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 R ˆ c 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 R ˆ c < 1 and unstable when R ˆ c > 1 . Further, we have also proved that a unique endemic equilibrium point exists when R ˆ c > 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.