Impact of seasonal cycles on host-pathogen dynamics and disease mitigation for Batrachochytrium salamandrivorans

Abstract

Seasonal cycles have a demonstrated effect on the dynamics of human and animal diseases. However, their quantitative implications for disease mitigation in wildlife are less well studied. We quantitatively investigate the effect of seasonality on chytridiomycosis caused by Batrachochytrium salamandrivorans in European fire salamanders (Salamandra salamandra). Floquet theory is a mathematical tool that allows the analysis of periodic systems. In epidemiology, it can be used to study the fate of a un-/managed host population when confronted with a new pathogen. Based on this theory, we develop a novel metric that captures outbreak dynamics similarly to the non-seasonal basic reproduction number R0, but also accounts for seasonal cycles. We use this Floquet-R0 to determine the management needed to defend a susceptible host population from disease outbreaks. In the B. salamandrivorans case, we found a limited effect of seasonality on disease dynamics and mitigation for two hypothetical European fire salamander populations with different seasonal cycles. However, a general model analysis suggested that Floquet-R0 could deviate up to ±33% from the non-seasonal R0, thus leading to insufficient or unnecessary management if seasonality is ignored. We recommend considering seasonal cycles – especially activity cycles with two peaks – when planning mitigation for chytridiomycosis and other wildlife diseases, because they add a considerable layer of uncertainty to analysis and decision-making. The Floquet-R0 metric we present is an intuitive tool to quantitatively evaluate seasonality of disease and its influence on management.