In this paper, we have considered a dynamical model of diseases that spread by droplet infection and also through direct contact. It is assumed that there is a time lag due to incubation period of pathogens, i.e. the development of an infection from the time the pathogen enters the body until signs or symptoms first appear. Pulse vaccination is an effective and important strategy for the elimination of infectious diseases and so we have analyzed this model with pulse vaccination and saturation incidence rate. We have defined two positive numbers $$R_{1}$$ R 1 and $$R_{2}$$ R 2 . It is proved that there exists an infection-free periodic solution which is globally attractive if $$R_{1}<1$$ R 1 < 1 and the disease is permanent if $$R_{2}>1.$$ R 2 > 1 . The important mathematical findings for the dynamical behaviour of the model are also numerically verified using MATLAB. Finally epidemiological implications of our analytical findings are addressed critically.