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Mathematical Biosciences and Engineering

2013, Volume 10, Issue 2: 425-444. doi: 10.3934/mbe.2013.10.425
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Mathematical modelling and control of echinococcus in Qinghai province, China

  • 1.
    Department of Mathematics, Shanghai University, 99 Shangda Road, Shanghai 200444
  • 2.
    Department of Mathematical Sciences, Montclair State University, 1 Normal Avenue, Montclair, NJ 07043
  • Received: 01 June 2012 Accepted: 29 June 2018 Published: 01 January 2013

  • MSC : 62J12, 93A30, 97M10.

  • In this paper, two mathematical models, the baseline model and theintervention model, are proposed to study the transmission dynamicsof echinococcus. A global forward bifurcation completelycharacterizes the dynamical behavior of the baseline model. That is,when the basic reproductive number is less than one, thedisease-free equilibrium is asymptotically globally stable; when the number isgreater than one, the endemic equilibrium is asymptotically globally stable. Forthe intervention model, however, the basic reproduction number aloneis not enough to describe the dynamics, particularly for the casewhere the basic reproductive number is less then one. The emergenceof a backward bifurcation enriches the dynamical behavior of themodel. Applying these mathematical models to Qinghai Province,China, we found that the infection of echinococcus is in an endemicstate. Furthermore, the model appears to be supportive of humaninterventions in order to change the landscape of echinococcusinfection in this region.

    Citation: Liumei Wu, Baojun Song, Wen Du, Jie Lou. Mathematical modelling and control of echinococcus in Qinghai province, China[J]. Mathematical Biosciences and Engineering, 2013, 10(2): 425-444. doi: 10.3934/mbe.2013.10.425

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  • In this paper, two mathematical models, the baseline model and theintervention model, are proposed to study the transmission dynamicsof echinococcus. A global forward bifurcation completelycharacterizes the dynamical behavior of the baseline model. That is,when the basic reproductive number is less than one, thedisease-free equilibrium is asymptotically globally stable; when the number isgreater than one, the endemic equilibrium is asymptotically globally stable. Forthe intervention model, however, the basic reproduction number aloneis not enough to describe the dynamics, particularly for the casewhere the basic reproductive number is less then one. The emergenceof a backward bifurcation enriches the dynamical behavior of themodel. Applying these mathematical models to Qinghai Province,China, we found that the infection of echinococcus is in an endemicstate. Furthermore, the model appears to be supportive of humaninterventions in order to change the landscape of echinococcusinfection in this region.


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