A General Model of Zoonosis Where the Diseases Can Only Be Transmitted from Animals to Humans - Advances in Pure Mathematics

APM > Vol.9 No.2, February 2019

A General Model of Zoonosis Where the Diseases Can Only Be Transmitted from Animals to Humans ()

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DOI: 10.4236/apm.2019.92005 1,369 Downloads 3,031 Views

Author(s)

Xueying Liu

Affiliation(s)

Department of Mathematics, Shanghai University, Shanghai, China.

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.

KEYWORDS

Zoonosis, Global Stability, Equilibrium, Sensitive Analysis

Share and Cite:

Liu, X. (2019) A General Model of Zoonosis Where the Diseases Can Only Be Transmitted from Animals to Humans. Advances in Pure Mathematics, 9, 67-77. doi: 10.4236/apm.2019.92005.

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