Internet epidemiology: healthy, susceptible, infected, quarantined, and recovered

Abstract

This paper presents a recurrent epidemic model (REM) to explore the dynamics of Internet epidemiology through the phases of susceptibility to recovery. From both theoretical and practical standpoint, it has two main differences compared to the bare worm propagation modeling. In the first place, it defines a unique stochastic model of a general infection spread. In the second place, it models the recovery process as a stochastic queueing system, which accurately partitions diagnose, quarantine, disinfection and recovery processes and complements it as a recurrent failure-repair management model, which is entirely unique. There still exists an open question to model propagation patterns of infections and accompanying recovery models needed for effectively managing the infected individuals. The REM model is a unique concept in determining the parameters for estimating the recovery efficiency of disrupted systems and for developing long-term recovery strategies under different epidemic situations. Existing infection and worm propagation models can also be used in cooperation with REM in order to analyse necessary quarantine and recovery processes. REM can also be applied for the accurate classification of the phases in epidemic dynamics and the states of affected systems in general, and also be used as a guideline for developing stochastic simulations covering various types of systems with recurrent state dynamics in order to facilitate reliability analysis of the systems.

Building epidemic models for living populations and computer networks

“…Consequently, at time t + T x , the number of objects in the respective population will be changed in a recursive manner. 1 Using notations from queuing theory, the stages (compartments) of the generic model will be described in the following sections. Arrivals of an object to a stage and operation completion (departure) from a stage are modeled as an M/M/ 1:(FCFS) queueing system.…”

“…Consequently, at time t + T x , the number of objects in the respective population will be changed in a recursive manner. 1…”

“…As detailed in Kondakci and Dincer, 1 lifecycle of an epidemic system generally consists of five stages, healthy, susceptible, infected, quarantined, and recovered. These are modeled as distinct states taking place in a chain of interrelated stochastic processes.…”

Mathematical modeling of the propagation of malware: a review

“…These models can also be classified attending to the nature and the mathematical tools on which they are based. In this sense, we find deterministic models (see, for example, ) and stochastic models (see, for example, ). Deterministic models are usually based on differential equations or difference equations.…”

Epidemiological dynamics of addiction.

“…They described the extension of the deterministic approach to a stochastic approach within the context of communicable disease epidemic modeling, with examples of stochastic simulations of value. See Kondakci and Dincer (2011) for an elegant and quite pertinent stochastic model, originally developed for the study of software "worm" infection epidemics and ripe for translation in an extension of the systems sciences as applied to extramedical drug use and its consequences. Examples with this degree of refi nement have not yet been found in the published literature focusing on extramedical drug use or the other behavioral expressions of addiction of interest to readers (e.g., gambling addiction, sex addiction).…”