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«by Paul Chafee Cross B.A. (University of Virginia) 1998 A dissertation submitted in partial satisfaction of the requirements for the degree of Doctor ...»

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Disease Invasion and Control in Structured Populations: Bovine Tuberculosis in the

Buffalo Population of the Kruger National Park


Paul Chafee Cross

B.A. (University of Virginia) 1998

A dissertation submitted in partial satisfaction of the requirements for the degree of

Doctor of Philosophy


Environmental Science, Policy and Management

in the


of the


Committee in charge:

Professor Wayne M. Getz, Chair Professor Steven R. Beissinger Professor Cheryl J. Briggs Professor Johan T. du Toit May 2005 Disease Invasion and Control in Structured Populations: Bovine Tuberculosis in the Buffalo Population of the Kruger National Park © 2005 by Paul Chafee Cross Abstract Disease Invasion and Control in Structured Populations: Bovine Tuberculosis in the Buffalo Population of the Kruger National Park by Paul Chafee Cross Doctor of Philosophy in Environmental Science, Policy and Management University of California, Berkeley Professor Wayne M. Getz, Chair From 1991 to 2004, bovine tuberculosis (Mycobacterium bovis, BTB) moved north and increased in prevalence in the African buffalo (Syncerus caffer) population of the Kruger National Park, South Africa. I use this epidemic as a case study to understand how host population structure affects disease dynamics. Radio-tracking data indicated that all sex and age groups moved between herds, but males over eight years old had higher mortality and dispersal rates than any other sex or age category. BTB appeared to have only minor effects upon survival. Models incorporating these data suggest that the success of vaccination programs will depend strongly upon the duration that a vaccine grants protection, which is currently unknown. Even with a lifelong vaccine, however, eradication is unlikely unless vaccination is combined with other control strategies.

To analyze the radio-tracking and association data, I proposed a new metric of association, the fission decision index (FDI) that significantly reduces the biases that exist in traditional association analyses in fission-fusion societies. Adult female and juvenile buffalo made non-random fission decisions while adult male choices were indistinguishable from a random coin toss. Incorporating the association data into a dynamic social network model suggested that the dynamic nature of the network has a strong influence on disease dynamics, particularly for diseases with shorter infectious periods. Buffalo herds were more tightly associated in 2002 than 2003, perhaps due to drier conditions in 2003 prompting additional movement that would facilitate the spread of disease among herds.

Using a metapopulation model, I illustrate how the group-level metric, R*, which is the average number of groups infected by the initial group, is a better predictor of disease invasion than the traditional individual-level R0 in structured host populations. R* is a function of group size, movement rate, infection rate, and length of the infectious period. Chronic diseases allow for more host mixing between groups;

thus they ‘perceive’ a more well-mixed host population. As a result, chronic diseases are more likely to invade structured populations than acute diseases, given the same R0, and it is more important to incorporate the spatial structure of the host population for acute diseases than chronic diseases.

Table of Contents Acknowledgements

Chapter One

Chapter Two

Chapter Three

Chapter Four

Chapter Five


–  –  –

First, I would like to thank my family for all of their support. Craig Hay, Justin Bowers, Julie Wolhuter, Khutani Bulunga, and Augusta Mabunda collected the vast majority of the field data included in this dissertation. Always professional and great companions, they made the last four years in Satara an amazing experience. I am grateful to the managers, scientists, and staff of the Kruger National Park for facilitating the project, and to the United States National Science Foundation Ecology of Infectious Disease Grant DEB-0090323 for funding this research. Drs. Markus Hofmeyr, Peter Buss, Lin-Mari de Klerk, Roy Bengis and Douw Grobler, as well as Marius Kruger, KNP Game Capture, State Veterinary technicians, and many University of Pretoria students assisted in buffalo capture operations. Roy Bengis, Steve Beissinger, Cherie Briggs, Justin Brashares, Charlie Nunn, and Anna Jolles all provided many helpful comments along the way. Martin Haupt and Elmarie Cronje at the University of Pretoria were invaluable in their assistance with equipment and finances. All the students in the Getz Lab including Peter Baxter, Chris Wilmers, Sadie Ryan, Andy Lyons, Allison Bidlack, Wendy Turner, Shirli Bar-David, John Eppley, George Wittemyer, James Lloyd-Smith, and Karen Levy, made it a fantastic environment to work in. In particular, Jamie Lloyd-Smith and George Wittemyer were a great support and source of ideas and inspiration throughout this dissertation. Lastly, I would like to thank Molly Smith, Johan du Toit, and Wayne Getz. To list all the ways that they helped would be its own dissertation.

–  –  –

Summary P.C. Cross Bovine tuberculosis (BTB), caused by Mycobacterium bovis, is an airborne bacterial pathogen that is re-emerging in wildlife and livestock worldwide. In the Kruger National Park (KNP) of South Africa, BTB is increasing in prevalence and moving northwards from its introduction from cattle along the southern border of the KNP in the early 1960s (Bengis et al. 1996, Bengis 1999, Rodwell et al. 2001). African buffalo (Syncerus caffer caffer) are a reservoir host, maintaining the disease at high prevalence (over 50% in some herds), while predators such as lions and leopards appear to be spillover hosts (Keet et al. 1996, Rodwell et al. 2000). It remains unclear how the effects of BTB, with its wide range of potential hosts, will ripple through the KNP ecosystem (Caron et al. 2003). Furthermore, Kruger National Park is the largest reserve in South Africa, covering over 20,000 km2 and is the source of many animal translocations.

BTB may limit the ability of KNP managers to translocate animals from the KNP, thereby decreasing a potential source of revenue for South African National Parks and creating a conservation island.

This dissertation is one component of a larger research program on BTB in the buffalo population of the KNP, the goal of which is to develop a better understanding of disease dynamics in wildlife systems as well as to evaluate potential management strategies. Here I investigate the role of host social and spatial structure on the spread and control of disease by integrating empirical data with a number of different epidemiological models and using BTB in buffalo as a case study. Early models of disease dynamics assumed a homogenous host population that was well-mixed (Kermack and McKendrick 1927, Anderson and May 1979, May and Anderson 1979, Anderson and May 1991). Recent studies have begun to investigate the role of spatial and social structure to disease invasion or persistence (e.g. Hess 1996, Swinton et al.

1998, Keeling 1999, Keeling and Gilligan 2000, Keeling and Grenfell 2000, Park et al.

2001, Eames and Keeling 2002, Fulford et al. 2002, Keeling and Rohani 2002, Newman 2002, Park et al. 2002, Read and Keeling 2003, Eames and Keeling 2004, Eubank et al.

2004, Hagenaars et al. 2004). In this dissertation, I investigate host structure in four different contexts. First, I investigate the effect of age and sex structure within a single herd on the efficacy of a proposed BTB vaccination program. Second, I illustrate how traditional association analyses may result in biased conclusions about host social structure in fission-fusion societies and propose a new metric of individual association that may be more appropriate in fission-fusion societies such as buffalo. Third, I illustrate how an empirically-derived social network affects disease dynamics for diseases of different infectious periods. Finally, I use a metapopulation model with explicit movement to illustrate how traditional metrics of disease invasion break down in structured populations.

As an exotic disease, KNP managers would like to control or eradicate BTB via culling, vaccination, or some combination of the two. Previous modeling work on BTB in buffalo, however, suggests that BTB may persist even when the buffalo population is reduced to low densities, making random culling, for the purpose of eradication, problematic (Rodwell 2000). Thus, vaccination, or some combination of vaccination and culling, is a more attractive management option. Early action is likely to be the most effective, however there are many uncertainties surrounding the potential impacts (or lack thereof) of BTB on the buffalo population and spill-over hosts, the efficacy and duration of the vaccine in buffalo, and the potential effectiveness of a vaccination or test-and-remove management strategy.

In the second chapter, we use a sex and age structured epidemiological model to assess the potential efficacy a vaccination program on controlling or eradicating BTB in a single buffalo herd. The model incorporates dispersal of individuals between the focal herd and a constant background population as well as the non-random mixing of sex and age categories within a herd. The model is parameterized with survival and dispersal estimates from over 130 radio-collared buffalo that were intensively monitored over a three-year period. We use the model to assess the importance of between-herd mixing, the potential effectiveness of a vaccination strategy, and whether a vaccination strategy can be improved by focusing on particular sex and age groups.

Radio-tracking data indicated that all sex and age categories move between mixed herds, and males over eight years old had higher mortality and dispersal rates than any other sex or age category. In part due to the high dispersal rates of buffalo, sensitivity analyses indicate that disease prevalence in the background population accounts for the most variability in the BTB prevalence and quasi-eradication within the focal herd. Vaccination rate and the transmission coefficient were the second and third most important parameters of the sensitivity analyses. Further analyses of the model without dispersal suggest that the amount of vaccination necessary for quasi-eradication (i.e. prevalence 5%) depends upon the duration that a vaccine grants protection.

Vaccination programs are more efficient (i.e. fewer wasted doses) when they focus on younger individuals. However, even with a lifelong vaccine and a closed population, the model suggests that 70% of the calf population would have to be vaccinated every year to reduce the prevalence to less than 1%. If the half-life of the vaccine is less than five years, even vaccinating every calf for 50 years may not eradicate BTB. Thus, although vaccination provides a means of controlling BTB prevalence it should be combined with other control measures if eradication is the objective.

In the third chapter, we investigate the social structure of buffalo in greater depth and develop new techniques for analyzing association patterns in fission-fusion societies. Previous studies of association patterns usually calculate an association index of the proportion of time or sightings that a pair of individuals is seen together. Using a simulation model we show how this method can yield biased results in fission-fusion societies. In particular, if sampling occurs more often than fission and fusion events, the proportion of time dyads spend together will show statistically significant clustering, even if individuals choose herds at random and independently of other individuals’ decisions. This follows because multiple samples taken within the same inter-fission interval are autocorrelated with respect to individual choices. Thus, we propose a new metric, the fission decision index (FDI), which is the number of times a pair of individuals chose to remain together when a group separates. The FDI eliminates autocorrelated data and presents an unbiased estimate of individual choices.

Traditional association analyses suggested that the buffalo population we studied was spatially and temporally structured into four different groups that were statistically different from random. The FDI approach, however, illustrated that the probability of a dyad remaining in the same group during a fission event was not closely correlated with the amount of time they spent together. Therefore, the non-random group structure apparent in the traditional association analysis was due in small part to non-random decisions made by individuals during all fission events, but in greater part to the variable lifetimes of the resulting fission groups. Consideration of FDI scores thus helped us to understand the mechanisms underlying results of traditional association analysis.

In the fourth chapter, we integrate the radio-tracking association data with a dynamic social network model of disease dynamics. Association data are often collected but, to the author’s knowledge, this is the first use of empirical data in a network disease model in a wildlife population. Although there are still aspects of this approach that need to be further developed before it can be applied more broadly, we believe it provides a flexible method of capturing the social structure of wildlife populations that are not well-described by more traditional methods such as metapopulation or cellular-automata models. Using this method, we investigate the importance of network topology and the amount of switching between groups to disease spread. We also analyze the effect of increasing the variance in association index. In other words, for disease spread does it matter if the individuals associate equally with their neighbors or if individuals have a set of close friends and loose associates?

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