This book deals with the prediction of possible future scenarios concerning the COVID-19 pandemic. Based on the well-known SIR model by Kermack and McKendrick a compartment model is established. This model comprises its own assumptions, transition rates and transmission dynamics, as well as a corresponding system of ordinary differential equations. Making use of numerical methods and a nonstandard-finite-difference scheme, two submodels are implemented in Matlab in order to make parameter estimations and compare different scenarios with each other.
Author(s): Sarah Marie Treibert
Series: BestMasters
Publisher: Springer Spektrum
Year: 2021
Language: English
Pages: 266
City: Wiesbaden
Contents
Abbreviations
List of Figures
List of Tables
1 Introduction
1.1 Thematic Background
1.2 Methods, Structure and Objectives
1.2.1 Methods
1.2.2 Structure
1.2.3 Objectives
2 The Severe Acute Respiratory Syndrome Corona Virus Type 2
2.1 Worldwide Incidence of the Novel Corona Virus
2.2 Aetiology and Transmission Paths
2.3 Disease Process and Symptomatology
2.3.1 Progression of the Corona Virus Disease 2019
2.3.2 Symptoms of the Corona Virus Disease 2019
2.4 Policies of Containing the Corona Virus Disease 2019
2.4.1 Clinical Diagnosis
2.4.2 Governmental Measures in Sweden and Germany
2.4.3 The Stringency Index
2.4.4 Vaccines and Vaccination Strategies
2.4.5 Mutations
2.5 Lethality in Corona Virus Disease 2019 Cases
2.5.1 Case-fatality in Corona Virus Disease 2019 Cases
2.5.2 Uncertainty in Case-fatality Computations
2.5.3 Excess Mortality
3 The SIR Model in Epidemic Modelling
3.1 The Basic SIR Model
3.1.1 Definition of the Basic SIR Model
3.1.2 Maximum number of infections in the Basic SIR Model
3.1.3 Incidence Rates
3.2 Simple Enhancements to the Basic SIR Model
3.2.1 SIRD Model
3.2.2 SEIR Model
3.2.3 SEIS Model
3.2.4 Stages Related to Disease Progression and Control Strategies
4 The SARS-CoV-2- tted SEIR Model
4.1 Differences to the Basic SIR Model and Model Assumptions
4.2 Compartments and Transitions in the SARS-CoV-2-fitted SIR Model
4.2.1 Sojourn Times
4.2.2 Distributions of the Incubation Period and the Serial Interval
4.2.3 The Susceptible Compartments
4.2.4 The Exposed Compartments
4.2.5 The Asymptomatic Infectious Compartments
4.2.6 The Symptomatic Compartments
4.2.7 The Hospitalized Compartment
4.2.8 The Intensive Care Unit Compartment
4.2.9 The Recovered Compartment
4.2.10 The Compartment of Deceased Individuals
4.2.11 The Compartment of Vaccinated Individuals
4.2.12 Overview of Compartments
4.3 Transmission in the SARS-CoV-2-fitted Model
4.3.1 Transmission Risk
4.3.2 Contact, Quarantine and Isolation Rates
4.3.3 Transmission Rates
4.3.4 Time Delay
5 Model Speci cations
5.1 Model Variants
5.1.1 Exclusion of Quarantine or the Quarantine Compartment
5.1.2 Pooling of Isolated and not Isolated Compartments
5.1.3 Exclusion of Unconfirmed Infected Cases
5.1.4 Pooling of Infected Compartments
5.2 Systems of Ordinary Differential Equations
5.2.1 Formulation of the Initial Value Problem
5.2.2 The S V I H C D R Model and the S V tildeAI II HCDR Model
5.2.3 The SARS-CoV-2-fitted Model
5.2.4 Age Group Model
5.3 Reproduction Numbers
6 Parameter Estimation in MATLAB
6.1 Problem Formulation and Implementation Process
6.1.1 The Nonlinear Least Squares Approach to Compartment Models
6.1.2 The Implementation Process
6.2 Parameter Definitions and Bounds
6.2.1 Parameters in the SIHCDR Model
6.2.2 Parameters in the SVID Age Group Model
6.3 Compartment Size Predictions with the S I H C D R Model
6.3.1 Prediction of the Second Wave
6.3.2 Prediction of the Third Wave
6.4 Compartment Size Predictions with the SVID Age Group Model
6.5 Application of Non-Standard Solvers
6.5.1 Definition of Nonstandard Finite Difference Schemes
6.5.2 Implementation of a Nonstandard Finite Difference Scheme for the SIHCDR Model
7 Markov Chain Epidemic Models
7.1 Multi-state Models
7.2 The Bayesian Inference Approach to Compartment Models
7.3 The Metropolis-Hastings Algorithm
8 Résumé
8.1 Conclusion
8.2 Future Work
A Bibliography
