title: Seasonal dynamics and thresholds governing recurrent epidemics.
abstract: Driven by seasonality, many common recurrent infectious diseases are characterized by strong annual, biennial and sometimes irregular oscillations in the absence of vaccination programs. Using the seasonally forced SIR epidemic model, we are able to provide new insights into the dynamics of recurrent diseases and, in some cases, specific predictions about individual outbreaks. The analysis reveals a new threshold effect that gives clear conditions for the triggering of future disease outbreaks or their absence. The threshold depends critically on the susceptibility S (0) of the population after an outbreak. We show that in the presence of seasonality, forecasts based on the susceptibility S (0) are more reliable than those based on the classical reproductive number R (0) from the conventional theory.
authors.affiliation: Biomathematics Unit, Faculty of Life Sciences, Tel Aviv University, Ramat Aviv 69978, Israel.
authors.forename: Ronen
authors.initials: R
authors.lastname: Olinky
authors.forename: Amit
authors.initials: A
authors.lastname: Huppert
authors.forename: Lewi
authors.initials: L
authors.lastname: Stone
mesh_terms: D015984:Causality; D003141:Communicable Diseases / Q000453:epidemiology*; D004196:Disease Outbreaks / Q000706:statistics & numerical data*; D004198:Disease Susceptibility / Q000453:epidemiology; D005544:Forecasting / Q000379:methods; D006801:Humans; D008962:Models, Theoretical; D017711:Nonlinear Dynamics; D010507:Periodicity; D012008:Recurrence; D012016:Reference Values; D018571:Sentinel Surveillance; D013269:Stochastic Processes