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Zbl 1260.92085
Wu, Liumei; Song, Baojun; Du, Wen; Lou, Jie
Mathematical modelling and control of echinococcus in Qinghai province, China. (English)
[J] Math. Biosci. Eng. 10, No. 2, 425-444, electronic only (2013). ISSN 1547-1063; ISSN 1551-0018/e

Summary: 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.

MSC 2000:: *92C60 Medical epidemiology
34D23 Global stability
34C23 Bifurcation (periodic solutions)
92D30 Epidemiology
93A30 Mathematical modelling of systems

Keywords: backward bifurcations; global stability

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