Before revision:  The main differences between this modified SIR model and original SIR one are presented and explained in terms of the zeroes of their respective conserved quantities  .
After revision:  The main differences between this modified SIR model and original SIR one are presented and explained in terms of the zeroes of their respective conserved quantities . Moreover, it is shown that the modified SIR model with time-dependent transmission rate can be also solved in closed form for certain realistic transmission rate functions .