Global dynamics of a vector-host epidemic model with age of infection
In this paper, a partial differential equation (PDE) model is proposed to explore the transmission dynamics of vector-borne diseases. The model includes both incubation age of the exposed hosts and infection age of the infectious hosts which describe incubation-age dependent removal rates in the lat...
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| Format: | Article |
| Language: | English |
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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.2017060 |
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| author | Yan-Xia Dang Zhi-Peng Qiu Xue-Zhi Li Maia Martcheva |
| author_facet | Yan-Xia Dang Zhi-Peng Qiu Xue-Zhi Li Maia Martcheva |
| author_sort | Yan-Xia Dang |
| collection | DOAJ |
| description | In this paper, a partial differential equation (PDE) model is proposed to explore the transmission dynamics of vector-borne diseases. The model includes both incubation age of the exposed hosts and infection age of the infectious hosts which describe incubation-age dependent removal rates in the latent period and the variable infectiousness in the infectious period, respectively. The reproductive number $\mathcal R_0$ is derived. By using the method of Lyapunov function, the global dynamics of the PDE model is further established, and the results show that the basic reproduction number $\mathcal R_0$ determines the transmission dynamics of vector-borne diseases: the disease-free equilibrium is globally asymptotically stable if $\mathcal R_0≤ 1$ , and the endemic equilibrium is globally asymptotically stable if $\mathcal{R}_0 \gt 1$ . The results suggest that an effective strategy to contain vector-borne diseases is decreasing the basic reproduction number $\mathcal{R}_0$ below one. |
| format | Article |
| id | doaj-art-fed38837d909426ea98803a7f6e31122 |
| institution | Kabale University |
| issn | 1551-0018 |
| language | English |
| publishDate | 2017-09-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | Mathematical Biosciences and Engineering |
| spelling | doaj-art-fed38837d909426ea98803a7f6e311222025-01-24T02:40:31ZengAIMS PressMathematical Biosciences and Engineering1551-00182017-09-01145&61159118610.3934/mbe.2017060Global dynamics of a vector-host epidemic model with age of infectionYan-Xia Dang0Zhi-Peng Qiu1Xue-Zhi Li2Maia Martcheva3Department of Public Education, Zhumadian Vocational and Technical College, Zhumadian 463000, ChinaSchool of Science, Nanjing University of Science and Technology, Nanjing 210094, ChinaDepartment of Mathematics and Physics, Anyang Institute of Technology, Anyang 455000, ChinaDepartment of Mathematics, University of Florida, 358 Little Hall, PO Box 118105, Gainesville, FL 32611-8105, USAIn this paper, a partial differential equation (PDE) model is proposed to explore the transmission dynamics of vector-borne diseases. The model includes both incubation age of the exposed hosts and infection age of the infectious hosts which describe incubation-age dependent removal rates in the latent period and the variable infectiousness in the infectious period, respectively. The reproductive number $\mathcal R_0$ is derived. By using the method of Lyapunov function, the global dynamics of the PDE model is further established, and the results show that the basic reproduction number $\mathcal R_0$ determines the transmission dynamics of vector-borne diseases: the disease-free equilibrium is globally asymptotically stable if $\mathcal R_0≤ 1$ , and the endemic equilibrium is globally asymptotically stable if $\mathcal{R}_0 \gt 1$ . The results suggest that an effective strategy to contain vector-borne diseases is decreasing the basic reproduction number $\mathcal{R}_0$ below one.https://www.aimspress.com/article/doi/10.3934/mbe.2017060age structurereproduction numberglobal stabilityvector-borne diseaselyapunov function |
| spellingShingle | Yan-Xia Dang Zhi-Peng Qiu Xue-Zhi Li Maia Martcheva Global dynamics of a vector-host epidemic model with age of infection Mathematical Biosciences and Engineering age structure reproduction number global stability vector-borne disease lyapunov function |
| title | Global dynamics of a vector-host epidemic model with age of infection |
| title_full | Global dynamics of a vector-host epidemic model with age of infection |
| title_fullStr | Global dynamics of a vector-host epidemic model with age of infection |
| title_full_unstemmed | Global dynamics of a vector-host epidemic model with age of infection |
| title_short | Global dynamics of a vector-host epidemic model with age of infection |
| title_sort | global dynamics of a vector host epidemic model with age of infection |
| topic | age structure reproduction number global stability vector-borne disease lyapunov function |
| url | https://www.aimspress.com/article/doi/10.3934/mbe.2017060 |
| work_keys_str_mv | AT yanxiadang globaldynamicsofavectorhostepidemicmodelwithageofinfection AT zhipengqiu globaldynamicsofavectorhostepidemicmodelwithageofinfection AT xuezhili globaldynamicsofavectorhostepidemicmodelwithageofinfection AT maiamartcheva globaldynamicsofavectorhostepidemicmodelwithageofinfection |