Be an Epidemiologist!
I was curious what this would look like so I made this quick and dirty hack in JavaScript: http://jsfiddle.net/andrewmaxwell/r8m54t9c/

// The probability that a healthy cell will be infected by an adjacent infected cell EACH FRAME.
var infectionProbability = 0.2

// The probability that the infection will mutate on transmission EACH FRAME.
var mutationProbability = 0.00001

// The maximum number of times a cell can be infected by the same infection.
var maxInfections = 3

// The number of frames a cell in infected before it becomes healthy again.
var infectionDuration = 3

// The width and heigh of the board
var size = 400

// The number of cells infected at the beginning.
var startingNum = 4

var imageData, // the visual representation of the board
    cells, // array of cells
    infectionCount // counter that is incremented whenever a mutation occurs

// Just some colors. The colors are re-used as the number of mutations increases.
var colors = [[255,0,0],[255,255,0],[0,255,0],[0,255,255],[0,0,255],[255,0,255],[128,0,0],[128,128,0],[0,128,0],[0,128,128],[0,0,128],[128,0,128],[255,128,128],[255,255,128],[128,255,128],[128,255,255],[128,128,255],[255,128,255]
]

// when a cell is infected, it isn't contagious until the next frame
function infect(person, infection){
    person.infect = true
    person.infectionCounts[infection] = (person.infectionCounts[infection] || 0) + 1
    person.currentInfection = infection
}

// when a mutation occurs, it is given a number and the counter is incremented
function mutation(){
    return infectionCount++
}

function reset(){

    cells = []
    infectionCount = 0
    imageData = T.createImageData(size, size)

    // initialize the cells, store them in a grid temporarily and an array for use in each frame
    var grid = []
    for (var i = 0; i &lt; size; i++){
        grid[i] = []
        for (var j = 0; j &lt; size; j++){
            cells.push(grid[i][j] = {
                infectionTime: 0, // how many frames until they are no longer infected, so 0 is healthy
                infectionCounts: [], // this stores how many times the cell has been infected by each mutation
                neighbors: [] // the neighboring cells
            })
        }
    }

    // store the neighbors of each cell, I just want to minimize the work done each frame
    var neighborCoords = [[0,-1],[1,0],[0,1],[-1,0]]
    for (var i = 0; i &lt; size; i++){
        for (var j = 0; j &lt; size; j++){
            for (var n = 0; n &lt; neighborCoords.length; n++){
                var row = i + neighborCoords[n][0]
                var col = j + neighborCoords[n][1]
                if (grid[row] &amp;&amp; grid[row][col]){
                    grid[i][j].neighbors.push(grid[row][col])
                }
            }
        }
    }

    // infect the initial cells
    for (var i = 0; i &lt; startingNum; i++){
        infect(cells[Math.floor(cells.length * Math.random())], 0)
    }
}

function loop(){
    requestAnimationFrame(loop)

    // for each cell marked as infected, set its infectionTime
    for (var i = 0; i &lt; cells.length; i++){
        var p = cells[i]
        if (p.infect){
            p.infect = false
            p.infectionTime = infectionDuration
        }
    }

    for (var i = 0; i &lt; cells.length; i++){
        var p = cells[i]

        // for each infected cell, decrement its timer
        if (p.infectionTime){
            p.infectionTime--

            // for each neighbor that isn't infected, if the probability is right and the neighbor isn't immune to that infection, infect it
            for (var n = 0; n &lt; p.neighbors.length; n++){
                var neighbor = p.neighbors[n]
                if (!neighbor.infectionTime &amp;&amp; Math.random() &lt; infectionProbability){
                    var infection = Math.random() &lt; mutationProbability ? mutation() : p.currentInfection
                    if (!neighbor.infectionCounts[infection] || neighbor.infectionCounts[infection] &lt; maxInfections){
                        infect(neighbor, infection)
                    }
                }
            }

            // colors! yay!
            var color = colors[p.currentInfection % colors.length]
            imageData.data[4 * i + 0] = color[0]
            imageData.data[4 * i + 1] = color[1]
            imageData.data[4 * i + 2] = color[2]
        } else {
            imageData.data[4 * i + 0] = imageData.data[4 * i + 1] = imageData.data[4 * i + 2] = 0
        }

        imageData.data[4 * i + 3] = 255
    }

    T.putImageData(imageData, 0, 0)
}

// init canvas and go
C.width = C.height = size
T = C.getContext('2d')
reset()
loop()