Master of Science / Department of Electrical and Computer Engineering / Caterina Maria Scoglio / Japanese Encephalitis (JE) is a vector-borne disease transmitted by mosquitoes and maintained in birds and pigs. An interconnected network model is proposed to examine the possible epidemiology of JE in the USA. Proposed JE model is an individual-level network model that explicitly considers the feral pig population and implicitly considers mosquitoes and birds in specific areas of Florida, North Carolina, and South Carolina. The virus transmission among feral pigs within a small geographic area (<60 sq mi areas) are modeled using two network topologies— fully connected and Erdos-Renyi networks. Connections between locations situated in different states (interstate links) are created with limited probability and based on fall and spring bird migration patterns. Simulation results obtained from the network models support the use of the Erdos-Renyi network because maximum incidence occurs during the fall migration period which is similar to the peak incidence of the closely related West Nile virus (WNV), another virus in the Japanese Encephalitis group (Flaviviridae) that is transmitted by both birds and mosquitoes. Simulation analysis suggested two important mitigation strategies: for low mosquito vectorial capacity, insecticidal spraying of infected areas reduces transmission and limits the outbreak to a single geographic area. Alternatively, in high mosquito vectorial capacity areas, birds rather than mosquitoes need to be removed/controlled.

Master of Science / Department of Electrical and Computer Engineering / Karen Garrett / Bala Natarajan / Caterina Scoglio / In this thesis, we propose a statistical model to predict disease dispersal in dynamic networks. We model the process of disease spreading using discrete time Markov chain. In this case, the vector of probability of infection is the state vector and every element of the state vector is a continuous variable between zero and one. In discrete time Markov chains, state probability vectors in each time step depends on state probability vector in the previous time step and one step transition probability matrix. The transition probability matrix can be time variant or time invariant. If this matrix’s elements are functions of elements of vector state probability in previous step, the corresponding Markov chain is non linear dynamical system. However, if those elements are independent of vector state probability, the corresponding Markov chain is a linear dynamical system. We especially focus on the dispersal of soybean rust. In our problem, we have a network of US counties and we aim at predicting that which counties are more likely to get infected by soybean rust during a year based on observations of soybean rust up to that time as well as corresponding observations to previous years. Other data such as soybean and kudzu densities in each county, daily wind data, and distance between counties helps us to build the model. The rapid growth in the number of Internet users in recent years has led malware generators to exploit this potential to attack computer users around the word. Internet users are frequent targets of malicious software every day. The ability of malware to exploit the infrastructures of networks for propagation determines how detrimental they can be to the network’s security. Malicious software can make large outbreaks if they are able to exploit the structure of the Internet and interactions between users to propagate. Epidemics typically start with some initial infected nodes. Infected nodes can cause their healthy neighbors to become infected with some probability. With time and in some cases with external intervention, infected nodes can be cured and go back to a healthy state. The study of epidemic dispersals on networks aims at explaining how epidemics evolve and spread in networks. One of the most interesting questions regarding an epidemic spread in a network is whether the epidemic dies out or results in a massive outbreak. Epidemic threshold is a parameter that addresses this question by considering both the network topology and epidemic strength.

Doctor of Philosophy / Department of Electrical and Computer Engineering / Caterina Scoglio / Society increasingly depends on networks for almost every aspect of daily life. Over the past decade, network science has flourished tremendously in understanding, designing, and utilizing networks. Particularly, network science has shed light on the role of the underlying network topology on the dynamic behavior of complex systems, including cascading failure in power-grids, financial contagions in trade market, synchronization, spread of social opinion and trends, product adoption and market penetration, infectious disease pandemics, outbreaks of computer worms, and gene mutations in biological networks. In the last decade, most studies on complex networks have been confined to a single, often homogeneous network. An extremely challenging aspect of studying these complex systems is that the underlying networks are often heterogeneous, composite, and interdependent with other networks. This challenging aspect has very recently introduced a new class of networks in network science, which we refer to as multilayer and interconnected networks. Multilayer networks are an abstract representation of interconnection among nodes representing individuals or agents, where the interconnection has a multiple nature. For example, while a disease can propagate among individuals through a physical contact network, information can propagate among the same individuals through an online information-dissemination network. Another example is viral information dissemination among users of online social networks; one might disseminate information received from a Facebook contact to his or her followers on Twitter. Interconnected networks are abstract representations where two or more simple networks, possibly with different dynamics over them, are interconnected to each other. For example, in zoonotic diseases, a virus can move from the network of animals, with some transmission dynamics, to a human network, with possibly very different dynamics. As communication systems are evolving more and more toward integration with computing, sensing, and control systems, the theory of multilayer and interconnected networks seems to be crucial to successful communication systems development in cyber-physical infrastructures. Among the most relevant dynamics over networks is epidemic spreading. Epidemic spreading dynamics over simple networks exhibit a clear example where interaction between non-complex dynamics at node level and the topology leads to a complex emergent behavior. A substantial line of research during the past decade has been devoted to capturing the role of the network on spreading dynamics, and mathematical tools such as spectral graph theory have been greatly useful for this goal. For example, when the network is a simple graph, the dominant eigenvalue and eigenvector of the adjacency matrix have been proven to be key elements determining spreading dynamics features, including epidemic threshold, centrality of nodes, localization of spreading sites, and behavior of the epidemic model close to the threshold. More generally, for many other dynamics over a single network, dependency of dynamics on spectral properties of the adjacency matrix, Laplacian matrix, or some other graph-related matrix, is well-studied and rigorously established, and practical applications have been successfully derived. In contrast, limited established results exist for dynamics on multilayer and interconnected networks. Yet, an understanding of spreading processes over these networks is very important to several realistic phenomena in modern integrated and composite systems, including cascading failure in power grids, financial contagions in trade market, synchronization, spread of social opinion and trends, product adoption and market penetration, infectious disease pandemics, and outbreak in computer worms. This dissertation focuses on spreading processes on multilayer and interconnected networks, organized in three parts. The first part develops a general framework for modeling epidemic spreading in interconnected and multilayer networks. The second part solves two fundamental problems: introducing the concept of an epidemic threshold curve in interconnected networks, and coexistence phenomena in competitive spreading over multilayer networks. The third part of this dissertation develops an epidemic model incorporating human behavior, where multi-layer network formulation enables modeling and analysis of important features of human social networks, such as an information-dissemination network, as well as contact adaptation. Finally, I conclude with some open research directions in the topic of spreading processes over multilayer and interconnected networks, based on the resulting developments of this dissertation.

Master of Science / Department of Electrical and Computer Engineering / Caterina M. Scoglio / The generalized epidemic modeling framework simulator (GEMFsim) is a tool designed by Dr. Faryad Sahneh, former PhD student in the NetSE group. GEMFsim simulates stochastic spreading process over complex networks. It was first introduced in Dr. Sahneh’s doctoral dissertation "Spreading processes over multilayer and interconnected networks" and implemented in Matlab. As limited by Matlab language, this implementation typically solves only small networks; the slow simulation speed is unable to generate enough results in reasonable time for large networks. As a generalized tool, this framework must be equipped to handle large networks and contain sufficient support to provide adequate performance. The C language, a low-level language that effectively maps a program to machine in- structions with efficient execution, was selected for this study. Following implementation of GEMFsim in C, I packed it into Python and R libraries, allowing users to enjoy the flexibility of these interpreted languages without sacrificing performance. GEMFsim limitations are not limited to language, however. In the original algorithm (Gillespie’s Direct Method), the performance (simulation speed) is inversely proportional to network size, resulting in unacceptable speed for very large networks. Therefore, this study applied the Next Reaction Method, making the performance irrelevant of network size. As long as the network fits into memory, the speed is proportional to the average node degree of the network, which is not very large for most real-world networks. This study also applied parallel computing in order to advantageously utilize multiple cores for repeated simulations. Although single simulation can not be paralleled as a Markov process, multiple simulations with identical network structures were run simultaneously, sharing one network description in memory.

Recent World Animal Health Organization (OIE) reports on Avian Influenza (AI) outbreaks in Asia, Europe and Canada suggest that there is a nonzero probability that an outbreak may occur anywhere in the world, including the US. To help evaluate possible policy in the face of such an event, this dissertation does an economic evaluation of the implications of using two mitigation strategies: one corresponding to the currently response strategy; and the other an OIE recommended one utilizing vaccination. To do this, the dissertation develops and uses an integrated economic-epidemic model. In this effort, I first estimate the cost of an AI outbreak under a deterministic disease spread assumption where a new vaccination strategy and the current strategy are compared. Subsequently, I introduce risk in the model and construct 95 percent confidence intervals for the outbreak costs, and I rank the outcomes of the alternative strategies using stochastic dominance criteria. In addition, during both phases, I develop and estimate the breakeven probability for an event where ex-ante fixed costs of vaccine stockpiling are justified by the reduction in disease event damages. Results under deterministic disease spread assumption suggest that the vaccination strategy lowers the cost of outbreaks as opposed to the current strategy. This happens because vaccination reduces the number of culled and quarantined flocks. The study is conducted in three locations, yielding the finding that the costs of an outbreak vary depending on the densities of poultry flocks. I also find that when consumer demand shifts due to the outbreak, the costs are much larger. Finally, I find that ex-ante vaccine stockpiling is justified for all the sub-regions if the probability of outbreak exceeds 0.07. The stochastic disease spread assumption results also show that the vaccination strategy dominates in first degree stochastic dominance sense. Consistent with stochastic dominance results, the 95 percent confidence intervals have narrower ranges under the vaccination strategy than without it. Finally, the distribution of the breakeven probability for vaccine stocking has a mode of 0.07 and that the probability is accurate with 82 percent likelihood. However, the threshold varies with the disease transmission parameters and could reach up to 0.32.

Foreign animal disease can cause serious damage to the United States (US) agricultural sector and foot-and-mouth disease (FMD), in particular, poses a serious threat. FMD causes death and reduced fecundity in infected animals, as well as significant economic consequences. FMD damages can likely be reduced through implementing pre-planned response strategies. Empirical studies have evaluated the economic consequences of alternative strategies, but typically employ simplified models. This dissertation seeks to improve US preparedness for avoiding and/or responding to an animal disease outbreak by addressing three issues related to strategy assessment in the context of FMD: integrated multi region economic and epidemic evaluation, inclusion of risk, and information uncertainty. An integrated economic/epidemic evaluation is done to examine the impact of various control strategies. This is done by combining a stochastic, spatial FMD simulation model with a national level, regionally disaggregated agricultural sector mathematical programming economic model. In the analysis, strategies are examined in the context of California's dairy industry. Alternative vaccination, disease detection and movement restriction strategies are considered as are trade restrictions. The results reported include epidemic impacts, national economic impacts, prices, regional producer impacts, and disease control costs under the alternative strategies. Results suggest that, including trade restrictions, the median national loss from the disease outbreak is as much as $17 billion when feed can enter the movement restriction zone. Early detection reduces the median loss and the standard deviation of losses. Vaccination does not reduce the median disease loss, but does have a smaller standard deviation of loss which would indicate it is a risk reducing strategy. Risk in foreign animal disease outbreaks is present from several sources; however, studies comparing alternative control strategies assume risk neutrality. In reality, there will be a desire to minimize the national loss as well as minimize the chance of an extreme outcome from the disease (i.e. risk aversion). We perform analysis on FMD control strategies using breakeven risk aversion coefficients in the context of an outbreak in the Texas High Plains. Results suggest that vaccination while not reducing average losses is a risk reducing strategy. Another issue related to risk and uncertainty is the response of consumers and domestic markets to the presence of FMD. Using a highly publicized possible FMD outbreak in Kansas that did not turn out to be true, we examine the role of information uncertainty in futures market response. Results suggest that livestock futures markets respond to adverse information even when that information is untrue. Furthermore, the existence of herding behavior and potential for momentum trading exaggerate the impact of information uncertainty related to animal disease.

Coral colonies, from a reef near Abu Dhabi, United Arab Emirates (UAE), were counted and assessed for condition using photo-transects. An epidemic model, used to track how a communicable disease moves through a population, was constructed to help predict the future condition of this coral reef. In situ data from a disease outbreak that occurred in September 2011 provided a baseline for the model. Coral Populations of Porites, Platygyra, Acropora and Dipsastrea were modelled using condition categories that included Healthy, Black Band Disease Infected, Cyanobacteria Infected, Recovered, Recruits or Dead. Results from the modelling indicate that populations of Platygyra and Dipsastrea are healthy and growing, even with continued presence of diseases, due to the high rates of recovery (chance for host colony to overcome infection; high recovery rate = high chance of colony recovering from the infection) and low mortality rates (chance of dying from an infection; low mortality rate = low chance of a infected colony dying from the infection) in the genus. Porites showed no signs of population growth, but stabilized near its initial population size, despite having a high infection rate because population growth (recruitment) and recovery rate were canceled by a high mortality rate. Acropora showed a loss in population numbers over time, losing 25% of its population before the disease was eliminated. Diseases may have been eliminated from the Acropora population because population density was low and coral died quickly after becoming infected with a disease, due to the high mortality rate of this genus, before infecting other colonies. Acropora was the only genus to display what seems to be a density dependent infection rate, since chance of infection was reduced and then eliminated by the rapid mortality of infected colonies, if the population was higher disease spread may have been higher. In addition to results obtained using in situ data, higher modified infection rates were used to assess how they might impact these coral populations. Results suggest that all four genera seem to be resilient, shown by in situ modeling and parameters extracted from the phototransects, and able to withstand acute (rapid increase of infection rate which was then again quickly brought back to normal infection rate, an infection “spike”) increases of disease infection, which is shown by either a high recovery rate (Dipsastrea and Platygyra), a high recruitment/low mortality rate (Porites), or a high mortality rate (Acropora) that may not allow for the diseases to spread. However, all four genera would be slowly driven to extinction by a sustained (chronic) increase of disease infection rate brought on by growing stressors such as an increase in average water temperature or pollutants within the Gulf. These results demonstrate fragility of Gulf coral genera when exposed to chronic episodes of disease, which over time causes total collapse of the coral populations.

No two species can indefinitely occupy the same ecological niche according to the competitive exclusion principle. When competing strains of the same pathogen invade a homogeneous population, the strain with the largest basic reproductive ratio R0 will force the other strains to extinction. However, over 51 pathogens are documented to have multiple strains [3] coexisting, contrary to the results from homogeneous models. In reality, the world is heterogeneous with the population varying in susceptibility. As such, the study of epidemiology, and hence the problem of pathogen coexistence should entail heterogeneity. Heterogeneous models tend to capture dynamics such as resistance to infection, giving more accurate results of the epidemics. This study will focus on the behavior of multi-pathogen heterogeneous models and will try to answer the question: what are the conditions on the model parameters that lead to pathogen coexistence? The goal is to understand the mechanisms in heterogeneous populations that mediate pathogen coexistence. Using the moment closure method, Fleming et. al. [22] used a two pathogen heterogeneous model (1.9) to show that pathogen coexistence was possible between strains of the baculovirus under certain conditions. In the first part of our study, we consider the same model using the hidden keystone variable (HKV) method. We show that under some conditions, the moment closure method and the HKV method give the same results. We also show that pathogen coexistence is possible for a much wider range of parameters, and give a complete analysis of the model (1.9), and give an explanation for the observed coexistence. The host population (gypsy moth) considered in the model (1.9) has a year life span, and hence, demography was introduced to the model using a discrete time model (1.12). In the second part of our study, we will consider a multi-pathogen compartmental heterogeneous model (3.1) with continuous time demography. We show using a Lyapunov function that pathogen coexistence is possible between multiple strains of the same pathogen. We provide analytical and numerical evidence that multiple strains of the same pathogen can coexist in a heterogeneous population.

A movimentação de animais em uma rede de fazendas e o espalhamento de algumas doenças animais estão intrinsecamente relacionados. Assim, compreender a dinâmica do espalhamento de doenças infecciosas nestas redes é um instrumento importante no controle dessas doenças. Usando as informações sobre as movimentações de bovinos no estado de Mato Grosso, Brasil, em 2007, reconstruiu-se a rede de trânsito e a rede de proximidade geográfica entre os estabelecimentos desse estado, além de redes hipotéticas seguindo os modelos de rede Molloy-Reed, Kalisky, Método A e Método B, onde simulou-se, usando diferentes configurações do modelo SLIRS, o espalhamento de doenças com parâmetros hipotéticos e reais (brucelose e febre aftosa). Além disso, simulou-se o controle do espalhamento dessas doenças considerando o controle por imunização e por restrição, com e sem rearranjo das movimentações após a restrição, selecionando os estabelecimentos a serem protegidos de forma aleatória, baseando-se no grau de movimentação dos animais e utilizando o conceito do paradoxo da amizade. Dentre os resultados, destacam-se que apesar dos padrões das curvas de prevalência nas redes hipotéticas serem semelhantes aos da rede real, os valores observados foram maiores nas redes hipotéticas, indicando que utilizá-las no planejamento de políticas de controle de doenças no lugar da rede real pode levar a um maior uso de recursos do que seria necessário. Além disso, no controle das doenças tanto com parâmetros hipotéticos quanto com parâmetros reais, nas simulações usando apenas a rede de trânsito dos animais, observou-se uma redução mais efetiva da prevalência ao se selecionar os estabelecimentos com maior grau total do que a da seleção aleatória, enquanto que nas simulações que consideraram a rede de proximidade geográfica dos estabelecimentos, a redução na prevalência das estratégias que selecionaram estabelecimentos específicos foram semelhantes aos da seleção aleatória. Sobre o efeito do rearranjo das movimentações, observou-se que este pode facilitar o espalhamento de doenças na rede, mesmo nas situações em que se aplica alguma estratégia de controle. Espera-se que os resultados das simulações matemáticas possam contribuir para a discussão do impacto relativo entre as estratégias de controle mencionadas e que futuramente possam auxiliar nas atividades dos órgãos responsáveis pela vigilância epidemiológica e no desenvolvimento de políticas de prevenção e controle de doenças em animais. / The animals&rsquo; movements in a farms network and the spread of some animal diseases are intrinsically related. Therefore, comprehending the dynamics of the spreading of infectious diseases in these networks is an important tool in controlling these diseases. Using the information about the bovine movements from the State of Mato Grosso, Brazil, in 2007, we rebuilt the network of animal movements and the geographic proximity network between the premises of this state, in addition to hypothetical networks following the network models Molloy-Reed, Kalisky, Method A and Method B, where we simulated, using different configurations of the model SLIRS, the spread of diseases with hypothetical parameters e real ones (brucellosis and foot and mouth disease). Moreover, we simulated the control of these diseases spreading, considering the control by immunization and by restriction, with and without the rearrangement of the movements after the restriction, selecting the premises to be protected randomly, based on the degree of animal&rsquo;s movements and using the concept of the friendship paradox. Among the results, stands out that although the pattern of the prevalence curves in the hypothetical networks were similar to the ones in the real network, the observed values were higher in the hypothetical networks, indicating that using them in the planning of policies to control diseases in place of the real network might lead to a greater expense of resources than it would be necessary. Furthermore, in the control of the diseases both with hypothetical parameters as well as with real parameters, in the simulations using only the animal&rsquo;s movements network, it was observed a more effective reduction of the prevalence when selecting the premises with the highest total degree than the random selection, while in the simulations that considered the network of geographic proximity of the premises, the reduction in the prevalence of the strategies that selected specific premises were similar to the random selection. On the effect of rearranging the movements, it was observed that it may facilitate the spread of diseases in the network even in situations where some control strategy is used. We hope that the results of the mathematical simulations may contribute to the discussion of the relative impact of the mentioned control strategies and that in the future they may assist in the activities of agencies responsible for disease surveillance and in the development of policies to prevent and control diseases in animals.

A dinâmica de movimentação de animais em uma rede de propriedades rurais e o espalhamento de algumas doenças animais estão intrinsecamente relacionados. Assim, compreender a dinâmica do espalhamento de doenças infecciosas nestas redes é um instrumento importante no controle destas. Neste projeto, foram implementados algoritmos para gerar redes de movimentação de animais hipotéticas e reconstruiu-se a rede de movimentações de bovinos do Estado do Mato Grosso, 2007, Brasil. Foram feitas diversas simulações a fim de verificar o espalhamento de doenças agudas e crônicas nessas redes. Diferentes dinâmicas de espalhamento de doenças infecciosas foram observadas em redes com a mesma distribuição de graus e diferentes estruturas topológicas. Espera-se que os resultados das simulações matemáticas possam auxiliar nas atividades dos órgãos responsáveis pela vigilância epidemiológica e incentivar outros Estados a seguirem o exemplo do Estado do Mato Grosso, a construírem bancos de dados que possam ser analisados utilizando a metodologia de redes. / The animals\' movements in a farms network and the spread of some animal diseases are intrinsically related. Therefore, comprehending the dynamics of the spreading of infectious diseases in these networks is an important tool in controlling these diseases. In this project, we have implemented algorithms to generate hypothetical networks of animals\' movements and rebuilt the network of bovine movements from the State of Mato Grosso, 2007, Brazil. We made several simulations in order to check the spreading of acute and chronic disease in these networks. Different dynamics of infectious disease spreading were observed in networks with the same degree distribution and different topological structure. We hope that the results of the mathematical simulations may assist in the activities of agencies responsible for disease surveillance and encourage other States to follow the example of the State of Mato Grosso, to build databases that can be analyzed using the methodology of networks.