The Reproductive Rate for Non-transient Diseases in SEIR Model

Abstract: Some infectious diseases exhibit seasonal variations endemically without the infective population ever receding completely. In this article, we present results that apply to such diseases. Measles prior to the introduction of immunization is such a disease. We look at such data for measles, acknowledging its seasonal variations, and study how the reproductive rate behaves. Using pre-immunization inter-epidemic data, we determine the expected prevalence and mortality of measles by fitting a quasi-periodic function to data. We then compute the implied transmission rate, and the reproductive rate as functions of time within a non-stratified SEIR model.