An epidemic model with a multistage vaccine.

Many diseases, such as the seasonal flu, tetanus, and smallpox, can be vaccinated against with a single dose of a vaccine. However, some diseases require multiple doses of a vaccine for immunity. For example, Hepatitis B requires three doses of a vaccine, with the second occurring about 1 month after the first and the third occurring about 5 months after the second, for immunity. Diseases requiring a multistage vaccine such as Hepatitis B can have extra complications with its vaccination program, as some who start the doses may forget to complete the program or could become infected before completing the program. This article concerns the setup and analysis of a model for disease spread with a multistage vaccine available to investigate how effective such a vaccine would be at establishing herd immunity for the disease as well as establishing the short-term and long-term effects of such a vaccine.