Exploration of infection spread.   The important parameter is wi which controls the fraction of possible “interations” that result in an infection.

This one is a type Polya Urn process.  
Do a Monte Carlo simulation of the Urn trials.  In the urn there are infected, cured, dead, and normal people. At each iteration we add or subtract.    

Governing equations 

Ni = infected, Nc = cured,  Nd = dead,  Np = normal people

dNi/dt =  + Ni * Np/ti - Ni/tc - Ni/td 
dNc/dt = + Ni/tc 
dNd/dt = +Ni/td  
dNp/dt = -Ni*Np/ti

trials = 10000; 

(* constants *)  
wi = 0.000007; (* chance of passing infection *)  
wc  = 0.003;  (* per unit time chance of getting cured *)
wd = 0.2*wc;  (* fchance of dying *)  

(* initial state *)  
infected= 2;
cured = 0;
dead = 0;
subjects = 1000; 

state0= {infected, cured, dead, subjects};  (* numbers at the start *)  
replace = 2;   
state = state0; 
statedata = {state}; 
newstate = state;  
Do[    total = Total[state];   (* total numnber of items *)  
{infected, cured, dead, subjects}= state;  
infected2  = infected + wi*infected*subjects - wc*infected-wd*infected; 
cured2 =  cured + wc*infected; 
dead2 = dead + wd*infected; 
subject2 = subjects -wi*infected*subjects; 
newstate = {infected2, cured2, dead2, subject2};  
AppendTo[statedata, newstate]; 
state = newstate 
, 
trials] ;

timedata  = Range[1000];

statedata ;

ListLinePlot[{Transpose[statedata][[1]], Transpose[statedata][[2]],
Transpose[statedata][[3]], Transpose[statedata][[4]]}, 
PlotRange->{{0,10000},{0,1000}}]

ListLinePlot[{Transpose[statedata][[1]], Transpose[statedata][[2]],
Transpose[statedata][[3]], Transpose[statedata][[4]]}, 
PlotRange->{{0,10000},{0,1000}}]