PREDICTION OF INFECTIOUS DISEASE OUTBREAKS BASED ON LIMITED INFORMATION VINCENT-ANTHONY MARMARÀ Doctor of Philosophy Mathematics University of Stirling September 2016 i DECLARATION I, Vincent-Anthony Marmarà, confirm that the work presented in this thesis is, to the best of my knowledge, original. Where information has been derived from other sources, I confirm that this has been indicated in the thesis. ______________________________ Vincent-Anthony Marmarà September 2016 ii ABSTRACT The last two decades have seen several large-scale epidemics of international impact, including human, animal and plant epidemics. Policy makers face health challenges that require epidemic predictions based on limited information. There is therefore a pressing need to construct models that allow us to frame all available information to predict an emerging outbreak and to control it in a timely manner. The aim of this thesis is to develop an early-warning modelling approach that can predict emerging disease outbreaks. Based on Bayesian techniques ideally suited to combine information from different sources into a single modelling and estimation framework, I developed a suite of approaches to epidemiological data that can deal with data from different sources and of varying quality. The SEIR model, particle filter algorithm and a number of influenza-related datasets were utilised to examine various models and methodologies to predict influenza outbreaks. The data included a combination of consultations and diagnosed influenza-like illness (ILI) cases for five influenza seasons. I showed that for the pandemic season, different proxies lead to similar behaviour of the effective reproduction number. For influenza datasets, there exists a strong relationship between consultations and diagnosed datasets, especially when considering time- dependent models. Individual parameters for different influenza seasons provided similar values, thereby offering an opportunity to utilise such information in future outbreaks. Moreover, my findings showed that when the temperature drops below 14°C, this triggers the first substantial rise in the number of ILI cases, highlighting that temperature data is an important signal to trigger the start of the influenza epidemic. Further probing was carried out among Maltese citizens and estimates on the under-reporting rate of the seasonal influenza were established. Based on these findings, a new epidemiological model and framework were developed, providing accurate real-time forecasts with a clear early warning signal to the influenza outbreak. This research utilised a combination of novel data sources to predict influenza outbreaks. Such information is beneficial for health authorities to plan health strategies and control epidemics. iii ACKNOWLEDGEMENTS Firstly, I would like to thank my supervisor Professor Adam Kleczkowski for his support and guidance throughout this journey, for his helpful advice, professional support, encouragement, and invaluable feedback that has shaped my way of thinking. Adam has helped me during this challenging journey with his patience, inspiration and expertise, which have been fruitful to my professional growth. I am grateful to the Malta Health Promotion Department, namely Dr. Charmaine Gauci, Dr. Tanya Mellilo and Dr. Jackie Mellilo, who provided the data for this study and who took the time to provide prompt replies to my questions. Thanks also go to the Malta Airport Meteorological Services for providing the Maltese temperature data. I would like to extend my gratitude to Professor Alex Cook for allowing me to use his particle filter algorithm R code. Furthermore, I would like to thank him for reviewing my research paper. I would like to acknowledge the Maltese key health officials who took an interest in my research and made time to discuss the outcomes of this thesis. Thanks go to Dr. Renzo Degabriele (Chief Executive Officer, Primary Health Care Department), Dr. Neville Calleja (Director, Health Information and Research) and Mr. Mike Farrugia (Ministry Advisor). Particular gratitude goes to the Minister for Health in Malta, Honourable Mr. Chris Fearne for taking the time to discuss my findings. I would also like to thank all the secretaries at the Department of Mathematics and Computing Science at the University of Stirling, who gave me secretarial and administrative support, and to my fellow PhD students, in particular Mr. Paul McMenemy, for being a source of personal support, for the teas and coffees, for the lifts to the airport, and for the regular dinners at Stirling’s Molly’s. I extend my acknowledgements to the ‘Times of Malta’ newspaper for reporting my research findings (Appendix J). iv I could not have done this without the support and encouragement of my wonderful family, my parents, Josephine and Charlie, my sisters, Fiona and Olivia-Ann, my nephews Matthew, Gabriel and Andre, and my in-laws. Thank you for always believing in me and for being there when I needed you most throughout this PhD. Lastly, I would like to thank my wife, Danika, for her unwavering support and patience, for being an excellent sounding board at the end of my thesis, and for her rational influence on me throughout this journey. Thank you for encouraging me to stick at it and for always believing that I could do this. v Understanding the facts that no one can see… This thesis is dedicated to my wife, Danika, who was my pillar of strength, for her love, understanding, and continuous support. vi PUBLICATIONS V. Marmara, A. Cook, A. Kleczkowski, Estimation of force of infection based on different epidemiological proxies: 2009/2010 Influenza epidemic in Malta, Epidemics, 9 (2014) 52-61. vii CONTENTS CHAPTER 1: INTRODUCTION & LITERATURE REVIEW 1 1.1 Introduction 2 1.2 Background 2 1.3 History of Malta’s Influenza Epidemics 3 1.4 Mathematical modelling in epidemiology 4 1.4.1 Deterministic and Stochastic compartmental disease models 6 1.4.2 The Bayesian Inference 7 1.4.2.1 The Markov Chain Monte Carlo models 7 1.4.2.2 Particle filter algorithm 8 1.4.2.3 Implementation to the S(E)IR models 10 1.4.3 The basic reproduction number (R0) 11 1.5 Influenza 13 1.5.1 Defining the seasonal influenza 13 1.5.2 The dynamics of influenza in relation to climate and temperature 14 1.5.3 The role of surveys in studies related to Influenza 16 1.5.4 Influenza forecasting 18 1.6 Thesis Overview 20 CHAPTER 2: MATERIALS AND METHODS 23 2.1 Introduction 24 2.2 A brief description of Malta 24 2.3 Malta’s healthcare system 25 2.3.1 The role of the research department 26 2.3.2 The role of the Malta Health Promotion department 26 2.3.3 Influenza vaccination in Malta 27 2.4 Key definitions 27 2.4.1 Pathways through influenza illness 27 2.5 Data used in the thesis 30 2.5.1 Influenza data 30 2.5.1.1 Doctors’ consultations and diagnosed cases 30 2.5.1.2 ILI Swabbed and H1N1 Positive cases 32 viii 2.5.2 Malta’s cross-sectional survey datasets 33 2.5.3 Temperature data 35 2.6 Models 35 2.6.1 The SEIR model 35 2.6.2 Rt for different datasets 37 2.6.3 Particle filtering algorithm 38 2.6.3.1 Initial stage 39 2.6.3.2 Iteration of particles 39 2.6.3.3 Weighting the particles 39 2.6.3.4 Particle degeneracy and re-sampling 39 2.6.3.5 Kernel smoothing 39 2.6.3.6 Increment 40 2.6.4 Linear Regression Model 40 2.6.5 Analysis for associations 42 2.6.5.1 Correlations analysis 42 2.6.5.2 Chi-Squared test 43 2.7 Software used 43 2.7.1 R 43 2.7.2 Microsoft Excel 44 2.7.3 SPSS 44 CHAPTER 3: ESTIMATION OF FORCE OF INFECTION BASED ON DIFFERENT EPIDEMIOLOGICAL PROXIES: 2009/2010 INFLUENZA EPIDEMIC IN MALTA 45 3.1 Introduction 46 Abstract 46 Introduction 46 Material and methods 48 Results 55 Discussion 60 Acknowledgements 65 References 65 CHAPTER 4: MODELLING SEASONAL INFLUENZA 70 4.1 Introduction 71 4.2 The influenza datasets 71 ix 4.3 Linear modelling of a relationship between diagnosed and consultations 75 4.4 The SEIR model 81 4.5 Combining the SEIR and Linear regression model in one single framework (joint model) 86 4.6 Discussion 91 CHAPTER 5: REAL-TIME FORECASTING: THE SEIR MODEL AND THE JOINT MODEL 102 5.1 Introduction 103 5.2 Method 103 5.3 Results 104 5.3.1 2009/2010 pandemic data 104 5.3.2 2011/2012 seasonal influenza data 108 5.3.3 2012/2013 seasonal influenza data 112 5.3.4 2013/2014 seasonal influenza data 116 5.3.5 2014/2015 seasonal influenza data 120 5.4 Discussion 123 CHAPTER 6: SENSITIVITY ANALYSIS 126 6.1 Introduction 127 6.2 Sensitivity Analysis for R(0) 127 6.3 Sensitivity Analysis for I(0) and E(0) 136 6.4 Discussion 145 CHAPTER 7: PROBING INTO SEASONAL INFLUENZA: EXPLORING UNDERLYING FACTORS 149 7.1 Introduction 150 7.2 Ethical considerations 151 7.3 Representativeness of the sample 151 7.4 Sample characteristics 152 7.5 Results 153 7.5.1 Participants’ general medical information 153 7.5.2 The seasonal influenza vaccine 154 7.5.3 Influenza-Like Illness (ILI) 155 7.5.4 Seasonal influenza 2014-2015 157 7.5.5 Seasonal influenza 2015-2016 161 7.5.5.1 Results of the 2015-2016 survey 161 x 7.6 Discussion 164 7.6.1 Validating the GPs data 164 7.6.2 Under-reporting 170 7.6.2.1 Case 1: Diagnosed ILI cases (GP data) against number of symptomatic cases (Survey data) 171 7.6.2.2 Case 2: Diagnosed ILI cases (GP data) against seasonal influenza cases (Survey data) 172 7.6.2.3 Case 3: Diagnosed ILI cases (GP data) against individuals’ temperature (Survey data) 173 7.6.2.4 Case 4: Diagnosed ILI cases (GP data) against seasonal influenza cases in households (Survey data) 174 7.6.3 Practical use 174 7.7 Conclusion 175 CHAPTER 8: FORECASTING SEASONAL