DIFFERENtIAl & DIFFERENCE EqUAtIONS ANd APPlICAtIONS

STOCHASTIC SIS AND SIR MULTIHOST EPIDEMIC MODELS
ROBERT K. MCCORMACK AND LINDA J. S. ALLEN
Pathogens that infect multiple hosts are common. Zoonotic diseases, such as Lyme disease,
hantavirus pulmonary syndrome, and rabies, by their very definition are animal diseases
transmitted to humans. In this investigation, we develop stochastic epidemic models
for a disease that can infect multiple hosts. Based on a system of deterministic epidemic
models with multiple hosts, we formulate a system of Itôstochasticdifferential equations.
Through numerical simulations, we compare the dynamics of the deterministic and the
stochastic models. Even though the deterministic models predict disease emergence, this
is not always the case for the stochastic models.
Copyright © 2006 R. K. McCormack and L. J. S. Allen. This is an open access article distributed
under the Creative Commons Attribution License, which permits unrestricted
use, distribution, and reproduction in any medium, provided the original work is properly
cited.
1. Introduction
Most pathogens are capable of infecting more than one host. Often these hosts, in turn,
transmit the pathogen to other hosts. Approximately sixty percent of human pathogens
are zoonotic including diseases such as Lyme disease, influenza, sleeping sickness, rabies,
and hantavirus pulmonary syndrome [18]. Generally, there is only a few species (often
only one species) considered reservoir species for a pathogen. Other species, infected by
the pathogen, are secondary or spillover species, where the disease does not persist. For
example, domestic dogs and jackals in Africa may both serve as reservoirs for the rabies
virus [7, 12]. Humans and other wild carnivores are secondary hosts. Hantavirus,
a zoonotic disease carried by wild rodents, is generally associated with a single reservoir
host [2, 11, 13]. Spillover infection occurs in other rodent species. Human infection
results in either hantavirus pulmonary syndrome or hemorrhagic fever with renal syndrome
[13].
To study the role played by multiple reservoirs and secondary hosts, in previous research,
we developed deterministic epidemic models with multiple hosts and showed
that the disease is more likely to emerge with multiple hosts [10]. In this research, we
Hindawi Publishing Corporation
Proceedings of the Conference on Differential & Difference Equations and Applications, pp. 775–785