Efficient management of epidemics is one of the primary motivations for computational modelling of disease dynamics. Examples range from reactive control measures, where the resources used to manage the epidemic in real time may be limited to prophylactic control measures such as deployment of genetically resistant plant varieties, which may lead to economic trade-offs. In such situations the question is how should resources for disease control be deployed to ensure the efficient management of the epidemic. Mathematical models are a powerful tool to investigate such questions since experiments are usually infeasible and the primary aim of this thesis is to study selected mathematical models of disease control to improve the current understanding of their behaviour. We initially analyse the dynamical behaviour that arises from incorporating an economic constraint into two simple, but widely used epidemic models with reactive control. Despite the selection of simple models, the addition of constrained control leads to mathematically rich dynamics, including the coexistence of multiple stable equilibria and stable limit cycles arising from global bifurcations. We use the analytical understanding obtained from the simple model to explore how to allocate a limited resource optimally between a number of separate populations that are exposed to an epidemic. Initially, we assume that the allocation is done at the beginning and cannot be changed later. We seek to answer the question of how the resource should be allocated efficiently to minimise the long-term number of infections. We show that the optimal allocation strategy can be approximated by a solution to a knapsack-type problem, that is the problem of how to select items of varying values and weights to maximise combined value without going over certain combined weight. The weights and values are given as functions of the population sizes, initial conditions, and the disease parameters. Later, we relax the assumptions to allow for reallocation and use the understanding of the dynamics gained from the simple models in the beginning to devise a new continuous time reallocation strategy, which outperforms previously considered approaches. In the final part of the thesis, we focus on plant disease and study a model of prophylactic control using a genetically resistant variety. We consider a trade-off where the genetic resistance carries with it a fitness penalty and therefore reduces yield. We identify the conditions on the parameters under which the resistant variety should be deployed and investigate how these change when the outbreak is uncertain. We show that deploying the resistant variety reduces the probability of an outbreak occurring and therefore can be optimal even when it would not be optimal to deploy it during the outbreak.

This paper considers a series of models and the effect of HIV antibody testing on the dynamics of the disease. We examine HIV antibody testing in conjunction with persuasive techniques designed to encourage tested infected to behave in a sexually responsible manner. The population under consideration is a homosexual population. Analytical methods are used to obtain information about the qualitative behaviour of the models. Areas requiring further study are discussed. / Thesis / Master of Science (MSc)

Malaria poses a serious threat to much of the developing world and an enormous effort is under way to design vaccines and other novel interventions. Nevertheless, we understand very little about the ecology and evolution of malaria parasites. For instance, while scientists have had considerable success identifying factors involved in regulating parasite growth within hosts, it is extremely hard to disentangle the relative influences of host immunity and other within-host factors on infection dynamics. Many mathematical models have been directed at understanding the dynamics of malaria infections, and these have provided valuable insights. However, these models have also been criticized, most notably for lacking any statistical analysis of the goodness of fit of model predictions to data. Here, we develop a new modeling approach that improves on previous work, and apply it to a novel data set from a simplified rodent malaria system. We find that resource availability and competition are important drivers of dynamics, and we identify a number of parasite traits that may underlie differences in virulence between parasite strains. These include the number of progeny parasites produced per infected cell (burst size) and the invasion rates of target cells. We test these predictions with further experiments and find broad support for the role of burst sizes in determining virulence, but the role of invasion rates is less certain. We also find evidence of potential plasticity in these parasite traits in response to within-host environmental factors. These within-host interactions between parasites and hosts have effects that will scale up to between-host processes; we discuss the growing body of theory that seeks to combine these levels (‘embedded models’). Using between-host and embedded models, we test the plausibility of various hypotheses to explain why there are so few transmissible malaria parasite forms, yet vast numbers of host-damaging asexual forms are produced. We show that a specific form of density-dependent transmission-blocking immunity and the occurrence of multiple infections can each generate selection for this pattern. Overall, this thesis contributes to a better under- standing of malaria parasites, while providing a framework for addressing unanswered questions in disease biology, and offering interesting paths for future empirical work. / Thesis (Ph.D, Biology) -- Queen's University, 2009-08-20 06:41:14.198

Understanding demographic and disease processes in wildlife populations tends to be hampered by incomplete observations which can include significant errors. Models provide useful insights into the potential impacts of key processes and the value of such models greatly improves through integration with available data in a way that includes all sources of stochasticity and error. To date, the impact on disease of spatial and social structures observed in wildlife populations has not been widely addressed in modelling. I model the joint effects of differential fecundity and spatial heterogeneity on demography and disease dynamics, using a stochastic description of births, deaths, social-geographic migration, and disease transmission. A small set of rules governs the rates of births and movements in an environment where individuals compete for improved fecundity. This results in realistic population structures which, depending on the mode of disease transmission can have a profound effect on disease persistence and therefore has an impact on disease control strategies in wildlife populations. I also apply a simple model with births, deaths and disease events to the long-term observations of TB (Mycobacterium bovis) in badgers in Woodchester Park. The model is a continuous time, discrete state space Markov chain and is fitted to the data using an implementation of Bayesian parameter inference with an event-based likelihood. This provides a flexible framework to combine data with expert knowledge (in terms of model structure and prior distributions of parameters) and allows us to quantify the model parameters and their uncertainties. Ecological observations tend to be restricted in terms of scope and spatial temporal coverage and estimates are also affected by trapping efficiency and disease test sensitivity. My method accounts for such limitations as well as the stochastic nature of the processes. I extend the likelihood function by including an error term that depends on the difference between observed and inferred state space variables. I also demonstrate that the estimates improve by increasing observation frequency, combining the likelihood of more than one group and including variation of parameter values through the application of hierarchical priors.

Brucellosis is a bacterial infection that primarily affects livestock and can also be transmitted to humans. In the Greater Yellowstone Ecosystem (GYE), elk (Cervus canadensis) and bison (Bison bison) are habitual carriers of Brucella abortus, which arrived to the region with cattle over a century ago. The disease was eliminated from cattle in the United States through widespread control efforts, but is now periodically transmitted back to cattle on open rangelands where they can come into contact with fetal tissues and fluids from disease-induced abortions that occur among elk during the late winter and spring. In Wyoming, south of Yellowstone National Park, there are 23 supplemental feedgrounds that operate annually and feed the majority of the region’s elk during a portion of the winter. The feedgrounds are controversial because of their association with brucellosis and may be shuttered in the future in part due to the arrival of chronic wasting disease. Using data collected at these feedgrounds, this study investigates the role of winter feedgrounds in the ecology of this host-pathogen relationship: it evaluates the full reproductive costs of the disease to affected elk, how herd demography influences pathogen transmission, and assesses management strategies aimed at reducing pathogen spread among elk. Using blood tests for pregnancy status and brucellosis exposure in female elk, I demonstrated a previously undocumented fertility cost associated with the pathogen which is not due to abortions, but which nearly doubles the estimated fertility cost to affected individuals. I also built mechanistic transmission models using time-series disease and count data from feedgrounds. Within that framework, I assessed various management actions including test-and-slaughter of test-positive elk, which I found to be counterproductive due to rapid recovery times and the protective effects of herd immunity. The overall picture that emerges of winter feedgrounds is one of imperfect practicality driven by social and political consideration, not pathogen control. These results illustrate the underappreciated importance that recruitment and population turnover have on the transmission dynamics of brucellosis in elk, a pathogen which itself flourishes in the reproductive tracts of individual animals and thus impacts vital rates at the population level. Together, this study contributes to the field of disease ecology using a unique long term disease data set of free-ranging wild ungulates.

Emerging infectious diseases (EID) pose significant threats to biodiversity. Human influence over the environment has increased opportunities for the introduction of novel pathogens to naïve hosts, potentially leading to host extinction. Understanding mechanisms of host persistence is critical for effectively conserving species affected by EIDs. Our study investigated the disease dynamics of white-nose syndrome (WNS), caused by the fungal pathogen Pseudogymnoascus destructans (Pd), in little brown bats (Myotis lucifugus) across a spatiotemporal gradient. We explored the relationship between bat roosting temperatures and Pd growth rates across three phases of pathogen invasion comprising years since WNS has been present at sites: invasion (0-3), established (4-8), and endemic (9+ years). Data used by this study comes from a combination of field-based data collection in New York where WNS has been present the longest and data from a long-running project which includes from other locations in the Northeast and Midwest regions of the United States. Our results reveal a weakening interaction between temperature and fungal growth rates time with WNS progresses. We additionally observed a decrease in early hibernation fungal loads and variation in infection prevalence over time, suggesting the onset of a coevolutionary relationship between bats and Pd. This study highlights the importance of investigating changing disease dynamics when understanding the reasonings for host persistence. / Master of Science / Emerging infectious diseases threaten species with the risk of extinction. Human activities have altered habitats which has increased the spread of new pathogens to vulnerable host populations. This research focuses on white-nose syndrome (WNS), an emerging disease caused by the fungal pathogen Pseudogymnoascus destructans (Pd). The arrival of Pd to North America resulted in widespread declines in little brown bat (Myotis lucifugus) populations, however, some populations persist at stable or growing rates. This study aims to investigate how the relationship between the growth rate of Pd and bat hibernation temperature may have changed over time. We used a combination of contemporary data collected in New York and a long-running dataset that documents the invasion and establishment of Pd across the Northeast and Midwestern regions of the United States to investigate fungal growth rates during different phases of Pd invasion: invasion, established, and endemic phases. Our results indicate the relationship between temperature and pathogen growth rate has weakened over time, suggesting potential changes in the host-pathogen relationship. Additionally, we found changes in fungal loads and infection prevalence throughout hibernation, suggesting the foundation of a coevolutionary relationship between bats and Pd. This research highlights the importance of understanding changes in disease dynamics to help understand how other species at risk of emerging infectious diseases may be able to persist.

Agent-based epidemic simulation (ABES) is a powerful and realistic approach for studying the impacts of disease dynamics and complex interventions on the spread of an infection in the population. Among many ABES systems, EpiSimdemics comes closest to the popular agent-based epidemic simulation systems developed by Eubank, Longini, Ferguson, and Parker. EpiSimdemics is a general framework that can model many reaction-diffusion processes besides the Susceptible-Exposed-Infectious-Recovered (SEIR) models. This model allows the study of complex systems as they interact, thus enabling researchers to model and observe the socio-technical trends and forces. Pandemic planning at the world level requires simulation of over 6 billion agents, where each agent has a unique set of demographics, daily activities, and behaviors. Moreover, the stochastic nature of epidemic models, the uncertainty in the initial conditions, and the variability of reactions require the computation of several replicates of a simulation for a meaningful study. Given the hard timelines to respond, running many replicates (15-25) of several configurations (10-100) (of these compute-heavy simulations) can only be possible on high-performance clusters (HPC). These agent-based epidemic simulations are irregular and show poor execution performance on high-performance clusters due to the evolutionary nature of their workload, large irregular communication and load imbalance. For increased utilization of HPC clusters, the simulation needs to be scalable. Many challenges arise when improving the performance of agent-based epidemic simulations on high-performance clusters. Firstly, large-scale graph-structured computation is central to the processing of these simulations, where the star-motif quality nodes (natural graphs) create large computational imbalances and communication hotspots. Secondly, the computation is performed by classes of tasks that are separated by global synchronization. The non-overlapping computations cause idle times, which introduce the load balancing and cost estimation challenges. Thirdly, the computation is overlapped with communication, which is difficult to measure using simple methods, thus making the cost estimation very challenging. Finally, the simulations are iterative and the workload (computation and communication) may change through iterations, as a result introducing load imbalances. This dissertation focuses on developing a cost estimation model and load balancing schemes to increase the runtime efficiency of agent-based epidemic simulations on high-performance clusters. While developing the cost model and load balancing schemes, we perform the static and dynamic load analysis of such simulations. We also statically quantified the computational and communication workloads in EpiSimdemics. We designed, developed and evaluated a cost model for estimating the execution cost of large-scale parallel agent-based epidemic simulations (and more generally for all constrained producer-consumer parallel algorithms). This cost model uses computational imbalances and communication latencies, and enables the cost estimation of those applications where the computation is performed by classes of tasks, separated by synchronization. It enables the performance analysis of parallel applications by computing its execution times on a number of partitions. Our evaluations show that the model is helpful in performance prediction, resource allocation and evaluation of load balancing schemes. As part of load balancing algorithms, we adopted the Metis library for partitioning bipartite graphs. We have also developed lower-overhead custom schemes called Colocation and MetColoc. We performed an evaluation of Metis, Colocation, and MetColoc. Our analysis showed that the MetColoc schemes gives a performance similar to Metis, but with half the partitioning overhead (runtime and memory). On the other hand, the Colocation scheme achieves a similar performance to Metis on a larger number of partitions, but at extremely lower partitioning overhead. Moreover, the memory requirements of Colocation scheme does not increase as we create more partitions. We have also performed the dynamic load analysis of agent-based epidemic simulations. For this, we studied the individual and joint effects of three disease parameter (transmissiblity, infection period and incubation period). We quantified the effects using an analytical equation with separate constants for SIS, SIR and SI disease models. The metric that we have developed in this work is useful for cost estimation of constrained producer-consumer algorithms, however, it has some limitations. The applicability of the metric is application, machine and data-specific. In the future, we plan to extend the metric to increase its applicability to a larger set of machine architectures, applications, and datasets. / Ph. D.

In mathematical epidemiology, disease transmission is commonly assumed to behave in accordance with the law of mass action; however, other disease incidence terms also exist in the literature. A homogeneous Susceptible-Infectious-Removed (SIR) model with a generalized incidence term is presented along with analytic and numerical results concerning effects of the generalization on the global disease dynamics. The spatial heterogeneity of the metapopulation with nonrandom directed movement between populations is incorporated into a heterogeneous SIR model with nonlinear incidence. The analysis of the combined effects of the spatial heterogeneity and nonlinear incidence on the disease dynamics of our model is presented along with supporting simulations. New global stability results are established for the heterogeneous model utilizing a graph-theoretic approach and Lyapunov functions. Numerical simulations confirm nonlinear incidence gives raise to rich dynamics such as synchronization and phase-lock oscillations.

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The history of mitigation programs to contain vector-borne diseases is a story of successes and failures. Due to the complex interplay among multiple factors that determine disease dynamics, the general principles for timely and specific intervention for incidence reduction or eradication of life-threatening diseases has yet to be determined. This research discusses computational methods developed to assist in the understanding of complex relationships affecting vector-borne disease dynamics. A computational framework to assist public health practitioners with exploring the dynamics of vector-borne diseases, such as malaria and dengue in homogenous and heterogeneous populations, has been conceived, designed, and implemented. The framework integrates a stochastic computational model of interactions to simulate horizontal disease transmission. The intent of the computational modeling has been the integration of stochasticity during simulation of the disease progression while reducing the number of necessary interactions to simulate a disease outbreak. While there are improvements in the computational time reducing the number of interactions needed for simulating disease dynamics, the realization of interactions can remain computationally expensive. Using multi-threading technology to improve performance upon the original computational model, multi-threading experimental results have been tested and reported. In addition, to the contact model, the modeling of biological processes specific to the corresponding pathogen-carrier vector to increase the specificity of the vector-borne disease has been integrated. Last, automation for requesting, retrieving, parsing, and storing specific weather data and geospatial information from federal agencies to study the differences between homogenous and heterogeneous populations has been implemented.