Stability Analysis of P2P Worm Propagation Model with Dynamic Quarantine Defense

Abstract

<span style="font-family: "Times New Roman"; font-size: 10pt; mso-fareast-font-family: 宋体; mso-ansi-language: EN-US; mso-fareast-language: EN-US; mso-bidi-language: AR-SA;" lang="EN-US">The propagation of P2P worm covers large area and causes great damage. </span><span style="font-family: "Times New Roman"; font-size: 10pt; mso-fareast-font-family: 宋体; mso-ansi-language: EN-US; mso-fareast-language: ZH-CN; mso-bidi-language: AR-SA;" lang="EN-US">A </span><span style="font-family: "Times New Roman"; font-size: 10pt; mso-fareast-font-family: 宋体; mso-ansi-language: EN-US; mso-fareast-language: EN-US; mso-bidi-language: AR-SA;" lang="EN-US">dynamic</span><span style="font-family: "Times New Roman"; font-size: 10pt; mso-fareast-font-family: 宋体; mso-ansi-language: EN-US; mso-fareast-language: ZH-CN; mso-bidi-language: AR-SA;" lang="EN-US"> quarantine protocol is designed to quarantine the suspicious host in the P2P system. Then a</span><span style="font-family: "Times New Roman"; font-size: 10pt; mso-fareast-font-family: 宋体; mso-ansi-language: EN-US; mso-fareast-language: EN-US; mso-bidi-language: AR-SA;" lang="EN-US"> mathematical model of </span><span style="font-family: "Times New Roman"; font-size: 10pt; mso-fareast-font-family: 宋体; mso-ansi-language: EN-US; mso-fareast-language: ZH-CN; mso-bidi-language: AR-SA;" lang="EN-US">PWPQ</span><span style="font-family: "Times New Roman"; font-size: 10pt; mso-fareast-font-family: 宋体; mso-ansi-language: EN-US; mso-fareast-language: EN-US; mso-bidi-language: AR-SA;" lang="EN-US"> is proposed which considering the dynamic process of peer joining and leaving. The effect of dynamic quarantine on active P2P worm is analyzed. Through stability analysis for </span><span style="font-family: "Times New Roman"; font-size: 10pt; mso-fareast-font-family: 宋体; mso-ansi-language: EN-US; mso-fareast-language: ZH-CN; mso-bidi-language: AR-SA;" lang="EN-US">PWPQ</span><span style="font-family: "Times New Roman"; font-size: 10pt; mso-fareast-font-family: 宋体; mso-ansi-language: EN-US; mso-fareast-language: EN-US; mso-bidi-language: AR-SA;" lang="EN-US"> model, a key argument of infection-free stable point which affect the P2P worm propagation, the basic reproduction number, is deduced. Simulation results show that the propagation model of P2P worms can reflect the P2P worm behaviors and the performance of our model is significantly better than other models, in terms of decreasing the number of infected hosts and reducing the worm propagation speed. When the basic reproduction number is less than 1, infection-free stable point is global stability and the P2P worm are eliminated. The </span><span style="font-family: "Times New Roman"; font-size: 10pt; mso-fareast-font-family: 宋体; mso-ansi-language: EN-US; mso-fareast-language: ZH-CN; mso-bidi-language: AR-SA;" lang="EN-US">PWPQ</span><span style="font-family: "Times New Roman"; font-size: 10pt; mso-fareast-font-family: 宋体; mso-ansi-language: EN-US; mso-fareast-language: EN-US; mso-bidi-language: AR-SA;" lang="EN-US"> model gives some way to cont...

A Defense Model of Reactive Worms Based on Dynamic Time

“…The first step is to initialize the number of online nodes in all states during a first time period, the second step is to calculate the change in numbers of online nodes in all states during the same period of time according to the formula (11)(12)(13)(14)(15), the third step is to reckon the actual number of online nodes during a second time period according to the formula (10), the fourth step is to initialize the number of online nodes in all states during a second time period according to the proportion of different states of online nodes that has been calculated in second step and the actual number of online nodes that has been reckon in third step, then the change in numbers of online nodes in all states during the second period of time can be calculated in the fifth step, The rest can be done in the same manner, until the number change of online nodes in all states for 24 hours within a day has been calculated.…”

“…Qin et al and Feng et al respectively modeled the propagation process and immune process of reactive worms on the basis of Kermack-Mckendrick model [10] [11], and also the prevalence condition of reactive worms was presented in these papers, pointing out the direction for defending against reactive worms in P2P environment. Yang et al designed a dynamic quarantine protocol to defend active worms in P2P networks by quarantining the suspicious hosts, and he developed a mathematical model of PWPQ to prove the effectiveness of this defense method [12]. Ouyang et al analyzed the trust mechanism and application model, set up a new kind of trust model based on P2P network [13], the simulation experiment showed this trust model helps improve the success rate of transaction.…”

Effects of dynamic quarantine and nonlinear infection rate in a model for computer worms propagation

“…Nevertheless, this type of quarantine is innefficient, due to the high values of the rate at which new hosts entering the network are patched. Dynamic quarantine methods, based on the principle 'assume guilty before proven innocent' have been proposed to mitigate this problem [14,9,12]. This dynamic quarantine method diminishes the negative effect of false alarms, produced by worm anomaly detection systems.…”

A Novel Computer Virus Model and Its Stability

“…And they are residing by erasing data, damage files, or modifying the normal operation. In recent years, some models of the computer virus is proposed [1][2][3][5][6][7][8][9][10][11][12]. The action of computer virus throughout a network can be studied by using epidemiological models for disease propagation [4].…”