Infectious Disease Control by Vaccines Giving Full or Partial Immunity

We use a simple Lotka-Volterra model of the disease transmission process to analyse the dynamic population structure in two scenarios. Firstly a vaccine is available\ on the market at a constant price through time. Secondly, the vaccine is publicly provided. The vaccine works either by giving partial or full immunity to the disease. We analyse market provision for vaccines providing partial immunity and public provision of both types of vaccine. In the case of market provision we find that there may be multiple stationary states and instability. This is in contrast with earlier results under full immunity. In the publicly provided scenario we find that in the partial immunity case a procyclical policy is desirable but for the full immunity case a countercyclical policy is preferable. This is robust to alternative specifications of the basic Lotka-Volterra system.