Preface

Acknowledgements

Contents

1 Introduction

1.1 Definitions

1.2 Historical notes

1.3 Identifiability in mathematical epidemiology

1.4 The concept of observers

2 Mathematical foundations

2.1 Preliminaries

2.2 Observability

2.3 About identifiability

2.4 Identifiability does not necessarily require observability

2.5 Identifiability via decoupled variables

3 Analysis of the Kermack-McKendrick model

3.1 History

3.2 The different forms of the SIR model

3.3 Observability and identifiability of the SIR model

4 Observers synthesis

4.1 Introduction

4.2 Observers with linear error dynamics

4.3 Observers for systems with Lipschitz non-linearity

4.4 Observers via decoupled variables

4.5 Reduced-order observers

4.6 The high-gain observer for nonlinear systems

4.7 Discussion

5 Practical and numerical considerations

5.1 Practical identifiability

5.2 Observers in practice

5.3 A case study: An observer to estimate state and parameter