Dynamics of an ”SAIQR” Influenza Model

Modifications or extensions of the classical Susceptible-Infected-Recovered (SIR) model that account for a Quarantine (Q) class have shown to be capable of supporting recurrent, that is, periodic disease outbreaks. The fact that in such outbreaks a significant proportion of individuals escape symptomatic or experience mild infections has not been explored extensively. Motivated by our interests on the transmission dynamics and evolution of influenza A in human populations, we proceed to explore the role of an asymptomatic class (A) of individuals on the long-term transmission dynamics of influenza. We focus on a Susceptible-Asymptomatic-Infectious-Quarantine-Recovered (SAIQR) model that limits the interactions of Q-individuals and assumes that A-individuals are infectious, possibly not as infectious as those with clear symptoms. The analysis is carried out taking advantage of the significant time scale differences provided by the demographic and epidemic processes involved. It is shown that SAIQR models with vital dynamics (births and deaths) support recurrent outbreaks under reasonable disease or intervention periods. Further, we show that recurrence is possible within regions of parameter space that are consistent with influenza A transmission in human populations.