Predicting and Controlling Spillover in Multispecies Disease Transmission Networks: Steady-State Analysis

In multispecies disease systems, pathogen spillover from a "reservoir community" can maintain disease in a "sink community" where it would otherwise die out. We develop and analyze models for spillover and disease spread in sink communities, focusing on questions of control: which species or transmission links are the most important to target to reduce the disease impact on a species of concern? Our analysis focuses on steady-state disease prevalence, assuming that the timescale of interest is long compared with that of disease introduction and establishment in the sink community. We identify three regimes as the sink community R-0 scales from 0 to 1. Up to R0 approximate to 0.3, overall infection patterns are dominated by direct exogenous infections and one-step subsequent transmission. For R0 approximate to 1, infection patterns are characterized by dominant eigenvectors of a force-of-infection matrix. In between, additional network details can be important; we derive and apply general sensitivity formulas that identify particularly important links and species.