Cyclic Dynamics Caused by Antigenic Drift

Abstract

<p> Traditionally, seasonal forcing has been considered to be the major cause of the influenza seasonality. However, Andreasen [2003] showed that repetitive introductions of new strains can lead to cyclic dynamics. The cyclic dynamic produced by his model is not seasonal, because the length of seasons cannot be defined in his model. In this report, we develop a model that combines a stochastic mutation process with a two-strain competition process governing the spread of the mutant strain. This model can produce stable seasonal dynamics. If we introduce a small seasonal forcing to the transmission rate, the length of a season can be regulated to one year if the unforced system oscillates with a period close to one year. If the system has a period that is far from one year, then the forced system may behave chaotically.</p>