A note on global stability for malaria infections model with latencies
A recent paper [Y. Xiao and X. Zou, On latencies in malaria infections and their impact on the disease dynamics, Math. Biosci. Eng., 10(2) 2013, 463-481.] presented a mathematical model to investigate the spread of malaria. The model is obtained by modifying the classic Ross-Macdonald model by incor...
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| Format: | Article |
| Language: | English |
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AIMS Press
2014-02-01
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| Series: | Mathematical Biosciences and Engineering |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/mbe.2014.11.995 |
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| author | Jinliang Wang Jingmei Pang Toshikazu Kuniya |
| author_facet | Jinliang Wang Jingmei Pang Toshikazu Kuniya |
| author_sort | Jinliang Wang |
| collection | DOAJ |
| description | A recent paper [Y. Xiao and X. Zou, On latencies in malaria infections and their impact on the disease dynamics, Math. Biosci. Eng., 10(2) 2013, 463-481.] presented a mathematical model to investigate the spread of malaria. The model is obtained by modifying the classic Ross-Macdonald model by incorporating latencies both for human beings and female mosquitoes. It is realistic to consider the new model with latencies differing from individuals to individuals. However, the analysis in that paper did not resolve the global malaria disease dynamics when $\Re_0>1$. The authors just showed global stability of endemic equilibrium for two specific probability functions: exponential functions and step functions. Here, we show that if there is no recovery, the endemic equilibrium is globally stable for $\Re_0>1$ without other additional conditions. The approach used here, is to use a direct Lyapunov functional and Lyapunov-LaSalle invariance principle. |
| format | Article |
| id | doaj-art-6a15a4ab560047cab89ac80ac1fbf29d |
| institution | Kabale University |
| issn | 1551-0018 |
| language | English |
| publishDate | 2014-02-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | Mathematical Biosciences and Engineering |
| spelling | doaj-art-6a15a4ab560047cab89ac80ac1fbf29d2025-01-24T02:28:18ZengAIMS PressMathematical Biosciences and Engineering1551-00182014-02-01114995100110.3934/mbe.2014.11.995A note on global stability for malaria infections model with latenciesJinliang Wang0Jingmei Pang1Toshikazu Kuniya2School of Mathematical Science, Heilongjiang University, Harbin 150080School of Mathematical Science, Heilongjiang University, Harbin 150080Graduate School of Mathematical Sciences, University of Tokyo, 3-8-1 Komaba Meguro-ku, Tokyo 153-8914A recent paper [Y. Xiao and X. Zou, On latencies in malaria infections and their impact on the disease dynamics, Math. Biosci. Eng., 10(2) 2013, 463-481.] presented a mathematical model to investigate the spread of malaria. The model is obtained by modifying the classic Ross-Macdonald model by incorporating latencies both for human beings and female mosquitoes. It is realistic to consider the new model with latencies differing from individuals to individuals. However, the analysis in that paper did not resolve the global malaria disease dynamics when $\Re_0>1$. The authors just showed global stability of endemic equilibrium for two specific probability functions: exponential functions and step functions. Here, we show that if there is no recovery, the endemic equilibrium is globally stable for $\Re_0>1$ without other additional conditions. The approach used here, is to use a direct Lyapunov functional and Lyapunov-LaSalle invariance principle.https://www.aimspress.com/article/doi/10.3934/mbe.2014.11.995global stabilitymalaria infectionlatency distributionlyapunov functional. |
| spellingShingle | Jinliang Wang Jingmei Pang Toshikazu Kuniya A note on global stability for malaria infections model with latencies Mathematical Biosciences and Engineering global stability malaria infection latency distribution lyapunov functional. |
| title | A note on global stability for malaria infections model with latencies |
| title_full | A note on global stability for malaria infections model with latencies |
| title_fullStr | A note on global stability for malaria infections model with latencies |
| title_full_unstemmed | A note on global stability for malaria infections model with latencies |
| title_short | A note on global stability for malaria infections model with latencies |
| title_sort | note on global stability for malaria infections model with latencies |
| topic | global stability malaria infection latency distribution lyapunov functional. |
| url | https://www.aimspress.com/article/doi/10.3934/mbe.2014.11.995 |
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