An age-structured vector-borne disease model with horizontal transmission in the host
We concern with a vector-borne disease model with horizontal transmission and infection age in the host population. With the approach of Lyapunov functionals, we establish a threshold dynamics, which is completely determined by the basic reproduction number. Roughly speaking, if the basic reproducti...
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| Format: | Article |
| Language: | English |
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AIMS Press
2018-09-01
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| Series: | Mathematical Biosciences and Engineering |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/mbe.2018049 |
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| author | Xia Wang Yuming Chen |
| author_facet | Xia Wang Yuming Chen |
| author_sort | Xia Wang |
| collection | DOAJ |
| description | We concern with a vector-borne disease model with horizontal transmission and infection age in the host population. With the approach of Lyapunov functionals, we establish a threshold dynamics, which is completely determined by the basic reproduction number. Roughly speaking, if the basic reproduction number is less than one then the infection-free equilibrium is globally asymptotically stable while if the basic reproduction number is larger than one then the infected equilibrium attracts all solutions with initial infection. These theoretical results are illustrated with numerical simulations. |
| format | Article |
| id | doaj-art-0bef20dafff34a1b8e4c57b77e091ff6 |
| institution | Kabale University |
| issn | 1551-0018 |
| language | English |
| publishDate | 2018-09-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | Mathematical Biosciences and Engineering |
| spelling | doaj-art-0bef20dafff34a1b8e4c57b77e091ff62025-01-24T02:41:02ZengAIMS PressMathematical Biosciences and Engineering1551-00182018-09-011551099111610.3934/mbe.2018049An age-structured vector-borne disease model with horizontal transmission in the hostXia Wang0Yuming Chen1College of Mathematics and Information Science, Xinyang Normal University, Xinyang 464000, Henan, ChinaDepartment of Mathematics, Wilfrid Laurier University, Waterloo, Ontario, N2L 3C5, CanadaWe concern with a vector-borne disease model with horizontal transmission and infection age in the host population. With the approach of Lyapunov functionals, we establish a threshold dynamics, which is completely determined by the basic reproduction number. Roughly speaking, if the basic reproduction number is less than one then the infection-free equilibrium is globally asymptotically stable while if the basic reproduction number is larger than one then the infected equilibrium attracts all solutions with initial infection. These theoretical results are illustrated with numerical simulations.https://www.aimspress.com/article/doi/10.3934/mbe.2018049vector-borne diseaseinfection ageglobal stabilityglobal attractorlyapunov functional |
| spellingShingle | Xia Wang Yuming Chen An age-structured vector-borne disease model with horizontal transmission in the host Mathematical Biosciences and Engineering vector-borne disease infection age global stability global attractor lyapunov functional |
| title | An age-structured vector-borne disease model with horizontal transmission in the host |
| title_full | An age-structured vector-borne disease model with horizontal transmission in the host |
| title_fullStr | An age-structured vector-borne disease model with horizontal transmission in the host |
| title_full_unstemmed | An age-structured vector-borne disease model with horizontal transmission in the host |
| title_short | An age-structured vector-borne disease model with horizontal transmission in the host |
| title_sort | age structured vector borne disease model with horizontal transmission in the host |
| topic | vector-borne disease infection age global stability global attractor lyapunov functional |
| url | https://www.aimspress.com/article/doi/10.3934/mbe.2018049 |
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