This dissertation seeks to understand and study the process of attention harvesting and knowledge production on typical online Q&A communities. Goals of this study include quantifying the attention harvesting and online knowledge, damping the effect of competition for attention on knowledge production, and examining the diversity of user behaviors on question answering. Project 1 starts with a simplistic discrete time model on a scale-free network and provides the method to measure the attention harvested. Further, project 1 highlights the effect of distractions on harvesting productive attention and in the end concludes which factors are influential and sensitive to the attention harvesting. The main finding is the critical condition to optimize the attention harvesting on the network by reducing network connection. Project 2 extends the scope of the study to quantify the value and quality of knowledge, focusing on the question answering dynamics. This part of research models how attention was distributed under typical answering strategies on a virtual online Q&A community. The final result provides an approach to measure the efficiency of attention transferred into value production and observes the contribution of different scenarios under various computed metrics. Project 3 is an advanced study on the foundation of the virtual question answering community from project 2. With highlights of different user behavioral preferences, algorithm stochastically simulates individual decisions and behavior. Results from sensitivity analysis on different mixtures of user groups gives insight of nonlinear dynamics for the objectives of success. Simulation finding shows reputation rewarding mechanism on Stack Overflow shapes the crowd mixture of behavior to be successful. In addition, project proposed an attention allocation scenario of question answering to improve the success metrics when coupling with a particular selection strategy.

Network analysis is a key conceptual orientation and analytical tool in the social sciences that emphasizes the embeddedness of individual behavior within a larger web of social relations. The network approach is used to better understand the cause and consequence of social interactions which cannot be treated as independent. The relational nature of network data and models, however, amplify the methodological concerns associated with inaccurate or missing data. This dissertation addresses such concerns via three projects. As a motivating substantive example, Project 1 examines factors associated with the selection of interaction partners by students at a large urban high school implementing a reform which, like many organizational improvement initiatives, is associated with a theory of change that posits changes to the structuring of social interactions as a central causal pathway to improved outcomes. A distinctive aspect of the data used in Project 1 is that it was a complete egocentric network census – in addition to being asked about their own relationships, students were asked about the relationships between alters that they nominated in the self-report. This enables two unique examinations of methodological challenges in network survey data collection: Project 2 examines the factors related to how well survey respondents assess the strength of social connections between others, finding that "informant" competence corresponds positively with their social proximity to target dyad as well as their centrality in the network. Project 3 explores using such third-party reports to augment network imputation methods, and finds that incorporating third-party reports into model-based methods provides a significant boost in imputation accuracy. Together these findings provide important implications for collecting and extrapolating data in research contexts where a complete social network census is highly desirable but infeasible.

Honeybees are important pollinators worldwide and pollinate about one-third of the food we consume. Recently though, honeybee colonies have been under increasing stress due to changing environments, pesticides, mites, and viruses, which has increased the incidence of
colony collapse. This paper aims to understand how these different factors contribute to the decline of honeybee populations by using two separate approaches: data analysis and mathematical modeling. The data analysis examines the relative impacts of mites, pollen, mites, and viruses on honeybee populations and colony collapse. From the data, low initial bee populations lead to collapse in September while mites and viruses can lead to collapse in December. Feeding bee colonies also has a mixed effect, where it increases both bee and mite populations. For the model, we focus on the population dynamics of the honeybee-mite interaction. Using a system of delay differential equations with five population components, we find that bee colonies can collapse from mites, coexist with mites, and survive without them. As long as bees produce more pupa than the death rate of pupa and mites produce enough phoretic mites compared to their death rates, bees and mites can coexist. Thus, it is possible for honeybee colonies to withstand mites, but if the parasitism is too large, the colony will collapse. Provided
this equilibrium exists, the addition of mites leads to the colony moving to the interior equilibrium. Additionally, population oscillations are persistent if they occur and are connected to the interior equilibrium. Certain parameter values destabilize bee populations, leading to large
oscillations and even collapse. From these parameters, we can develop approaches that can help us prevent honeybee colony collapse before it occurs.

The most advanced social insects, the eusocial insects, form often large societies in which there is reproductive division of labor, queens and workers, have overlapping generations, and cooperative brood care where daughter workers remain in the nest with their queen mother and care for their siblings. The eusocial insects are composed of representative species of bees and wasps, and all species of ants and termites. Much is known about their organizational structure, but remains to be discovered.

The success of social insects is dependent upon cooperative behavior and adaptive strategies shaped by natural selection that respond to internal or external conditions. The objective of my research was to investigate specific mechanisms that have helped shaped the structure of division of labor observed in social insect colonies, including age polyethism and nutrition, and phenomena known to increase colony survival such as egg cannibalism. I developed various Ordinary Differential Equation (ODE) models in which I applied dynamical, bifurcation, and sensitivity analysis to carefully study and visualize biological outcomes in social organisms to answer questions regarding the conditions under which a colony can survive. First, I investigated how the population and evolutionary dynamics of egg cannibalism and division of labor can promote colony survival. I then introduced a model of social conflict behavior to study the inclusion of different response functions that explore the benefits of cannibalistic behavior and how it contributes to age polyethism, the change in behavior of workers as they age, and its biological relevance. Finally, I introduced a model to investigate the importance of pollen nutritional status in a honeybee colony, how it affects population growth and influences division of labor within the worker caste. My results first reveal that both cannibalism and division of labor are adaptive strategies that increase the size of the worker population, and therefore, the persistence of the colony. I show the importance of food collection, consumption, and processing rates to promote good colony nutrition leading to the coexistence of brood and adult workers. Lastly, I show how taking into account seasonality for pollen collection improves the prediction of long term consequences.

For colonies of ponerine ant species, sterility regulation after a founding queen's death is not totally achieved in the worker caste, and the possibility of sexual reproduction is opened to workers. The persisting survival of these colonies is dependent on capturing the optimal reproductive ratio; yet, an informational gap bounds the mechanisms detailing the selection of new reproductives and the suppression of ovarian development in rejected reproductives. We investigated the mechanisms of worker policing, one of the primary methods of ovarian suppression, through continuous video observation for a period of five days at the start of colony instability. Observations suggest policing in H. saltator is performed by a majority of a colony, including potential reproductives, and requires multiple events to fully discourage ovarian growth.

This dissertation explores the impact of environmental dependent risk on disease dynamics within a Lagrangian modeling perspective; where the identity (defined by place of residency) of individuals is preserved throughout the epidemic process. In Chapter Three, the impact of individuals who refuse to be vaccinated is explored. MMR vaccination and birth rate data from the State of California are used to determine the impact of the anti-vaccine movement on the dynamics of growth of the anti-vaccine sub-population. Dissertation results suggest that under realistic California social dynamics scenarios, it is not possible to revert the influence of anti-vaccine

contagion. In Chapter Four, the dynamics of Zika virus are explored in two highly distinct idealized environments defined by a parameter that models highly distinctive levels of risk, the result of vector and host density and vector control measures. The underlying assumption is that these two communities are intimately connected due to economics with the impact of various patterns of mobility being incorporated via

the use of residency times. In short, a highly heterogeneous community is defined by its risk of acquiring a Zika infection within one of two "spaces," one lacking access to health services or effective vector control policies (lack of resources or ignored due to high levels of crime, or poverty, or both). Low risk regions are defined as those with access to solid health facilities and where vector control measures are implemented routinely. It was found that the better connected these communities are, the existence of communities where mobility between risk regions is not hampered, lower the overall, two patch Zika prevalence. Chapter Five focuses on the dynamics of tuberculosis (TB), a communicable disease, also on an idealized high-low risk set up. The impact of mobility within these two highly distinct TB-risk environments on the dynamics and control of this disease is systematically explored. It is found that collaboration and mobility, under some circumstances, can reduce the overall TB burden.

In this dissertation the potential impact of some social, cultural and economic factors on

Ebola Virus Disease (EVD) dynamics and control are studied. In Chapter two, the inability

to detect and isolate a large fraction of EVD-infected individuals before symptoms onset is

addressed. A mathematical model, calibrated with data from the 2014 West African outbreak,

is used to show the dynamics of EVD control under various quarantine and isolation

effectiveness regimes. It is shown that in order to make a difference it must reach a high

proportion of the infected population. The effect of EVD-dead bodies has been incorporated

in the quarantine effectiveness. In Chapter four, the potential impact of differential

risk is assessed. A two-patch model without explicitly incorporate quarantine is used to

assess the impact of mobility on communities at risk of EVD. It is shown that the

overall EVD burden may lessen when mobility in this artificial high-low risk society is allowed.

The cost that individuals in the low-risk patch must pay, as measured by secondary

cases is highlighted. In Chapter five a model explicitly incorporating patch-specific quarantine

levels is used to show that quarantine a large enough proportion of the population

under effective isolation leads to a measurable reduction of secondary cases in the presence

of mobility. It is shown that sharing limited resources can improve the effectiveness of

EVD effective control in the two-patch high-low risk system. Identifying the conditions

under which the low-risk community would be willing to accept the increases in EVD risk,

needed to reduce the total number of secondary cases in a community composed of two

patches with highly differentiated risks has not been addressed. In summary, this dissertation

looks at EVD dynamics within an idealized highly polarized world where resources

are primarily in the hands of a low-risk community – a community of lower density, higher

levels of education and reasonable health services – that shares a “border” with a high-risk

community that lacks minimal resources to survive an EVD outbreak.

Foraging strategies in social animals are often shaped by change in an organism's natural surrounding. Foraging behavior can hence be highly plastic, time, and condition dependent. The motivation of my research is to explore the effects of dispersal behavior in predators or parasites on population dynamics in heterogeneous environments by developing varied models in different contexts through closely working with ecologists. My models include Ordinary Differential Equation (ODE)-type meta population models and Delay Differential Equation (DDE) models with validation through data. I applied dynamical theory and bifurcation theory with carefully designed numerical simulations to have a better understanding on the profitability and cost of an adaptive dispersal in organisms. My work on the prey-predator models provide important insights on how different dispersal strategies may have different impacts on the spatial patterns and also shows that the change of dispersal strategy in organisms may have stabilizing or destabilizing effects leading to extinction or coexistence of species. I also develop models for honeybee population dynamics and its interaction with the parasitic Varroa mite. At first, I investigate the effect of dispersal on honeybee colonies under infestation by the Varroa mites. I then provide another single patch model by considering a stage structure time delay system from brood to adult honeybee. Through a close collaboration with a biologist, a honeybee and mite population data was first used to validate my model and I estimated certain unknown parameters by utilizing least square Monte Carlo method. My analytical, bifurcations, sensitivity analysis, and numerical studies first reveal the dynamical outcomes of migration. In addition, the results point us in the direction of the most sensitive life history parameters affecting the population size of a colony. These results provide novel insights on the effects of foraging and Varroa mites on colony survival.

Insects have intricate systems they depend on for survival. They live in societies where every individual plays an important role. Ants are a great example of this observation. They are known for having structurally sound societies that ensure the livelihood of the colony. The ant species analyzed for this research, Harpegnathos saltator, portrays a structured colony and serves as a useful example of levels of hierarchy. In the colony of H. saltator, one can find a queen, gamergates, workers, and male ants living underground in Southern India. Recording and analyzing egg-laying rates are important in this study because of the amount of information it provides. It is used especially when observing the relationship among the gamergates in colonies with varying colony sizes. Three different methods were used to record the egg-laying rates, each providing insight into valuable information. Results show that the smaller colonies with fewer identified gamergates do share an equal amount of egg-laying. In larger colonies, it appears that there are more active identified gamergates than others. Egg-laying duration times are smaller in colonies with fewer gamergates. It is also found that the presence of brood does not affect egg-laying rates and reproductive inhibition could be a possibility based on two of the colonies observed F65 and F21. Based on the data found, a more active colony that attempts to maintain stability by demonstrating aggression may be affecting the reproduction of gamergates. Future work that would further strengthen the research and conclusions made would involve further observation of colonies, both large and small, with varying numbers of gamergates. More observation involving behavior among gamergates and workers would also be beneficial. Mathematical modeling could also be incorporated to create equations that could determine information about colonies based on size, number of gamergates, and egg-laying rates.

Division of Labor among social insects is frequently discussed in regards to the colony's worker population. However, before a colony achieves a worker population, a queen is required to perform all of the tasks necessary for her survival: foraging, building the colony, and brood care. A simple ODE model was developed through the use of a framework of replicator equations in dynamical environments to investigate how queen ants perform and distribute all of the tasks necessary for her and her colony's survival by incorporating individual internal thresholds and environmental stimulus. Modi�cations to the internal threshold, risk of performing the task, and the rate of increase of the environmental stimulus were also explored. Because of the simplicity of the model, it could also be used to measure the task performance of larger populations of social insects. However, the model has only been applied to the data collected from Pogonomyrmex barbatus single queen ants.