Abstract:
Defending against virus attacks in network is a vital part of network security. With the rapid evolution of viruses, its defense mechanism has also been evolved over the years. But given the diversity and complexity of virus propagation and its attack behavior, no defense mechanism is equipped fully to protect the network from such attacks. Several antiviruses are available in the market. But none can give full proof solution to malicious attacks in communication networks. In this paper we present a mechanism to measure and compare the relative ability of antivirus against various kinds of viruses. We construct a hierarchical structure for different virus defense mechanism. Using Analytical Hierarchy Process (AHP) we construct a pair wise comparison matrix and find the value of corresponding Eigen vectors; we then apply the theory of AHP to calculate weight of each defense index. We validated our technique with an example. Our method can provide a strong reference to design an optimal network security solution.

Abstract:
SEIQR (Susceptible, Exposed, Infectious, Quarantined, and Recovered) models for the transmission of malicious objects with simple mass action incidence and standard incidence rate in computer network are formulated. Threshold, equilibrium, and their stability are discussed for the simple mass action incidence and standard incidence rate. Global stability and asymptotic stability of endemic equilibrium for simple mass action incidence have been shown. With the help of Poincare Bendixson Property, asymptotic stability of endemic equilibrium for standard incidence rate has been shown. Numerical methods have been used to solve and simulate the system of differential equations. The effect of quarantine on recovered nodes is analyzed. We have also analyzed the behavior of the susceptible, exposed, infected, quarantine, and recovered nodes in the computer network.

Abstract:
An epidemic model for active infectious nodes in computer sub-networks has been proposed where nodes continuously interact with each other. Nodes become infectious due to the attack of malicious objects (virus, worms, trojan horse etc.) either through internet or through secondary devices. Threshold condition and the doubling time for an epidemic to start have been obtained and it has been found that larger the basic reproductive rate, shorter is the doubling time. Numerical method has been employed to solve the system of equations and the behavior of the proportion for active and non-active nodes of infectious class has been critically analyzed. The simulation results may be helpful in simulating malicious objects epidemics in network.

Abstract:
An attempt has been made to formulate the final size formula for infected nodes in a computer network due to the attack of different malicious agents like viruses, Trojan horse, worms, etc. We assume that the population of the nodes in a computer network is homogenous and there does not exist any heterogeneous mixing. The concept of self-replication of infected nodes and the time lag for self-replication (replication period), latent period and temporary immune period is introduced. The Susceptible Infected Recovered Susceptible (SIRS) class populations is assumed to be bounded by the total size of the population N (t) which is constant at any time instant. The stability of the result is stated in the terms of reproductive number R0. The system is stable if reproductive number is >1 and unstable if reproductive number is <1. Numerical method is employed to solve the system of integro-differential equations and is used to analyze the behavior of the susceptible, infected and recovered nodes in a computer network.

Abstract:
We propose a defense mechanism in computer network using gate-translator, double honeynet, sticky honeypot and antivirus engine of CloudAV, which attracts polymorphic worms. An algorithm is proposed to detect and remove the polymorphic worms and innocuous traffic related packets. Future antivirus is implemented on logically detached unused system.

Abstract:
This study shows appropriate mathematical concepts for describing persistence by means of simple predator-prey models framed in system of integro-differential equations. Two mathematical models are proposed to study the predator-prey system inside a computer system. In mathematical model 1, the prey consists of infected and the uninfected nodes, whereas, the predator consists of malicious objects. In mathematical model 2, malicious objects constitute the prey and anti-malicious software is the predator. Stability of the result is stated in terms of threshold parameter R0. Explicit formula for the reproductive number R0 is derived and it has been shown that the malicious objects infection-free equilibrium, whose component of infective is zero, is asymptotically stable (globally) if threshold parameter is less than or equal to one and unstable if greater then one. Numerical method is employed to solve the system of equations developed. The simulated results may help us to understand the spread and control of malicious objects in computer network.

Abstract:
An e – epidemic model has been developed with optimal shelter for malicious objects in computer network. We first find the basic reproduction number and study the malicious code free equilibrium whichconcludes that whether the malicious objects invade the network or dies out. By using MATLAB and numerical methods, we give some numerical simulations in the support of our mathematical conclusions which show the stability of the system of differential equations developed.

Abstract:
The present study deals with a mathematical model describing the resistance to flow across mild stenosis situated symmetrically on steady blood flow through arteries with uniform or non-uniform cross-section. This mathematical model involves the usual assumption that the blood is Non-Newtonian, incompressible and homogeneous fluid.