Dynamical behaviors of an Echinococcosis epidemic model with distributed delays
In this paper, a novel spreading dynamical model for Echinococcosis with distributed time delays is proposed. For the model, we firstly give the basic reproduction number $\mathcal{R}_0$ and the existence of a unique endemic equilibrium when $\mathcal{R}_0 \gt 1$. Furthermore, we analyze the dynamic...
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AIMS Press
2017-09-01
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| Series: | Mathematical Biosciences and Engineering |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/mbe.2017074 |
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| author | Kai Wang Zhidong Teng Xueliang Zhang |
| author_facet | Kai Wang Zhidong Teng Xueliang Zhang |
| author_sort | Kai Wang |
| collection | DOAJ |
| description | In this paper, a novel spreading dynamical model for Echinococcosis with distributed time delays is proposed. For the model, we firstly give the basic reproduction number $\mathcal{R}_0$ and the existence of a unique endemic equilibrium when $\mathcal{R}_0 \gt 1$. Furthermore, we analyze the dynamical behaviors of the model. The results show that the dynamical properties of the model is completely determined by $\mathcal{R}_0$. That is, if $\mathcal{R}_0 \lt 1$, the disease-free equilibrium is globally asymptotically stable, and if $\mathcal{R}_0 \gt 1$, the model is permanent and the endemic equilibrium is globally asymptotically stable. According to human Echinococcosis cases from January 2004 to December 2011 in Xinjiang, China, we estimate the parameters of the model and study the transmission trend of the disease in Xinjiang, China. The model provides an approximate estimate of the basic reproduction number $\mathcal{R}_0=1.23$ in Xinjiang, China. From theoretic results, we further find that Echinococcosis is endemic in Xinjiang, China. Finally, we perform some sensitivity analysis of several model parameters and give some useful measures on controlling the transmission of Echinococcosis. |
| format | Article |
| id | doaj-art-5c9d77d7ae594bfeb9f50618917a943a |
| institution | Kabale University |
| issn | 1551-0018 |
| language | English |
| publishDate | 2017-09-01 |
| publisher | AIMS Press |
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| series | Mathematical Biosciences and Engineering |
| spelling | doaj-art-5c9d77d7ae594bfeb9f50618917a943a2025-01-24T02:40:31ZengAIMS PressMathematical Biosciences and Engineering1551-00182017-09-01145&61425144510.3934/mbe.2017074Dynamical behaviors of an Echinococcosis epidemic model with distributed delaysKai Wang0Zhidong Teng1Xueliang Zhang2. Department of Medical Engineering and Technology, Xinjiang Medical University, Urumqi, Xinjiang 830054, China. Department of Medical Engineering and Technology, Xinjiang Medical University, Urumqi, Xinjiang 830054, China. Department of Medical Engineering and Technology, Xinjiang Medical University, Urumqi, Xinjiang 830054, ChinaIn this paper, a novel spreading dynamical model for Echinococcosis with distributed time delays is proposed. For the model, we firstly give the basic reproduction number $\mathcal{R}_0$ and the existence of a unique endemic equilibrium when $\mathcal{R}_0 \gt 1$. Furthermore, we analyze the dynamical behaviors of the model. The results show that the dynamical properties of the model is completely determined by $\mathcal{R}_0$. That is, if $\mathcal{R}_0 \lt 1$, the disease-free equilibrium is globally asymptotically stable, and if $\mathcal{R}_0 \gt 1$, the model is permanent and the endemic equilibrium is globally asymptotically stable. According to human Echinococcosis cases from January 2004 to December 2011 in Xinjiang, China, we estimate the parameters of the model and study the transmission trend of the disease in Xinjiang, China. The model provides an approximate estimate of the basic reproduction number $\mathcal{R}_0=1.23$ in Xinjiang, China. From theoretic results, we further find that Echinococcosis is endemic in Xinjiang, China. Finally, we perform some sensitivity analysis of several model parameters and give some useful measures on controlling the transmission of Echinococcosis.https://www.aimspress.com/article/doi/10.3934/mbe.2017074echinococcosisdistributed delaystransmission dynamicsbasic reproduction numberglobal stability |
| spellingShingle | Kai Wang Zhidong Teng Xueliang Zhang Dynamical behaviors of an Echinococcosis epidemic model with distributed delays Mathematical Biosciences and Engineering echinococcosis distributed delays transmission dynamics basic reproduction number global stability |
| title | Dynamical behaviors of an Echinococcosis epidemic model with distributed delays |
| title_full | Dynamical behaviors of an Echinococcosis epidemic model with distributed delays |
| title_fullStr | Dynamical behaviors of an Echinococcosis epidemic model with distributed delays |
| title_full_unstemmed | Dynamical behaviors of an Echinococcosis epidemic model with distributed delays |
| title_short | Dynamical behaviors of an Echinococcosis epidemic model with distributed delays |
| title_sort | dynamical behaviors of an echinococcosis epidemic model with distributed delays |
| topic | echinococcosis distributed delays transmission dynamics basic reproduction number global stability |
| url | https://www.aimspress.com/article/doi/10.3934/mbe.2017074 |
| work_keys_str_mv | AT kaiwang dynamicalbehaviorsofanechinococcosisepidemicmodelwithdistributeddelays AT zhidongteng dynamicalbehaviorsofanechinococcosisepidemicmodelwithdistributeddelays AT xueliangzhang dynamicalbehaviorsofanechinococcosisepidemicmodelwithdistributeddelays |