058807
ISBN: 9781032069708 (hbk)
ISBN: 9781032069746 (pbk)
ISBN: 9781003204794 (ebk)
DOI: 10.1201/9781003204794
Typeset in Palatino
by codeMantra
Dedicated to
All victims of Novel Coronavirus 2019

Contents
Preface .............................................................................................................................................xv
Acknowledgments .....................................................................................................................xvii
Authors .........................................................................................................................................xix
1. Mathematical Modeling Approach to COVID-19: Vetted Real Data ..........................1
1.1 Introduction ...................................................................................................................1
1.1.1 Main Objectives of This Book ........................................................................3
1.2 Anatomical Structure of COVID-19 Virus ...............................................................10
1.3 Virus Incubation Period .............................................................................................11
1.3.1 Disease Carriers .............................................................................................12
1.3.2 Case Fatality Rate (CFR, %) ..........................................................................14
1.3.3 COVID-19 Transmission Mechanisms ........................................................15
1.4 Epidemiological Aspects of nCov2019 (SARS-Cov-19) ..........................................15
1.5 Economic Impacts of Novel Coronavirus ................................................................17
1.6 Mathematical Model for the Prediction of Novel Coronavirus (nCov2019) .......18
1.6.1 Variables Used for Model Building .............................................................19
1.6.2 Endemic and Epidemic Equilibria ..............................................................21
1.7 Model Discussion ........................................................................................................25
1.7.1 Model Conclusions ........................................................................................26
1.8 Epidemiological Model for the Estimation of Hazard Rate and Geometric
Progression of nCov2019 ............................................................................................27
1.8.1 Formulation of the Epidemiological Risk Assessment COVID Model ....28
1.9 Epidemiological Model Approach of New Diseases .............................................36
1.9.1 Model Formulation ........................................................................................37
1.9.1.1 Latent growth model of novel coronavirus ..................................38
1.9.2 Gauss–Markov Theorem (GMT) ..................................................................38
1.9.3 Maximum Likelihood Estimation (MLE) of
Gauss–Markov Theorem (GMT) ..................................................................43
1.9.4 Gauss–Markov Weighted Least Squares Analysis ...................................44
1.10 Susceptible–Infective–Recovered (SIR) Epidemiological Model of COVID .......47
1.10.1 Model Formulation ........................................................................................49
1.10.2 SIR Model Discussion ...................................................................................50
1.11 EP Model with Varying Population .........................................................................52
1.11.1 Reproduction Number Approach to Binomial Distribution (R ) ............53
0
1.12 Machine Learning Model for SARS-Cov-19 ............................................................57
1.12.1 Machine Learning Model .............................................................................59
1.13 Models of Machine Learning ....................................................................................59
( )
1.13.1 Measurement Error u ..................................................................................60
( )
1.13.2 Stochastic Error u ........................................................................................60
1.13.3 Hidden Gauss–Markov Theorem (HGMT) ................................................62
1.14 COVID-19 Mathematical Model Approach to Selective Sample ..........................65
1.14.1 Model Formulation ........................................................................................66
1.15 Recommendations.......................................................................................................72
vii
viii Contents
1.16 Study Limitations ........................................................................................................74
1.17 Conflict of Interest .......................................................................................................74
References ...............................................................................................................................74
2. Time Series Stochastic Projection Models for the Estimation of COVID Trend ....79
2.1 Introduction .................................................................................................................79
2.2 Time Series Stochastic Models ..................................................................................80
2.2.1 Exponential Smoothing by Bootstrap Techniques ....................................80
2.2.2 Holt–Winters (HW) Triple Exponential Smoothing Method ..................80
2.3 ARIMA Forecasting Model Approach to COVID Progression Estimation ........81
2.4 Model Discussion ........................................................................................................92
2.5 Conclusions ..................................................................................................................92
2.6 Random Walk Markov Chain Stochastic Transient (RMCST) Model .................92
2.7 Optimization of COVID Cases from Transition Matrix ........................................95
2.8 Model Diagnostic Test ................................................................................................96
2.9 Discussion ....................................................................................................................96
2.10 Conclusions ..................................................................................................................97
References ...............................................................................................................................98
3. Study of Anxiety and Fear of COVID-19 .......................................................................101
3.1 Introduction ...............................................................................................................101
3.2 Methods ......................................................................................................................102
3.3 Results .........................................................................................................................103
3.4 Discussion ..................................................................................................................111
3.5 Conclusions ................................................................................................................113
References .............................................................................................................................114
4. COVID-19 Gene Sequencing Modeling ........................................................................117
4.1 Introduction ...............................................................................................................117
4.2 Maxam and Gilbert Method ....................................................................................118
4.3 Sanger Sequencing ....................................................................................................118
4.3.1 Chain Termination PCR ..............................................................................119
4.3.2 Separation Based on Size Using Gel Electrophoresis .............................120
4.3.3 Analysis of Gel and Identification of DNA Sequence ............................120
4.4 Long-Read Sequencing Methods ............................................................................121
4.4.1 Single-Molecule Real-Time (SMRT) Sequencing .....................................122
4.4.2 Nanopore DNA Sequencing .......................................................................122
4.4.3 Merits of Nanopore DNA Sequencing ......................................................122
4.4.4 Massive Parallel Signature Sequencing (MPSS) ......................................123
4.4.5 Statistical Methods for Testing MPSS Data ..............................................125
4.5 Cauchy Distribution .................................................................................................126
4.6 Exponential Distribution .........................................................................................127
4.7 Gamma Distribution ................................................................................................128
4.8 Log-Normal Distribution .........................................................................................129
4.9 Logistic Distribution .................................................................................................131
4.10 Poisson Distribution .................................................................................................132
4.11 Weibull Distribution Model ....................................................................................133
4.12 Next-Generation Sequencing ..................................................................................134
4.13 Illumina Solexa Sequencing ....................................................................................134
4.13.1 Procedure for Illumina Sequencing ..........................................................136
Contents ix
4.14 Model Formulation ...................................................................................................140
4.15 Pyrosequencing .........................................................................................................144
4.16 Gene Sequencing Alignment ..................................................................................145
4.17 Alignment Parameters .............................................................................................146
4.18 COVID Sequencing ...................................................................................................146
4.19 Gene Alignment and Its Applications ...................................................................148
4.19.1 Global Alignment ........................................................................................148
4.19.2 Scoring Matrices ...........................................................................................149
4.20 Whole Genomic Analysis (WGA) ...........................................................................149
4.21 Discussion ..................................................................................................................155
4.22 Conclusions ................................................................................................................158
References .............................................................................................................................158
5. Real-Time PCR (RT-PCR) for COVID-19 Diagnosis and Changes in
Threshold Cycle (C) in Association with Different Parameters ..............................163
t
5.1 Introduction ...............................................................................................................163
5.2 A High Threshold Value of C in COVID-19..........................................................165
t
5.3 Model Formulation ...................................................................................................166
5.4 Model Output ............................................................................................................168
5.5 Discussion ..................................................................................................................171
5.6 Conclusions ................................................................................................................172
References .............................................................................................................................173
6. COVID-19 Vaccination Modeling Approach to Public Health Policy .....................175
6.1 Introduction ...............................................................................................................175
6.2 What Else Does a Vaccine Contain? .......................................................................177
6.3 Model Formulation—Need for Model Formulation ............................................178
6.4 Methods ......................................................................................................................179
6.5 Determination of Vaccination Effects by Statistical Tools or Methods .............184
6.6 Herd Immunity .........................................................................................................184
6.7 COVID Vaccination Predictive Statistical Models ................................................194
6.8 Model Construction ..................................................................................................195
6.9 Projection Modeling of COVID Vaccination .........................................................205
6.10 Model Output ............................................................................................................206
6.11 Real Probability of Bayes for Estimation of Vaccination Effect .........................209
6.12 Bayes Stochastic Vaccination Model .......................................................................210
6.13 Discussion ..................................................................................................................212
6.14 Conclusions ................................................................................................................215
6.15 Recommendations.....................................................................................................215
References .............................................................................................................................215
7. Trend of COVID-19 Surge Projection ............................................................................217
7.1 Introduction ...............................................................................................................217
7.2 Model Construction ..................................................................................................220
7.3 Bayes Weighted Regression Model .........................................................................221
7.4 Model Results ............................................................................................................226
7.4.1 Projective Model of the Third Wave by Using I Score ..........................231
A
7.4.2 Calculation Summary .................................................................................231
7.5 Discussion ..................................................................................................................232
7.6 Conclusions ................................................................................................................234
References .............................................................................................................................235