Modelling the effect of booster vaccination on the transmission dynamics of diseases that spread by droplet infection

Although vaccination is a highly effective method of preventing infections, one dose of vaccine does not protect all recipients. Natural infection with diseases induces permanent immunity whereas vaccine induced immunity has a temporary effect. The reduction in vaccine induced immunity leads us to introduce a booster programme. A mathematical model that can be used to study the effect of multiple doses of vaccine under the booster programme on the transmission dynamics of a disease that spreads by droplet infection has been proposed. A threshold condition for disease control involving the booster reproductive number Rˆc has been derived from the analysis of the model and it has been shown that the disease free equilibrium point is locally asymptotically stable when Rˆc<1 and unstable when Rˆc>1. Further, we have also proved that a unique endemic equilibrium point exists when Rˆc>1. With the help of numerical simulation it has been shown that the booster vaccination programme may further reduce the severity and the level of the disease as compared to a one-time vaccination programme.