# Solution Library

# Simulate Topological Malware Propagation Using MATLAB

**Question**

You are required to simulate topological malware propagation in a simplified network by using discrete-time simulation technique. Until nowadays we still do not have a good analytical model to model malware spreading in a topological network. Email virus/worm, social-network based virus/worm, smart phone virus/worm based on Bluetooth communication, etc., all of them can be treated as topological malware.

** A strict two-dimensional grid topology.**

Considering a computer network follows a strictly defined two-dimensional grid topology like the following:

Each node represents a computer that can be compromised by the malware. A malware-infected node can only infect nodes directly connected with it. Each node is uniquely identified by its position in the grid. For example, *Node*(*m,n*) represents the node at the *m*-th row and *n*-th column in the grid. Suppose the network under study has *m* rows and *n* columns (i.e., node population is *N* = *m**´**n*).

**Infection process**: Once a node is infected at the discrete time *t*, it will send out infectious traffic once and only once *to arrive* at all its neighbors at the time tick *t+x+1**,* where ** x** is a random variable following Poisson distribution with parameter

*l*

*(*

**could take values of 0,1,2,3,….). Then at the time**

*x***If the neighbor is already infected, such traffic will be ignored; if the neighbor is still vulnerable, it will be infected with the fixed probability**

*t+x+1,**p*at the current discrete time

*.*

**t + x+1****Simulation**: Suppose the parameters are: *m*=300, *n*=300, *l*=10, *p* = 0.6. You need to conduct the simulation for 40 runs, in each simulation run the following 10 nodes are infected initially (i.e., at *t=0*): *Node(1,1), Node(2,2), Node(3,3),….Node(10,10)*; and stop each simulation run when there will be no infectious traffic being generated any more. Obtain the total number of infected computers at each discrete time *t*, represented by *I(t)*. In the end, obtain the average value of *I(t)* at each discrete time *t *over those 40 runs.

**Report**:

(1). Draw a figure shows this average value of *I(t)* averaged over these 40 simulation runs.

(2). Draw a figure shows the value of *I(t)* for the first 3 simulation runs.

(3). Since we have obtained 40 values of *I(t)* for any given time *t* from those 40 simulation runs, what is the mean value and variance of this random variable *I(t)* when *t* goes to infinite? What is the mean and variance of *I(t)* when *t*=100?

**Summary**

This question belongs to MATLAB software and discusses about to simulate topological malware propagation in a simplified network by using discrete-time simulation technique.

**Answer is in MATLAB format**

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