The exact analytical solution in closed form of a modified SIR system where recovered individuals are removed from the population is presented. In this dynamical system the populations S(t) and R(t) of susceptible and recovered individuals are found to be generalized logistic functions, while infective ones I(t) are given by a generalized logistic function times an exponential, all of them with the same characteristic time. The dynamics of this modified SIR system is analysed and the exact computation of some epidemiologically relevant quantities is performed , since both models have been recently used in order to describe the essentials of the dynamics of the COVID-19 pandemic . 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  .
The exact analytical solution in closed form of a modified SIR system where recovered individuals are removed from the population is presented. In this dynamical system the populations S(t) and R(t) of susceptible and recovered individuals are found to be generalized logistic functions, while infective ones I(t) are given by a generalized logistic function times an exponential, all of them with the same characteristic time. The dynamics of this modified SIR system is analyzed and the exact computation of some epidemiologically relevant quantities is performed . 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 .
R
analysed
analyzed
D
, since both models have been recently used in order to describe the essentials of the dynamics of the COVID-19 pandemic
A
. 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