  The World Health Organization describes zoonotic diseases as a major pandemic
threat, and modeling the behavior of such diseases is a key component of their
control. Many emerging zoonoses, such as SARS, Nipah, and Hendra, mutated from
their wild type while circulating in an intermediate host population, usually a
domestic species, to become more transmissible among humans, and moreover, this
transmission route will only become more likely as agriculture and trade
intensifies around the world. Passage through an intermediate host enables many
otherwise rare diseases to become better adapted to humans, and so
understanding this process with mathematical epidemiological models is
necessary to prevent epidemics of emerging zoonoses, guide policy interventions
in public health, and predict the behavior of an epidemic. In this paper, we
account for spillovers of a zoonotic disease mutating in an intermediate host
by means of modeling transmission dynamics within and between three host
species, namely, wild reservoir, intermediate domestic animals, and humans. We
calculate the basic reproductive number of the pathogen, present critical
conditions for the emergence dynamics of zoonosis, and perform stability
analysis of admissible disease equilibria. Our analytical results agree well
with long-term simulations of the system. We find that in the presence of
biologically realistic interspecies transmission parameters, a zoonotic disease
can establish itself in humans even if it fails to persist in its reservoir and
intermediate host species. Our model and results can be used to understand the
dynamic behavior of any zoonosis with intermediate hosts and assist efforts to
protect public health.
