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

Xueying Liu

doi:10.4236/apm.2019.92005

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.

Highlights

Infectious diseases seriously endanger human health and the development of community economy all over the world [1] [2] [3], historically, infectious diseases have caused millions of deaths
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
We construct a general model of zoonoses transmitted from animals to humans

Summary

Introduction

Infectious diseases seriously endanger human health and the development of community economy all over the world [1] [2] [3], historically, infectious diseases have caused millions of deaths. In 2002 van Driessche and Watmough [12] provided a method of establishing Lyapunov function which furnishes strong theoretical support for the latter study of the dynamic process of the infections. On this basis, more and more scholars established different models for different infectious diseases [13] [14] [15]. Some models consider human transmission to human or animal [17] [18], there are some zoonosis that can only be transmitted from animals to humans such as rabies, brucellosis, tapeworm disease and so on. A general model of the interaction between infected animals and humans are established.

Model Formulation

The Basic Reproduction Number

Dynamic Analysis on Disease-Free Equilibrium

Dynamic Analysis on Endemic Equilibrium

Numerical Simulation

Numerical Results

Sensitive Analysis

Conclusion