Mathematical modelling and control of echinococcus in Qinghai province, China

Liumei Wu; Baojun Song; Wen Du; Jie Lou

doi:10.3934/mbe.2013.10.425

Article Contents

2013, Volume 10, Issue 2: 425-444. Doi: 10.3934/mbe.2013.10.425

This issue Previous Article Competition of motile and immotile bacterial strains in a petri dish Next Article Dynamics of an infectious diseases with media/psychology induced non-smooth incidence

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: June 2012

Revised: December 2012

Published: December 2012

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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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Mathematics Subject Classification: 62J12, 93A30, 97M10.

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