TITLE:
A General Model of Zoonosis Where the Diseases Can Only Be Transmitted from Animals to Humans
AUTHORS:
Xueying Liu
KEYWORDS:
Zoonosis, Global Stability, Equilibrium, Sensitive Analysis
JOURNAL NAME:
Advances in Pure Mathematics,
Vol.9 No.2,
February
19,
2019
ABSTRACT:
Zoonosis is an important factor
affecting human economic development and population mortality. This paper
introduces a general model of zoonosis, in which the diseases can only be
transmitted from animals to humans, such as rabies, brucellosis and so on. The
basic reproduction number R0 is derived.
And then the global stability of the disease-free equilibrium and endemic
equilibrium models is analyzed by using the method of comparison principle and Lyapunov
function. Next, a numerical analysis is performed to elaborate the consistency
of theoretical and numerical results and to prove the practical significance of
zoonosis research. The numerical results show that our models are applicable to
zoonosis with animal size larger than or smaller than population size. Finally,
in order to see the most important factor for the epidemic of zoonosis a
sensitive analysis is analyzed.