three difference equationss nc vts ( nc vts ti ( nc ti ( note that we have isolated the new unknown quantities nc nc and rnc on the left-hand sidesuch that these can readily be computed if and rn are known to get such procedure startedwe need to know obviouslywe also need to have values for the parameters and we also list the system of three differential equationss vsii vsi ir ( ( ( this differential equation model (and also its discrete counterpart aboveis known as an sir model the input data to the differential equation model consist of the parameters and as well as the initial conditions and forward euler method for the differential equation system let us apply the same principles as we did in sect to discretize the differential equation system by the forward euler method we already have time mesh and time-discrete quantities rn the three differential equations are assumed to be valid at the mesh points at the point tn we then have tn vs tn / tn / tn vs tn / tn tn / tn tn /( ( ( for this is an approximation since the differential equations are originally valid at all times (usually in some finite interval oe using forward finite differences for the derivatives results in an additional approximations nc vs nc vs rnc rn in ( ( ( as we seethese equations are identical to the difference equations that naturally arise in the derivation of the model howeverother numerical methods than the forward euler scheme will result in slightly different difference equations