# Mathematical modelling and control of echinococcus in Qinghai Province, China

Liumei Wu, Baojun Song, Wen Du, Jie Lou

Research output: Contribution to journalArticle

4 Citations (Scopus)

### 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 425-444 20 Mathematical Biosciences and Engineering 10 2 https://doi.org/10.3934/mbe.2013.10.425 Published - 1 Apr 2013

### Fingerprint

Echinococcus
Mathematical Modeling
China
mathematical models
Theoretical Models
Basic Reproduction Number
Basic Reproductive number
Globally Asymptotically Stable
Infection
Dynamical Behavior
Baseline
Model
Mathematical Model
Mathematical models
Backward Bifurcation
Basic Reproduction number
Endemic Equilibrium
infection
Bifurcation

### Keywords

• Backward bifurcation
• Echinococcosis
• Global stability
• Mathematical model

### Cite this

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

In: Mathematical Biosciences and Engineering, Vol. 10, No. 2, 01.04.2013, p. 425-444.

Research output: Contribution to journalArticle

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

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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

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