  Understanding dynamics of an infectious disease helps in designing
appropriate strategies for containing its spread in a population. Recent
mathematical models are aimed at studying dynamics of some specific types of
infectious diseases. In this paper we propose a new model for infectious
diseases spread having susceptible, infected, and recovered populations and
study its dynamics in presence of incubation delays and relapse of the disease.
The influence of treatment and vaccination efforts on the spread of infection
in presence of time delays are studied. Sufficient conditions for local
stability of the equilibria and change of stability are derived in various
cases. The problem of global stability is studied for an important special case
of the model. Simulations carried out in this study brought out the importance
of treatment rate in controlling the disease spread. It is observed that
incubation delays have influence on the system even under enhanced vaccination.
The present study has clearly brought out the fact that treatment rate in
presence of time delays would contain the disease as compared to popular belief
that eradication can only be done through vaccination.
