In today's network-dependent society, cyber attacks with network worms have become the predominant threat to confidentiality, integrity, and availability of network computing resources. Despite ongoing research efforts, there is still no comprehensive network-security solution aimed at controling large-scale worm propagation. The aim of this work is fivefold: (1) Developing an accurate combinatorial model of worm propagation that can facilitate the analysis of worm control strategies, (2) Building an accurate epidemiological model for the propagation of a worm employing local strategies, (3) Devising distributed architecture and algorithms for detection of worm scanning activities, (4) Designing effective control strategies against the worm, and (5) Simulation of the developed models and strategies on large, scale-free graphs representing real-world communication networks. The proposed pair-approximation model uses the information about the network structure--order, size, degree distribution, and transitivity. The empirical study of propagation on large scale-free graphs is in agreement with the theoretical analysis of the proposed pair-approximation model. We, then, describe a natural generalization of the classical cops-and-robbers game--a combinatorial model of worm propagation and control. With the help of this game on graphs, we show that the problem of containing the worm is NP-hard. Six novel near-optimal control strategies are devised: combination of static and dynamic immunization, reactive dynamic and invariant dynamic immunization, soft quarantining, predictive traffic-blocking, and contact-tracing. The analysis of the predictive dynamic traffic-blocking, employing only local information, shows that the worm can be contained so that 40\% of the network nodes are not affected. Finally, we develop the Detection via Distributed Blackholes architecture and algorithm which reflect the propagation strategy used by the worm and the salient properties of the network. Our distributed detection algorithm can detect the worm scanning activity when only 1.5% of the network has been affected by the propagation. The proposed models and algorithms are analyzed with an individual-based simulation of worm propagation on realistic scale-free topologies.

<div>Wildlife diseases are an increasingly growing concern for public health managers, conservation biologists, and society at large. These diseases may be zoonotic -- infective wildlife are able to spread pathogens to human populations. Animal or plant species of conservation concern may also be threatened with extinction or extirpation due to the spread of novel pathogens into their native ranges. In this thesis, I develop some mathematical methods for understanding the dynamics of vector-borne diseases in wildlife populations which include several elements of host and vector biology. </div><div><br></div><div>We consider systems where a vector-borne pathogen is transmitted to a host population wherein individuals either die to disease or recover, remaining chronically infective. Both ordinary differential equations (ODE) and individual based (IBM) models of such systems are formulated then applied to a specific system of wildlife disease: avian malaria in Hawaiian honeycreeper populations -- where some species endure disease-induced mortality rates exceeding 90\%. The ODE model predicts that conventional management methods cannot fully stop pathogen transmission.</div><div><br></div><div>Vector dispersal and reproductive biology may also play a large role in the transmission of vector-borne diseases in forested environments. Using an IBM which models dispersal and mosquito reproductive biology, we predict that reducing larval habitat at low elevations is much more effective than at higher elevations. The ODE model is extended to include distinct populations of sensitive and tolerant hosts. We find that the form which interaction between the hosts takes has a significant impact on model predictions.</div>