31,148 research outputs found
Markovian and stochastic differential equation based approaches to computer virus propagation dynamics and some models for survival distributions
This dissertation is divided in two Parts. The first Part explores probabilistic modeling of propagation of computer \u27malware\u27 (generally referred to as \u27virus\u27) across a network of computers, and investigates modeling improvements achieved by introducing a random latency period during which an infected computer in the network is unable to infect others. In the second Part, two approaches for modeling life distributions in univariate and bivariate setups are developed.
In Part I, homogeneous and non-homogeneous stochastic susceptible-exposed-infectious- recovered (SEIR) models are specifically explored for the propagation of computer virus over the Internet by borrowing ideas from mathematical epidemiology. Large computer networks such as the Internet have become essential in today\u27s technological societies and even critical to the financial viability of the national and the global economy. However, the easy access and widespread use of the Internet makes it a prime target for malicious activities, such as introduction of computer viruses, which pose a major threat to large computer networks. Since an understanding of the underlying dynamics of their propagation is essential in efforts to control them, a fair amount of research attention has been devoted to model the propagation of computer viruses, starting from basic deterministic models with ordinary differential equations (ODEs) through stochastic models of increasing realism.
In the spirit of exploring more realistic probability models that seek to explain the time dependent transient behavior of computer virus propagation by exploiting the essential stochastic nature of contacts and communications among computers, the present study introduces a new refinement in such efforts to consider the suitability and use of the stochastic SEIR model of mathematical epidemiology in the context of computer viruses propagation. We adapt the stochastic SEIR model to the study of computer viruses prevalence by incorporating the idea of a latent period during which computer is in an \u27exposed state\u27 in the sense that the computer is infected but cannot yet infect other computers until the latency is over. The transition parameters of the SEIR model are estimated using real computer viruses data. We develop the maximum likelihood (MLE) and Bayesian estimators for the SEIR model parameters, and apply them to the \u27Code Red worm\u27 data.
Since network structure can be a possibly important factor in virus propagation, multi-group stochastic SEIR models for the spreading of computer virus in heterogeneous networks are explored next. For the multi-group stochastic SEIR model using Markovian approach, the method of maximum likelihood estimation for model parameters of interest are derived. The method of least squares is used to estimate the model parameters of interest in the multi-group stochastic SEIR-SDE model, based on stochastic differential equations. The models and methodologies are applied to Code Red worm data.
Simulations based on different models proposed in this dissertation and deterministic/ stochastic models available in the literature are conducted and compared. Based on such comparisons, we conclude that (i) stochastic models using SEIR framework appear to be relatively much superior than previous models of computer virus propagation - even up to its saturation level, and (ii) there is no appreciable difference between homogeneous and heterogeneous (multi-group) models. The \u27no difference\u27 finding of course may possibly be influenced by the criterion used to assign computers in the overall network to different groups. In our study, the grouping of computers in the total network into subgroups or, clusters were based on their geographical location only, since no other grouping criterion were available in the Code Red worm data.
Part II covers two approaches for modeling life distributions in univariate and bivariate setups. In the univariate case, a new partial order based on the idea of \u27star-shaped functions\u27 is introduced and explored. In the bivariate context; a class of models for joint lifetime distributions that extends the idea of univariate proportional hazards in a suitable way to the bivariate case is proposed. The expectation-maximization (EM) method is used to estimate the model parameters of interest. For the purpose of illustration, the bivariate proportional hazard model and the method of parameter estimation are applied to two real data sets
Mathematical modeling of tumor therapy with oncolytic viruses: Effects of parametric heterogeneity on cell dynamics
One of the mechanisms that ensure cancer robustness is tumor heterogeneity,
and its effects on tumor cells dynamics have to be taken into account when
studying cancer progression. There is no unifying theoretical framework in
mathematical modeling of carcinogenesis that would account for parametric
heterogeneity. Here we formulate a modeling approach that naturally takes stock
of inherent cancer cell heterogeneity and illustrate it with a model of
interaction between a tumor and an oncolytic virus. We show that several
phenomena that are absent in homogeneous models, such as cancer recurrence,
tumor dormancy, an others, appear in heterogeneous setting. We also demonstrate
that, within the applied modeling framework, to overcome the adverse effect of
tumor cell heterogeneity on cancer progression, a heterogeneous population of
an oncolytic virus must be used. Heterogeneity in parameters of the model, such
as tumor cell susceptibility to virus infection and virus replication rate, can
lead to complex, time-dependent behaviors of the tumor. Thus, irregular,
quasi-chaotic behavior of the tumor-virus system can be caused not only by
random perturbations but also by the heterogeneity of the tumor and the virus.
The modeling approach described here reveals the importance of tumor cell and
virus heterogeneity for the outcome of cancer therapy. It should be
straightforward to apply these techniques to mathematical modeling of other
types of anticancer therapy.Comment: 45 pages, 6 figures; submitted to Biology Direc
Distributed interaction between computer virus and patch: A modeling study
The decentralized patch distribution mechanism holds significant promise as
an alternative to its centralized counterpart. For the purpose of accurately
evaluating the performance of the decentralized patch distribution mechanism
and based on the exact SIPS model that accurately captures the average dynamics
of the interaction between viruses and patches, a new virus-patch interacting
model, which is known as the generic SIPS model, is proposed. This model
subsumes the linear SIPS model. The dynamics of the generic SIPS model is
studied comprehensively. In particular, a set of criteria for the final
extinction or/and long-term survival of viruses or/and patches are presented.
Some conditions for the linear SIPS model to accurately capture the average
dynamics of the virus-patch interaction are empirically found. As a
consequence, the linear SIPS model can be adopted as a standard model for
assessing the performance of the distributed patch distribution mechanism,
provided the proper conditions are satisfied
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