Copyright is owned by the Author of the thesis. Permission is given for a copy to be downloaded by an individual for the purpose of research and private study only. The thesis may not be reproduced elsewhere without the permission of the Author. The Role of a Wildlife Reservoir in the Epidemiology of Bovine Tuberculosis A thesis presented in partial fulfilment of the requirements for the degree of Doctor of Philosophy at Massey University D. U. Pfeiffer 1994 ABSTRACT The objective of this project was to study the epidemiology of bovine tuberculosis in the presence of a wildlife reservoir species. Cross-sectional and longitudinal studies of possum populations with endemic bovine tuberculosis infection were analysed. The results were used to develop a computer simulation model of the dynamics of bovine tuberculosis infection in possum populations. A case-control study of breakdowns to tuberculosis infection in cattle herds in the Central North Island of New Zealand was conducted to identify risk factors other than exposure to tuberculosis in local possum populations. The cross-sectional study was based on data gathered some years earlier in the Hauhungaroa Ranges from a number of traplines with a total length of 60km, hence it provided information about the epidemiology of possum tuberculosis on a large geographical scale with varying environmental conditions. The results from the study showed that disease occurrence was clustered in space with local prevalence reaching up to 20% while the overall prevalence was about 1.2%. The longitudinal study was conducted using an area of 21 hectare of mixed pasture and bush on a sheeplbeef farm. The study showed that incidence and prevalence of tuberculosis infection in possum populations has distinct spatial and temporal patterns. Environmental conditions were a major factor in determining the temporal pattern. Spatial and temporal analysis of the occurrence of different strains of Mycobacterium bovis allowed inferences to be made about the importance of particular transmission paths. Survival of possums depended on environmental conditions and tuberculosis disease status. Adverse weather conditions increased mortality and the incidence of clinical disease in possums. On average clinically tuberculous possums survived for about 2 to 3 months from the onset of clinical disease. The simulation model uses a Monte-Carlo modelling approach and incorporates geographical features. Biological mechanisms which are considered important for population and infection dynamics were implemented in the model. These include mating, density­ dependent and -independent mortality, pseudo-vertical transmission, transmission through spatial or temporal proximity, and transmission during mating contact. Each possum's movements and behaviour are simulated on a day-by-day basis. Simulations are conducted using a geography and possum population based on data from the longitudinal field study. For preliminary validation, model output was compared with field data from the longitudinal study. Sensitivity analyses and some initial simulation experiments were conducted to identify areas in the model structure which require the collection of additional field data. Use of the model for simulation of a possum population occupying a 400ha area in the Central North Island of New Zealand is demonstrated. The case-control study of breakdowns to tuberculosis infection in cattle herds showed that in the Waikato area of New Zealand exposure to tuberculosis infection in local possum /I populations was not the dominant cause of breakdowns when the study was conducted in 1 989/90, at a time when tuberculous possums were first discovered in the region. Farmers who had breakdowns tended to foHow cattle purchase and management practices which traditionally have been considered to put farms at risk of introducing tuberculosis. The results of the study indicate that there was a lack understanding among farmers about the epidemiology of tuberculosis. III ACKNOWLEDGEMENTS Since my arrival in New Zealand in February 1 988 I have been a member of the epidemiology research group in the Department of Veterinary Clinical Sciences at Massey University. These six years have passed by very quickly and I have enjoyed every moment of the time. I am particularly grateful to my mentor and chief supervisor, Professor Roger Morris. Almost 1 0 years ago when I first met with him in Colombia, South America, his optimism and enthusiasm gave me the courage to become an epidemiologist while working with him in a country which in this world could not be further away from home. None of this work would have been possible without his friendship, originality, and vision. Thanks are also due to Associate Professor Roger Marshall and Dr. Nigel Barlow, my other supervisors, who have provided advice and offered suggestions whenever required. There are a number of people especially from within the epidemiology research group whom I would like to thank for inspiring discussions and for their participation in the field work. I would also like to thank Mr. Anthony Harris, who selected the area for the field study and assisted me in running the field project, Mr. Ron Goile and Mr. Bill Maunsell who allowed us to work on Waio farm and Mr. Mark Stem who undertook most of the programming for the computer simulation model. I thank Dr. Ron Jackson who has always been willing to listen, discuss issues and make constructive suggestions. A special thanks to my parents, lnge and Arnold Pfeiffer, who have provided me with the education, support and freedom which allowed me to pursue this and other projects away from Germany in the past. My greatest appreciation and acknowledgement is to my wife, Susanne, and my son, Patrick, who have been very patient when I spent time working on this thesis which should have been spent with them. I will not forget that Susanne helped me during the early part of the field work, which at times was very hard for her. Both Patrick and Susanne were always there when I needed their support and encouragement. Without them this thesis would never have been written. D. U. PFEIFFER, Department of Veterinary Clinical Sciences, Massey University, New Zealand March 1 994 TABLE OF CONTENTS ABSTRACT ACKNOWLEDGEMENTS TABLE OF CONTENTS LIST OF FIGURES LIST OF TABLES CHAPTER 1 INTRODUCTION CHAPTER 2 BACKGROUND TO THE STUDY CHAPTER 3 REVIEW OF THE LITERATURE EPIDEMIOLOGY OF TUBERCULOSIS IN HUMANS EPIDEMIOLOGY IN DOMESTIC ANIMALS Cattle Farmed Deer Other Domestic Animals EPIDEMIOLOGY IN WILDLIFE Badger Brush-Tailed Possum Feral Buffalo and Bison Wild Deer Other Wild Animals Other Species IV I I I IV x XVII I 1 4 8 9 14 14 16 17 17 17 19 21 23 23 24 CHAPTER 4 A CROSS-SECTIONAL STUDY OF MYCOBACTERIUM BOv/S INFECTION IN POSSUMS IN THE HAUHUNGAROA RANGES, NEW ZEALAND 25 INTRODUCTION MATERIALS AND METHODS Study Design and Data Collection Data Analysis RESULTS Trapping Statistics Ecological Characteristics of the Possum Population under Study Characteristics of the Total Population Comparison of Geographically Grouped Populations Comparison of Population Density Indices Possum Tuberculosis Epidemiology of Tuberculosis in Possums Differences in Condition, Breeding Status, Sex and Age Class Comparison between Geographic Areas and Part of Summer 26 26 26 28 3 1 31 32 32 34 42 43 44 44 46 v Distribution of Lesions in Tuberculous Possums 47 Spatial Patterns of Infection 51 Possum and Cattle Tuberculosis 54 DISCUSSION 58 Limitations on Interpretation 58 Ecology of Possums in the Study Area 58 Epidemiology of Bovine Tuberculosis Infection in Possums 60 CHAPTER 5 A LONGITUDINAL STUDY OF BOVINE TUBERCULOSIS IN POSSUMS AND CATTLE 68 INTRODUCTION 69 MA TERIALS AND METHODS 69 Selection of Study Site 69 Field Procedures 71 Study Site and Study Design 71 General Procedure for Animal Examination 74 Details on Sample Collection 76 a) Blood collection 76 b) Collection of other specimens 76 Other Investigations 76 Data Analysis 77 RESULTS 83 Meteorological Data 83 Trapping Statistics 86 Reproduction 88 Population Dynamics 90 General Body Condition 93 Home Range 94 Denning 95 Immigration 97 Dispersal 99 Descriptive Epidemiology 101 Pathological Findings 103 Survival of Tuberculous Possums 105 Temporal Dynamics of Tuberculosis Infection 111 Spatial Dynamics of Tuberculosis Infection 113 Spatio-temporal Dynamics of Tuberculosis Infection 119 Epidemiological Analysis based on Restriction Endonuclease Analysis Types of Mycobacterium bovis 122 Cattle Tuberculosis 128 Catch Methods 129 DISCUSSION Ecological Findings Reproduction and Mortality Population Size and Demographic Characteristics '-JHome Ranges and Den Use Home Range and Dispersal Tuberculosis Epidemiology Research Design Prevalence and Incidence Age and Sex Distribution of Infection Time to Death or Disease for Different Categories of Possums Insights from Epidemiological Differentiation of Strain Variants Temporal Course of the Disease Process Spatial Aspects of the Disease Process 129 129 130 131 132 134 136 136 136 137 139 140 142 144 VI Evaluation of Potential Transmission Mechanisms 144 Sharing of Grazing Area 147 Transmission through Behavioural Interaction of Possums 148 Pseudo-vertical Transmission 149 Den Sharing 151 Transmission through Interactions between Males 152 A Tentative Hypothesis for Transmission of Tuberculosis on the Study Site 153 CHAPTER 6 A COMPUTER SIMULATION MODEL OF THE DYNAMICS OF TUBERCULOSIS INFECTION IN A WILD POSSUM POPULATION 1 56 SIMULATION MODELLING 157 EPIDEMIOLOGICAL SIMULATION MODELLING 158 SIMULATION MODELLING APPROACHES 159 DEVELOPMENT OF A SIMULATION MODEL 160 Simulation, Model Verification! Validation and the Philosophy of Scientific Inquiry 162 DEVELOPMENT OF A SIMULATION MODEL OF BOVINE TUBERCULOSIS IN A WILD POSSUM POPULATION 165 Objectives of the Modelling Undertaking 165 General Model Characteristics 165 Temporal Scale 167 Spatial Scale 167 Description of Model Structure and Functionality 168 Den Site Selection 170 Reproduction 171 Infection with Mycobacterium bovis 172 Survival of Possums 174 Ageing Mechanisms for Possums 175 Immigration of Possums 176 Input Parameters for the Model 177 Start Population 177 . Den Site Parameters 178 Reproductive Parameters 179 Infection Parameters 180 Survival Parameters 187 Ageing Parameters 189 Immigration Parameters 191 Cyclical Effects 191 Simulation Program Operation 195 Parameter Settings for Population and Disease Mechanisms used in Simulation Run 197 Random Number Generation 198 Generation of Random Variates from Non-Uniform Probability Distributions 199 Variance Reduction Techniques in Simulation Modelling 200 Verification and Validation of the Simulation Model 201 Methods of Analysis 204 Preliminary Simulation Experiment 204 Simulation of a Population with Tuberculosis Infection 210 General PopUlation Dynamics 210 Tuberculosis Infection Dynamics 2 I 9 Seasonal Pattern of Tuberculosis Infection 221 Survival Analysis of Simulation Output 225 �Spatio-Temporal Patterns of Tuberculosis Infection 227 Detailed Spatio-Temporal Patterns of Tuberculosis Infection 23 I Time-Series Analysis of Simulation Output 239 Time-Series Analysis in Time Domain 240 Time-Series Analysis in Frequency Domain Comparison of Antithetic Pairs Approach and Mean of Random Runs Approach Effect on Population Size Effect on Prevalence of Clinical Tuberculosis Infection VII 241 244 245 248 Effect on Time to Extinction of Clinical Tuberculosis 251 Sensitivity Analysis 253 Baseline Simulation without Clinical TB in Immigrants 253 Effect of Spatial Parameters on Infection Dynamics 254 Radius of Area around an Infected Den with Increased Risk of Infection 254 Maximum Mating Travel Distance 256 Maximum Search Distance for a Den 258 Transmission Mechanisms for Mycobacterium bovis infection 260 Statistical Comparison of Simulations Runs 264 Model Experimentation 267 Simulation Run using Base Parameter Files without Immigration 267 Single Reduction in Population Size without Immigration 268 Single Reduction in Population Size in the Presence of Immigration Free from Clinical Tuberculosis 270 Single Reduction in Population Size with Clinical Tuberculosis in Immigrants 272 Permanent Reduction in Den Site Density in the Absence of Immigration 273 Permanent Reduction in Den Site Density in the Presence of Immigrants free from Clinical Tuberculosis 275 Permanent Reduction in Den Site Density with Clinical Tuberculosis in Immigrants 276 Repeated Population Reduction at Three - Yearly Intervals in the Presence of Clinical Tuberculosis in Immigrants 278 Repeated Control Operations at Six - Yearly Intervals in the Presence of Clinical Tuberculosis in Immigrants 279 Simulation over a 400 Hectare Area 282 Model Performance 288 DISCUSSION Comparison of Model Output and Field Data Evaluation of Disease Control Options with the Current Model Improvements on the Current Model Next Stage of Model Development CHAPTER 7 A CASE-CONTROL STUDY OF TUBERCULOSIS BREAKDOWN 289 289 291 293 295 I N CATTLE HERDS IN THE WAIKA TO REGION, NEW ZEALAND 296 INTRODUCTION MA TERIALS AND METHODS Study Design Data Collection Data Analysis General Outline of Approach to Data Analysis Methods used in Multivariate Analysis Stepwise Multiple Logistic Regression Path Analysis Path analysis using regression techniques Path analysis using LISREL Classification Tree Analysis RESULTS Descriptive Analysis General Management and Farm Characteristics Farmer's Interest in Disease Control and Knowledge about the Epidemiology ofTB Herd Characteristics Purchase Patterns of Farmers in Study Area 297 298 298 301 302 304 305 305 306 307 308 311 3 14 314 314 314 315 316 VIII Stock Management 316 Univariate Analysis 316 Multivariate Analysis 328 Multidimensional Preference Mapping 328 Stepwise Logistic Regression Models 329 Path Analysis using Standard Regression Procedures 338 Path Analysis using LlSREL 344 Classification Tree Analysis 349 DISCUSSION 353 Likelihood of Involvement of Infection from Wildlife Reservoir Species 354 Farmer's Self Concept 355 Farmers' Views about Disease Control and Knowledge about Tuberculosis Infection 356 General Management and Farm Characteristics 357 Patterns of Stock Purchase 358 Herd Characteristics 359 Stock Management 359 Synthesis 360 CHAPTER 8 GENERAL DISCUSSION - TOWARDS A STRATEGIC APPROACH TO WILDLIFE D ISEASE CONTROL 362 INTRODUCTION 363 WILDLIFE RESERVOIRS OF DISEASE 363 Rinderpest 364 Rabies 365 Fox Rabies 365 Rabies in Other Species 367 African Swine Fever 370 BOVINE TUBERCULOSIS 371 EPIDEMIOLOGICAL COMPARISONS OF TUBERCULOSIS AND OTHER WILDLIFE DISEASES 374 EPIDEMIOLOGICAL STUDY METHODS FOR DISEASES IN WILDLIFE 377 EV ALUA TION OF THE STUDY METHODS ADOPTED FOR TUBERCULOSIS 379 Longitudinal Study of Bovine Tuberculosis in Possums 379 Cross-sectional Study of Bovine Tuberculosis in Possums 380 Case-control Study of Tuberculosis Breakdowns in Cattle Herds 381 RESEARCH TECHNIQUES 382 Analysis of Difficult Longitudinal Data 383 Analysis of Data including a Temporal Component 383 Analysis of Data including a Spatial Component 383 Analysis of Data including Both a Temporal and Spatial Component 384 Analysis of Multivariate Data 384 COMPUTER SIMULATION MODELLING AS A TOOL IN DISEASE CONTROL 385 Simulation and Disease Control in Animal Populations 386 Strategies for Pest Management 387 Pest Control and Animal Population Dynamics 388 Modelling of Infectious Diseases 389 Modelling and Planning for the Control of Bovine Tuberculosis in New Zealand 391 Simulation Models of Infectious Diseases in Epidemiological Research 394 BOVINE TUBERCULOSIS DISEASE CONTROL 396 IX Strategies available in the Medium-Term 399 Strategies available in the Long-Term 400 DIRECTIONS FOR FUTURE RESEARCH 401 SYNTHESIS 402 BIBLIOGRAPHY 403 APPENDIX 427 APPENDIX I: FORM FOR RECORDING OF DATA COLLECTED DURING CLINICAL EXAMINATION OF POSSUMS 428 APPENDIX II: FORM FOR RECORDING TRAP CATCH DATA 429 APPENDIX III: FORM FOR RECORDING OF POSSUM NECROPSY DATA 430 APPENDIX IV: FORM FOR RECORDING OF DEN SITE TRACKING DATA 431 APPENDIX V: QUESTIONNAIRE FOR CASE FARMS INCLUDED IN TUBERCULOSIS CASE- CONTROL STUDY 432 APPENDIX VI: TURBO PASCAL FOR WINDOWS PROGRAM CODE FOR SIMULATION MODEL 456 x LIST OF FIGURES Figure 1: Vegetation map of the Hauhungaroa Ranges, Central North Island, with location of farms and base trap lines 27 Figure 2: Possum catch stratified by geographic zone and month 31 Figure 3: Kidney fat index and breeding status in adult female possums 33 Figure 4: Weight-length relationship in possums 34 Figure 5: Possum catch stratified by geographic area and part of summer 35 Figure 6: Average weights and lengths of adult possums stratified by geographic area 36 Figure 7: Proportion of breeding females in total adult females and proportion of female in adult possums stratified by geographic area 39 Figure 8: Proportion of breeding females in total adult females stratified by geographic area and part of summer 40 Figure 9a: Possum population density indices based on PELLET and BA TCHELER 42 Figure 9b: Possum popUlation density indices based on OTIS, LESLIE and CATCH 43 Figure 10: Tuberculosis infection status and kidney fat index 45 Figure I I : Tuberculosis infection and weight-length relationship in adult possums 46 Figure 12: Spread of disease within body in tuberculous possums 47 Figure 13a: Spread of disease within body in tuberculous possums stratified by age class 48 Figure 13b: Proportion of single site lesions stratified by sex class 49 Figure 14: Proportion of possums with "open" lesions stratified by month 50 Figure 15: Histogram of size of clusters of tuberculosis infection 51 Figure 16: Histogram of tuberculosis prevalence within clusters of infection 52 Figure 17: Tuberculosis prevalence within clusters of infection and size of cluster 53 Figure 18a: Contour map of the Hauhungaroa Ranges with cattle and possum tuberculosis information, farm and trap line locations 55 Figure 18b: Correlation between cattle tuberculosis incidence and possum tuberculosis prevalence 56 Figure 19: Possum tuberculosis prevalence and cattle tuberculosis incidence by subzone 57 Figure 20: Location of all traps which were used during the three project phases draped over digital terrain model of the area 71 Figure 21: Paddock boundaries for Waio farm draped over a contour map 72 Figure 22a: Photograph of the study area 73 Figure 22b: Trapgrid draped over digital terrain model of the study area 73 Figure 22c: Possum captured in most commonly used trap model 74 Figure 23: Possum with ear notches and ear tag 75 Figure 24a: Distribution of monthly total rainfall during the period 1972 - 1990 84 Figure 24b: Distribution of monthly average ratio between minimum and maximum daily temperature during the period 1972 - 1990 85 Figure 24c: Distribution of monthly average daily temperature during the period 1972 - 1990 85 Figure 25a: Trapcatch statistics 86 Figure 25b: Individual possum captures and clinical examinations 87 Figure 26: Distribution of ages in possums at post-mortem examination stratified by sex class 88 Figure 27: Fertility distribution of births and rearing periods in possums Figure 28a: Temporal dynamics of Jolly-Seber population parameters for the possum population Figure 28b: Temporal dynamics of Jolly-Seber population parameters for the possum population emphasising XI 89 90 relationship immigrationlbirths and disappearance 91 Figure 28c: Comparison of population size estimates based on jackknife (with 95% confidence limits) and J 0 \ly-Seber estimator 91 Figure 29a: Temporal pattem of average body weights of possums 93 Figure 29b: Seasonal pattern of average body weights of adult possums stratified by sex class 94 Figure 30: Distribution of number of different possums captured at individual trap locations stratified by sex class 95 Figure 31a: Scatter plot of den site tracking effort and number of different den locations per possum 96 Figure 31 b: Histogram of maximum distance between den sites stratified by sex class 97 Figure 32a: Captures of new possums stratified by age groups 97 Figure 32b: Captures of new juvenile possums stratified into immigrants and locally recruited animals 98 Figure 32c: Number of months for which possums were recaptured after initial capture depending on month of first capture 98 Figure 33a: Distances of possum dispersal movements (dots represent trap site and den site locations) 99 Figure 33b: Location data available for possum no. D3565 100 Figure 34: Temporal distribution of new tuberculosis cases in possums stratified by age and sex class !OI Figure 35: Temporal distribution of incident tuberculosis cases in adult female possums stratified by pregnancy status 102 Figure 36a: Possum with a draining lesion in axillary lymph center 104 Figure 36b: Tuberculous lesion in axillary lymph node of a possum 104 Figure 36c: Tuberculous lesions in the lung of a possum 105 Figure 37: Kaplan-Meier survival curves for infected and uninfected possums 106 Figure 38: Kaplan-Meier survival curve for tuberculous possums, by age group 108 Figure 39: Kaplan-Meier curve of cumulative probability of not developing tuberculous lesions 110 Figure 40: Incidence and prevalence of tuberculosis in possums and cattle III Figure 41: Tuberculosis incidence in possums and weather conditions 112 Figure 42a: Distribution of distances to the nearest den site utilized by tuberculous possums 113 Figure 42b: Distribution of distances to the tuberculous possum with nearest arithmetic center of activity 114 Figure 43: Contour map of the spatial distribution of proportion tuberculous possums in total catch 115 Figure 44: Contour map of the spatial distribution of total captures 116 Figure 45: Spatial distribution of den sites used by infected and non-infected possums 117 Figure 46a: Histogram of the distribution of slope aspect for den sites which had been used by tuberculous possum and which had only been used by non-tuberculous possums 118 Figure 46b: Histogram of the distribution of height above sea level for den sites which had been used by tuberculous possum and which had only been used by non-tuberculous possums 118 Figure 47a: Time-space interaction between tuberculosis cases stratified by sex class 120 Figure 47b: Temporal and spatial distribution of tuberculosis infected possums stratified by season and year 121 Figure 48a: Details from case histories and post mortem examinations of tuberculous possums with REA type data 123 Figure 48b: Joint plots of the second and third against the fIrst dimension of the result of mUltiple correspondence analysis describing the association between REA type, sex class, age group and season XII 124 Figure 48c: Temporal distribution of restriction endonuclease types of Mycobacterium bovis isolates 125 Figure 48d: Spatial distribution of restriction endonuclease types of Mycobacterium bovis isolates based on capture and den site locations used by tuberculous possums 126 Figure 48e: Spatial distribution of restriction endonuclease types of Mycobacterium bovis isolates based on den site locations used by tuberculous possums 127 Figure 48f: Time-space interaction between tuberculosis cases stratifIed by combination of major REA types 128 Figure 49: Structural steps of the simulation modelling process 162 Figure 50: Important factors in the epidemiology of possum tuberculosis 166 Figure 51: Overview of the model structure 169 Figure 52: Structure of the den site selection module 171 Figure 53: Structure of the reproduction module 172 Figure 54: Structure of the tuberculosis infection module 174 Figure 55: Structure of the survival module 175 Figure 56: Structure of the ageing module 176 Figure 57: Structure of the immigration module 177 Figure 58a: Distribution of distances to the tuberculous possum with nearest arithmetic center of activity 183 Figure 58b: Variogram of difference in prevalence between trap locations on longitudinal study site 183 Figure 58c: Frequency histogram of geographical distances between centres of activity for tuberculous possums detected within 3 month intervals from each other stratified by REA type 184 Figure 59a: Contour map of the spatial distribution of proportion tuberculous possums in total catch 186 Figure 59b: Histogram of period prevalence per trap location 186 Figure 59c: Histogram of period prevalence for locations with tuberculosis based on a 20m grid cell size 187 Figure 60: Temporal pattern of possum disappearance in the longitudinal study 189 Figure 61a: Distribution for sampling age of independence in possums 190 Figure 61 b: Distribution used for sampling age of sexual maturity 190 Figure 62: Example of a poisson probability distribution with a mean of 7 expected immigrants per month 191 Figure 63 a: Parameter settings for the bad year simulation scenario 193 Figure 63b: Parameter settings for the average year simulation scenario 193 Figure 63c: Parameter settings for the goodyear simulation scenario 194 Figure 64a: Startup screen after program execution 195 Figure 64b: First screen for defming simulation run parameters 196 Figure 65: Second entry screen for defming simulation run parameters 196 Figure 66: Screen display during computer simulation run 197 Figure 67: Worksheet model for creation and editing of parameter fIles 198 Figure 68a: Time series plot of monthly data for population size from the original and antithetic run of the preliminary simulation experiment 206 Figure 68b: Time series plot of monthly data of the proportion of sexually mature animals in the population based on data from the original and antithetic run of the preliminary simulation experiment 206 Figure 68b: Time series plot of monthly data of the proportion of female animals in the popUlation based on data from the original and antithetic run of the preliminary simulation experiment 207 XIII Figure 68d: Average age structure in simulated population of preliminary simulation experiment 207 Figure 68e: Error bar chart for population size for each month of the year based on data from the original and antithetic run of the preliminary simulation experiment 208 Figure 68f: Error bar chart for proportion of female possums in total population for each month of the year based on data from the original and antithetic run of the preliminary simulation experiment 208 Figure 68g: Error bar chart for proportion of immature possums in the total population for each month of the year based on data from the original and antithetic run of the preliminary simulation experiment 209 Figure 69a: Time series plot of monthly data for population size, proportion of females and immature animals in the population for the original simulation run using base parameter files 214 Figure 69b: Time series plot of monthly data for population size, proportion of females and immature animals in the population for the antithetic simulation run using base parameter files 214 Figure 69c: Graphical comparison of average population size (incl. standard deviation bars) during the course of a year between output from the simulation model for base parameter files and data obtained from the longitudinal study 2 I 5 Figure 69d: Graphical comparison of average proportion females in total popUlation (incl. standard deviation bars) during the course of a year between output from the simulation model using base parameter files and data obtained from the longitudinal study 216 Figure 6ge: Graphical comparison of average proportion immatures in total population (inc!. standard deviation bars) during the course of a year between output from the simulation model using base parameter files and data obtained from the longitudinal study 216 Figure 69f: Proportion of adult female possums with a dependent young present for each month of the calendar year based on summarized simulation output (base parameter files; incl. standard deviation bars) and data from the longitudinal study 217 Figure 69g: Average and cumulative number of possums represented as bars using different number of den sites during the period of a month summarized over the whole simulation period (base parameter files) 217 Figure 69h: Average number of possums (y-axis) using different numbers of den sites categorized into three groups (shaded areas) during the months of a year summarized over the whole simulation period (base parameter files) 218 Figure 69i: Average number of possums (as vertical bars) spending a given number of days per month without fmding a suitable den site summarized over the whole simulation period (base parameter files) 218 Figure 69j: Average number of days (y-axis) spent by possums without fmding a suitable den site over the course of a year summarized over the whole simulation period (base parameter files) 219 Figure 70a: Time series plot of monthly data for popUlation size, prevalence and incidence of clinical tuberculosis in the population for a simulation run using base parameter files based on simulation output from original run 220 Figure 70b: Time series plot of monthly data for popUlation size, prevalence and incidence of clinical tuberculosis in the population for a simulation run using base parameter files based on simulation output from antithetic run 220 Figure 71a: Average monthly clinical tuberculosis prevalence (including standard deviation bars) over the course of a year for simulation output and data points obtained during the longitudinal study (base parameter files) 222 Figure 7Ib: Average monthly clinical tuberculosis incidence (including standard deviation bars) over the course of a year for simulation output and data points obtained during the longitudinal study (base parameter files) 222 Figure 7Ic: Average monthly clinical tuberculosis prevalence (including standard deviation bars) in immature possums over the course of a year for simulation output and data points obtained during the longitudinal study (base parameter files) 223 Figure 71d: Average monthly clinical tuberculosis prevalence (including standard deviation bars) in mature possums over the course of a year for simulation output and data points obtained during the XIV longitudinal study (base parameter files) 223 Figure 71e: Average monthly clinical tuberculosis prevalence (including standard deviation bars) in male possums over the course of a year for simulation output and data points obtained during the longitudinal study (base parameter files) 224 Figure 71f: Average monthly clinical tuberculosis prevalence (including standard deviation bars) in female possums over the course of a year for simulation output and data points obtained during the longitudinal study (base parameter files) 224 Figure 71g: Average monthly tuberculosis infection prevalence (including standard deviation bars) in dependent young possums over the course of a year for simulation output (base parameter files) 225 Figure 72a: Survival of possums with subclinical and clinical tuberculosis (base parameter files) 227 Figure 72b: Transition from subclinical to clinical tuberculosis (base parameter files) 227 Figure 73a: Cumulative spatial distribution of den sites used by possums with clinical tuberculosis infection during the simulation run (base parameter files; original and antithetic run) overlaid on map of total den site locations (circles represent TB den sites and dashes non-TB den sites) 229 Figure 73b: Cumulative spatial distribution of den sites used by possums with clinical tuberculosis infection during the two simulation runs (original and antithetic run) with height representing cumulative distribution of TB den sites 230 Figure 73c: Density of all mapped den sites per 20m2 used for simulation runs 231 Figure 74a: Spatio-temporal pattern of clinical tuberculosis during year 1 to 5 of a simulation run (original run) 233 Figure 74b: Spatio-temporal pattern of clinical tuberculosis for years 6 to 10 of a simulation (original run) 234 Figure 74d: Spatio-temporal pattern of clinical tuberculosis for years II to 15 of a simulation (original run) 235 Figure 74e: Spatio-temporal pattern of clinical tuberculosis for years 16 to 20 of a simulation (original run) 236 Figure 74 f: Spatio-temporal pattern of clinical tuberculosis for years 21 to 25 of a simulation (original run) 237 Figure 74f: Spatio-temporal pattern of clinical tuberculosis for years 26 to 28 of a simulation (original run) 238 Figure 75: Time series decomposition plot of clinical tuberculosis prevalence (base parameter files) 241 Figure 76a: Spectrogram for subclinical and clinical TB prevalence 243 Figure 76b: Spectrogram for subclinical and clinical TB incidence 243 Figure 76c: Spectrogram for popUlation size 244 Figure 77a: Error bar chart for popUlation size (inc!. standard deviation) based on 10 original and 10 antithetic runs and 10 averages of antithetic pairs from the 10 simulation runs over the period of a simulation year 246 Figure 77b: Box-and-whisker plots for popUlation size based on 10 independent runs, 10 antithetic runs and averages of antithetic pairs from 10 simulation runs for the whole simulation period of 10000 days 246 Figure 77c: Box-and-whisker plots for population size based on 5 independent runs, 5 antithetic runs and 5 averages of antithetic pairs for the whole simulation period of 10000 days 247 Figure 78a: Error bar chart for clinical tuberculosis prevalence (inc!. standard deviation) based on 10 independent runs and 10 averages of antithetic pairs over the period of a simulation year 249 Figure 78b: Error bar chart for clinical tuberculosis prevalence (incl. standard deviation) based on 10 independent runs and 10 average of antithetic pairs during the first 24 months of the simulation runs 249 Figure 78c: Box-and-whisker plots for clinical tuberculosis prevalence based on 10 independent runs, 10 antithetic runs and 10 averages of antithetic pairs for the whole simulation period of 10000 days 250 Figure 78d: Box-and-whisker plots for clinical tuberculosis prevalence based on 5 independent runs, 5 antithetic runs and 5 averages of antithetic pairs for the whole simulation period of 10000 days 250 xv Figure 79a: Survival plot of time to extinction of clinical tuberculosis based on 10 independent runs, 10 antithetic runs and 10 averages of antithetic pairs for the whole simulation period of 328 months 251 Figure 79b: Survival plot of time to extinction of clinical tuberculosis based onfirst set of 5 independent runs, 5 antithetic runs and 5 averages of antithetic pairs for the whole simulation period of 328 months 252 Figure 80: Time plots of prevalence and incidence of clinical tuberculosis and population size for simulation output from original and antithetic runs used as baseline simulation scenario for sensitivity analysis 253 Figure 81a: Time plots of prevalence and incidence of clinical tuberculosis and popUlation size for simulation output from original and antithetic runs testing the effect of a 25m radius of increased risk of infection around infected dens 255 Figure 81 b: Time plots of prevalence and incidence of clinical tuberculosis and popUlation size for simulation output from original and antithetic runs testing the effect of a 75m radius of increased risk of infection around infected dens 256 Figure 82a: Time plots of prevalence and incidence of clinical tuberculosis and population size for simulation output from original and antithetic runs testing the effect of a 75m mating travel distance 257 Figure 82b: Time plots of prevalence and incidence of clinical tuberculosis and population size for simulation output from original and antithetic runs testing the effect of a 125m mating travel distance 258 Figure 83a: Time plots of prevalence and incidence of clinical tuberculosis and popUlation size for simulation output from original and antithetic runs testing the effect of a 75m den search distance 259 Figure 83b: Time plots of prevalence and incidence of clinical tuberculosis and popUlation size for simulation output from original and antithetic runs testing the effect of a 125m den search distance 260 Figure 84a: Time plots of prevalence and incidence of clinical tuberculosis and population size for simulation output from original and antithetic runs with the transmission mechanism in den sites disabled 261 Figure 84b: Time plots of prevalence and incidence of clinical tuberculosis and popUlation size for simulation output from original and antithetic runs with transmission through spatial proximity disabled 262 Figure 84c: Time plots of prevalence and incidence of clinical tuberculosis and popUlation size for simulation output from original and antithetic runs with transmission through mating contact disabled 263 Figure 84d: Time plots of prevalence and incidence of clinical tuberculosis and popUlation size for simulation output from original and antithetic runs with pseudo-vertical transmission disabled 264 Figure 85a: Box-and-whisker plots for popUlation size based on combined simulation output from origina I and antithetic runs for each of the sensitivity analysis scenarios 266 Figure 85b: Box-and-whisker plots for clinical tuberculosis prevalence based on combined simulation output from original and antithetic runs for each of the sensitivity analysis scenarios 266 Figure 86: Time plot of prevalence and incidence of clinical tuberculosis and population size for simulation output from original and antithetic run testing the effect of removing immigration 268 Figure 87: Time plot of prevalence and incidence of clinical tuberculosis and population size for simulation output from original and antithetic run testing the effect of a single reduction in popUlation density to 25% without immigration 270 Figure 88: Time plot of results of original and antithetic run for prevalence and incidence of clinical tuberculosis and population size for a simulation scenario testing the effect of a single reduction in population density to 25% in the presence of immigration free from clinical tuberculosis 271 Figure 89: Time plot of results of original and antithetic run for prevalence and incidence of clinical tuberculosis and population size for a simulation scenario testing the effect of a single reduction in popUlation density to 25% in the presence of 5% clinical tuberculosis prevalence in the immigrants 273 Figure 90: Time plot of prevalence and incidence of clinical tuberculosis and population size based on original and antithetic run for simulation output showing the effects of a permanent reduction in den site density in the absence of immigration 274 Figure 91: Time plot of prevalence and incidence of clinical tuberculosis and population size based on original and antithetic run for simulation output showing the effects of a permanent reduction in den site density in the presence of immigration free from clinical tuberculosis 276 Figure 92: Time plot of prevalence and incidence of clinical tuberculosis and population size based on original and antithetic run for simulation output showing the effects of a permanent reduction in XVI den site density, in the presence of immigration with 5% clinical tuberculosis prevalence 277 Figure 93: Time plot of prevalence and incidence of clinical tuberculosis and population size based on original and antithetic run for simulation output showing the effects of repeated population control operations at 3 yearly intervals in the presence of 5% clinical tuberculosis infection in immigrants 279 Figure 94: Time plot of prevalence and incidence of clinical tuberculosis and population size based on original and antithetic run for simulation output showing the effects of repeated population control operations at 6 yearly intervals in the presence of 5% clinical tuberculosis infection in immigrants 280 Figure 95: Rasterized map of major vegetation cover classes in simulation area and locations of random den sites 283 Figure 96a: Time plots of incidence/prevalence of clinical tuberculosis and population size for both simulation runs over 400 hectare area 284 Figure 96b: Locations of den sites used by possums with clinical tuberculosis for years 1 to 12 for original run over 400 hectare area 285 Figure 96c: Locations of den sites used by possums with clinical tuberculosis for years 13 to 24 for original run over 400 hectare area 286 Figure 96d: Locations of den sites used by possums with clinical tuberculosis for years 25 to 28 for original run over 400 hectare area 287 Figure 96e: Digital elevation model with height representing frequency with which clinically tuberculous possums use den sites and shades of grey representing vegetation type based on cumulative TB den site locations used between years 10 and 28 of the original run of the simulation over 400 hectare area 287 Figure 97: Histogram of time required to simulate one year of simulation time based on data from simulation runs over the 21 ha longitudinal study area 288 Figure 98a: Map of farm locations 299 Figure 98b: Vegetation map of study area with farm locations 300 Figure 98c: Digital terrain model of study area with farm locations 301 Figure 99: Farm size distribution of properties included in study 314 Figure 100: Cattle herd size distribution of properties included in study in livestock units 315 Figure 101 a: Beef component per cattle livestock unit stratified by case-control status 3 19 Figure 101 b: Total beef cattle in livestock units stratified by case-control status 319 Figure 10 I e: Total cattle in livestock units stratified by case-control status 320 Figure lOI d: Total cattle livestock units purchased stratified by case-control status 320 Figure 10 I e: Proportion of heifers/steers per cattle livestock unit stratified by case-control status 321 Figure 101f: Distance to next case farm stratified by case-control status 321 Figure 101 g: Distance to next endemic TB area stratified by case-control status 322 Figure 10 I h: Total area pasture stratified by case-control status 322 Figure 101 i: Permanent labour units stratified by case-control status 323 Figure 101j: Total labour units stratified by case-control status 323 Figure 10 l k: Total livestock units stratified by case-control status 324 Figure 10 11: Proportion of weaners/yearlings per cattle livestock unit stratified by case-control status 324 Figure 10 1 m: Proportion of weaners/heifers/steers per cattle livestock unit stratified by case-control status 325 Figure lOI n: Scores for knowledge about possible mechanisms of tuberculosis transmission between cattle and humans stratified by case-control status 325 Figure 1010: Purchase of replacements and number of different sources stratified by case-control status 326 XVII Figure 10 I p: Scores for knowledge about MAF TB control methods stratified by case-control status 326 Figure 101q: Scores for knowledge about species involved in epidemiology of tuberculosis stratified by case- control status 327 Figure 102: Personality trait means for interviewees by case-control status 328 Figure 103: Biplot of multidimensional preference mapping of study farms within the preference space describing their self concept 329 Figure 104: Diagnostic plot of difference chi-square versus predicted probability with plot symbol proportional to standardized influence measure for fmal logistic regression model comparing cases and random controls 333 Figure 105a: Null hypothesis path diagram for comparison of cases with random controls 340 Figure 105b: Final path diagram for comparison of cases with random controls 340 Figure 106a: Null hypothesis path diagram for comparison of cases with matched controls 343 Figure 106b: Final path diagram for comparison of cases with matched controls 343 Figure 107a: Q-plots of normalized residuals for fmal path models 347 Figure 107b: Path diagram for fmal path model comparing cases and matched controls 348 Figure 107c: Path diagram for fmal path model comparing cases and random controls 348 Figure 108a: Classification tree for comparison of cases and matched controls 352 Figure 108b: Classification tree for comparison of cases and random controls 352 XVIII LIST OF TABLES Table 1: Possum catch stratified by sex and age Table 2: Possum catch stratified by sex and geographic area Table 3a: Possum catch stratified by age class and geographic area Table 3b: Catch of male possums stratified on age class and geographic area Table 4: Catch of adult possums stratified on sex and geographic area Table 5: Breeding status of female adult possums stratified by geographic area Table 6: Average body length and tuberculosis infection status Table 7: Distribution of single lesion sites Table 8: Bovine tuberculosis history of cattle herd on study farm from 1979 until 1989 Table 9a: Total monthly rainfall summarized over the period 1972 until 1990 Table 9b: Average ratio of minimum and maximum daily temperature summarized over the period 1972 until 32 37 37 37 38 39 45 48 70 83 1990 84 Table 10: Statistical tests of the assumptions for Jackknife estimator 92 Table I I : Home range estimates for adult males and female possums 95 Table 12: Summary of stepwise selection procedure for the 'best' discrete hazard rate regression model of time until death or disappearance 107 Table 13: Summary of stepwise selection procedure for the 'best' discrete hazard rate regression model of time until development of detectable tuberculous lesions 109 Table 14: Distance to nearest tuberculous possum or den site utilized by infected possums 113 Table 15: Results of multivariate analysis of den site utilization by tuberculous possums 119 Table 16: Structure of the start population 178 Table 17: Monthly probabilities of a successful mating 179 Table 18: Worksheet for modelling of parameters for probability of transition from subclinical to clinical tuberculosis 181 Table 18: Worksheet model for estimation of infection probabilities for the three variable transmission mechanisms in the model 187 Table 19: Worksheet for calculation of monthly survival in dependent possums 188 Table 20: Worksheet for estimation of monthly survival probabilities which are not density-dependent 188 Table 21: Monthly distribution of average number of immigrants per year 191 Table 22: Characteristics of the three types of years (good, average, bad) based on results of k-means cluster analysis 192 Table 23: Parameters used to estimate different probability arrays for the three types of years (good, average, �� I� Table 24a: General characteristics of preliminary simulation experiment 205 Table 24b: Results of descriptive analysis of output from preliminary simulation experiment 205 Table 25: General characteristics of the simulation experiment 210 Table 26a: Summary statistics of population parameters for simulation run using base parameter files 213 Table 26b: Summary statistics of population parameters by simulation run and type of year using base parameter files 213 Table 27: Summary statistics of tuberculosis infection dynamics by simulation run and type of year using base parameter files 225 XIX Table 28: Classical decomposition model for clinical tuberculosis prevalence based on simulation output from original run using base parameter set files 241 Table 29: Summary statistics for population size based on simulation output for the three different methods of treatment of random numbers (using 5 and 10 runs) 245 Table 30: Summary statistics for clinical tuberculosis prevalence based on simulation output for the three different methods of treatment of random numbers (using 5 and 10 runs) 248 Table 31: Summary of simulation output used as baseline simulation scenario for sensitivity analysis 254 Table 32a: Summary of simulation output for simulation scenario testing the effect of a 25m radius of increased risk of infection around infected dens 255 Table 32b: Summary of simulation output for simulation scenario testing the effect of a 75m radius of increased risk of infection around infected dens 256 Table 33a: Summary of simulation output for simulation scenario testing the effect of a 75m mating travel distance 257 Table 33b: Summary of simulation output for simulation scenario testing the effect of a 125m mating travel distance 258 Table 34a: Summary of simulation output for simulation scenario testing the effect of a 75m den search distance 259 Table 34b: Summary of simulation output for simulation scenario testing the effect of a 125m den search distance 260 Table 35a: Summary of simulation output for simulation scenario testing the effect of disabling transmission through infected den sites 261 Table 35b: Summary of simulation output for simulation scenario testing the effect of disabling transmission through spatial proximity 262 Table 35c: Summary of simulation output for simulation scenario testing the effect of disabling transmission through mating contact 263 Table 35d: Summary of simulation output for simulation scenario testing the effect of disabling pseudo-vertical transmission 264 Table 36: Statistical comparison of sensitivity analysis scenarios with the baseline simulation scenario using Scheffe's test combining data from original and antithetic run 265 Table 37: Summary of simulation output for model testing the effect of removing immigration 268 Table 38: Summary of simulation output for model testing the effect of a single reduction in popUlation density to 25% without immigration 270 Table 39: Summary of simulation output for model testing the effect of a single reduction in popUlation density to 25% in the presence of immigration free from clinical tuberculosis 272 Table 40: Summary of simulation output for model testing the effect of a single reduction in popUlation density to 25% in the presence of 5% clinical tuberculosis prevalence in immigrants 273 Table 41: Summary of simulation output for model testing the effect of a permanent reduction in den site density in the absence of immigration 275 Table 42: Summary of simulation output for model testing effect of permanent reduction in den site density in the presence of immigration free from clinical tuberculosis 276 Table 43: Summary of simulation output for model testing effect of permanent reduction in den site density, in the presence of immigration with 5% clinical tuberculosis prevalence 278 Table 44: Summary of simulation output for model testing effect of repeated population control operations at 3 yearly intervals in the presence of 5% clinical tuberculosis in immigrants 279 Table 45: Summary of simulation output for model testing effect of repeated population control operations at 6 yearly intervals in the presence of 5% clinical tuberculosis in immigrants 281 Table 46: Codes and descriptions of variables used in the multivariate analysis 313 Table 47a: Some results of univariate analysis for random controls using logistic regression 317 xx Table 47b: Some results of univariate analysis for matched controls using logistic regression 3 I 8 Table 48a: Stepwise logistic regression analysis for cases compared with random controls 330 Table 48b: Summary of the results of stepwise logistic regression analysis for cases compared with random controls 331 Table 49: Final logistic regression model comparing cases and random controls 332 Table 50a: Stepwise logistic regression analysis for cases compared with matched controls using the unconditional approach 334 Table 50b: Summary of the results of unconditional stepwise logistic regression analysis for cases compared with matched controls 335 Table 50c: Stepwise logistic regression analysis for cases compared with matched controls using the conditional approach 336 Table 50d: Summary of the results of conditional stepwise logistic regression analysis for cases compared with matched controls 337 Table 51: Comparison of coefficients of logistic regression models for cases and matched controls using the unconditional and the conditional approach 337 Table 52: Final conditional logistic regression model comparing cases and matched controls 338 Table 53: Results of regression analyses for final path model comparing cases with random controls 339 Table 54: Results of regression analyses for fmal path model comparing cases with matched controls 342 Table 55a: Goodness of fit of the final path models 345 Table 55b: Total and direct effects on case-control status in the final path models 346 Table 56a: Summary of infonnation about the fmal classification trees 350 Table 56b: Variable rankings according to relative importance 351