### Abstract

In this paper, two mathematical models, the baseline model and the intervention model, are proposed to study the transmission dynamics of echinococcus. A global forward bifurcation completely characterizes the dynamical behavior of the baseline model. That is, when the basic reproductive number is less than one, the disease-free equilibrium is asymptotically globally stable; when the number is greater than one, the endemic equilibrium is asymptotically globally stable. For the intervention model, however, the basic reproduction number alone is not enough to describe the dynamics, particularly for the case where the basic reproductive number is less then one. The emergence of a backward bifurcation enriches the dynamical behavior of the model. Applying these mathematical models to Qinghai Province, China, we found that the infection of echinococcus is in an endemic state. Furthermore, the model appears to be supportive of human interventions in order to change the landscape of echinococcus infection in this region.

Original language | English |
---|---|

Pages (from-to) | 425-444 |

Number of pages | 20 |

Journal | Mathematical Biosciences and Engineering |

Volume | 10 |

Issue number | 2 |

DOIs | |

State | Published - 1 Apr 2013 |

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### Keywords

- Backward bifurcation
- Echinococcosis
- Global stability
- Mathematical model

### Cite this

*Mathematical Biosciences and Engineering*,

*10*(2), 425-444. https://doi.org/10.3934/mbe.2013.10.425

}

*Mathematical Biosciences and Engineering*, vol. 10, no. 2, pp. 425-444. https://doi.org/10.3934/mbe.2013.10.425

**Mathematical modelling and control of echinococcus in Qinghai Province, China.** / Wu, Liumei; Song, Baojun; Du, Wen; Lou, Jie.

Research output: Contribution to journal › Article › Research › peer-review

TY - JOUR

T1 - Mathematical modelling and control of echinococcus in Qinghai Province, China

AU - Wu, Liumei

AU - Song, Baojun

AU - Du, Wen

AU - Lou, Jie

PY - 2013/4/1

Y1 - 2013/4/1

N2 - In this paper, two mathematical models, the baseline model and the intervention model, are proposed to study the transmission dynamics of echinococcus. A global forward bifurcation completely characterizes the dynamical behavior of the baseline model. That is, when the basic reproductive number is less than one, the disease-free equilibrium is asymptotically globally stable; when the number is greater than one, the endemic equilibrium is asymptotically globally stable. For the intervention model, however, the basic reproduction number alone is not enough to describe the dynamics, particularly for the case where the basic reproductive number is less then one. The emergence of a backward bifurcation enriches the dynamical behavior of the model. Applying these mathematical models to Qinghai Province, China, we found that the infection of echinococcus is in an endemic state. Furthermore, the model appears to be supportive of human interventions in order to change the landscape of echinococcus infection in this region.

AB - In this paper, two mathematical models, the baseline model and the intervention model, are proposed to study the transmission dynamics of echinococcus. A global forward bifurcation completely characterizes the dynamical behavior of the baseline model. That is, when the basic reproductive number is less than one, the disease-free equilibrium is asymptotically globally stable; when the number is greater than one, the endemic equilibrium is asymptotically globally stable. For the intervention model, however, the basic reproduction number alone is not enough to describe the dynamics, particularly for the case where the basic reproductive number is less then one. The emergence of a backward bifurcation enriches the dynamical behavior of the model. Applying these mathematical models to Qinghai Province, China, we found that the infection of echinococcus is in an endemic state. Furthermore, the model appears to be supportive of human interventions in order to change the landscape of echinococcus infection in this region.

KW - Backward bifurcation

KW - Echinococcosis

KW - Global stability

KW - Mathematical model

UR - http://www.scopus.com/inward/record.url?scp=84874857006&partnerID=8YFLogxK

U2 - 10.3934/mbe.2013.10.425

DO - 10.3934/mbe.2013.10.425

M3 - Article

VL - 10

SP - 425

EP - 444

JO - Mathematical Biosciences and Engineering

JF - Mathematical Biosciences and Engineering

SN - 1547-1063

IS - 2

ER -