# Could short-lasting non-specific immunity explain seasonal spacing of epidemic diseases?

## TL;DR

This paper introduces a dynamic model showing that short-lasting, non-specific immunity can explain seasonal epidemic patterns of respiratory viruses without needing environmental seasonal drivers.

## Contribution

The model extends classical SIRS to include interacting diseases with temporary, non-specific immunity, providing a unified explanation for diverse seasonal epidemic patterns.

## Key findings

- Recurrent epidemics can occur without seasonal environmental factors.
- The model predicts sequential epidemic patterns consistent with observed data.
- Interactions via short-term immunity can produce complex epidemic dynamics.

## Abstract

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.