The internet of things (IoT) has gained worldwide attention in recent years. It transforms the everyday objects that surround us into proactive actors of the Internet, generating and consuming information. An important issue related to the appearance of such large-scale self-coordinating IoT is the reliability and the collaboration between the objects in the presence of environmental hazards. High failure rates lead to significant loss of data. Therefore, data survivability is a main challenge of the IoT. In this paper, we have developed a compartmental e-Epidemic SIR (Susceptible-Infectious-Recovered) model to save the data in the network and let it survive after attacks. Furthermore, our model takes into account the dynamic topology of the network where natural death (crashing nodes) and birth are defined and analyzed. Theoretical methods and simulations are employed to solve and simulate the system of equations developed and to analyze the model.
In the literature, we can find several mathematical models which illustrate the dynamical behavior of the transmission of biological diseases and or computer viruses. Based on the Kermack and McKendrick SIR classical epidemic model @cite_10 @cite_22 , dynamical models for malicious objects propagation were proposed. Due to the numerous similarities between biological viruses and computer viruses, several approaches and models are proposed to study the spreading and attacking behavior of computer viruses in different phenomena, e.g. virus propagation @cite_11 @cite_27 @cite_13 , e-mail propagation schemes @cite_23 , virus immunization @cite_24 @cite_7 , quarantine @cite_29 @cite_15 , vaccination @cite_1 , etc. The authors in @cite_3 propose an improved SEI (susceptible-exposed-infected) model to simulate virus propagation. @cite_14 propose an SEIS-V epidemic model with vertical transmission using vaccination (that is, run of anti-virus software time and again with full efficiency) so that a temporary recovery from the infection of worms can be obtained.
@cite_14 @cite_22 @cite_7 @cite_10 @cite_29 @cite_1 @cite_3 @cite_24 @cite_27 @cite_23 @cite_15 @cite_13 @cite_11
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The strong analogy between biological viruses and their computational counterparts has motivated the authors to adapt the techniques of mathematical epidemiology to the study of computer virus propagation. In order to allow for the most general patterns of program sharing, a standard epidemiological model is extended by placing it on a directed graph and a combination of analysis and simulation is used to study its behavior. The conditions under which epidemics are likely to occur are determined, and, in cases where they do, the dynamics of the expected number of infected individuals are examined as a function of time. It is concluded that an imperfect defense against computer viruses can still be highly effective in preventing their widespread proliferation, provided that the infection rate does not exceed a well-defined critical epidemic threshold. > Theoretical modeling of computer virus worm epidemic dynamics is an important problem that has attracted many studies. However, most existing models are adapted from biological epidemic ones. Although biological epidemic models can certainly be adapted to capture some computer virus spreading scenarios (especially when the so-called homogeneity assumption holds), the problem of computer virus spreading is not well understood because it has many important perspectives that are not necessarily accommodated in the biological epidemic models. In this article, we initiate the study of such a perspective, namely that of adaptive defense against epidemic spreading in arbitrary networks. More specifically, we investigate a nonhomogeneous Susceptible-Infectious-Susceptible (SIS) model where the model parameters may vary with respect to time. In particular, we focus on two scenarios we call semi-adaptive defense and fully adaptive defense, which accommodate implicit and explicit dependency relationships between the model parameters, respectively. In the semi-adaptive defense scenario, the model’s input parameters are given; the defense is semi-adaptive because the adjustment is implicitly dependent upon the outcome of virus spreading. For this scenario, we present a set of sufficient conditions (some are more general or succinct than others) under which the virus spreading will die out; such sufficient conditions are also known as epidemic thresholds in the literature. In the fully adaptive defense scenario, some input parameters are not known (i.e., the aforementioned sufficient conditions are not applicable) but the defender can observe the outcome of virus spreading. For this scenario, we present adaptive control strategies under which the virus spreading will die out or will be contained to a desired level. An e-epidemic SEIRS model for the transmission of worms in computer network through vertical transmission is formulated. It has been observed that if the basic reproduction number is less than or equal to one, the infected part of the nodes disappear and the worm dies out, but if the basic reproduction number is greater than one, the infected nodes exists and the worms persist at an endemic equilibrium state. Numerical methods are employed to solve and simulate the system of equations developed. We have analyzed the behavior of the susceptible, exposed, infected and recovered nodes in the computer network with real parametric values. Analogies with biological disease with topological considerations added, which show that the spread of computer viruses can be contained, and the resulting epidemiological model are examined. The findings of computer virus epidemiology show that computer viruses are far less rife than many have claimed, that many fail to thrive, that even successful viruses spread at nowhere near the exponential rate that some have claimed, and that centralized reporting and response within an organization is an extremely effective defense. A case study is presented, and some steps for companies to take are suggested. >