  Common respiratory viruses cause seasonal epidemics in sequential patterns.
The underlying mechanisms for this pattern have been debated for some time. For
influenza, contenders include temperature, humidity, and vitamin D levels.
While such seasonal drivers may be sufficient to explain midwinter peaking it
is unclear if other respiratory viruses peaking in spring, summer, or fall have
individual environmental drivers. Here we present a dynamic model of
interacting diseases, in an effort to explain observed seasonal patterns
without requiring multiple seasonal drivers. Our model extends the classical
SIRS-model to include multiple diseases that interact via a short-lasting,
non-specific immunity component. This temporal protection is triggered by
exposure to any epidemic disease and lasts only a couple of weeks. We show that
the inhibiting disease-interaction allows recurrent epidemic behaviour without
any seasonal driving. In the presence of a single seasonal driver our model
parsimoniously predicts epidemic patterns such as sequentially occurring
epidemic diseases. We also present a two-disease simulation reproducing
multiple features observed in time series of parainfluenza strains PIV-3 and
biennial PIV-1 epidemic patterns. Complex epidemic patterns of seasonal
diseases may be explained by non-specific innate or cloub cell (T-cell)
mediated immune responses that result in interaction between unrelated
respiratory epidemic diseases.
