Global Analysis and Optimal Control of a Periodic Visceral Leishmaniasis Model
In this paper, we propose and analyze a mathematical model for the dynamics of visceral leishmaniasis with seasonality. Our results show that the disease-free equilibrium is globally asymptotically stable under certain conditions when R 0 , the basic reproduction number, is less than unity. W...
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| Format: | Article |
| Language: | English |
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MDPI AG
2017-12-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/5/4/80 |
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| author | Ibrahim M. ELmojtaba Santanu Biswas Joydev Chattopadhyay |
| author_facet | Ibrahim M. ELmojtaba Santanu Biswas Joydev Chattopadhyay |
| author_sort | Ibrahim M. ELmojtaba |
| collection | DOAJ |
| description | In this paper, we propose and analyze a mathematical model for the dynamics of visceral leishmaniasis with seasonality. Our results show that the disease-free equilibrium is globally asymptotically stable under certain conditions when R 0 , the basic reproduction number, is less than unity. When R 0 > 1 and under some conditions, then our system has a unique positive ω -periodic solution that is globally asymptotically stable. Applying two controls, vaccination and treatment, to our model forces the system to be non-periodic, and all fractions of infected populations settle on a very low level. |
| first_indexed | 2024-12-14T19:14:44Z |
| format | Article |
| id | doaj.art-551105afc3d24a649a6ec3c4708db385 |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-12-14T19:14:44Z |
| publishDate | 2017-12-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-551105afc3d24a649a6ec3c4708db3852022-12-21T22:50:39ZengMDPI AGMathematics2227-73902017-12-01548010.3390/math5040080math5040080Global Analysis and Optimal Control of a Periodic Visceral Leishmaniasis ModelIbrahim M. ELmojtaba0Santanu Biswas1Joydev Chattopadhyay2Department of Mathematics and Statistics, College of Science, Sultan Qaboos University, Muscat 123, OmanAgricultural and Ecological Research Unit, Indian Statistical Institute, 203, B. T. Road, Kolkata 700108, IndiaAgricultural and Ecological Research Unit, Indian Statistical Institute, 203, B. T. Road, Kolkata 700108, IndiaIn this paper, we propose and analyze a mathematical model for the dynamics of visceral leishmaniasis with seasonality. Our results show that the disease-free equilibrium is globally asymptotically stable under certain conditions when R 0 , the basic reproduction number, is less than unity. When R 0 > 1 and under some conditions, then our system has a unique positive ω -periodic solution that is globally asymptotically stable. Applying two controls, vaccination and treatment, to our model forces the system to be non-periodic, and all fractions of infected populations settle on a very low level.https://www.mdpi.com/2227-7390/5/4/80visceral leishmaniasisnon-autonomous systemperiodic solutionsglobal stability analysisoptimal control |
| spellingShingle | Ibrahim M. ELmojtaba Santanu Biswas Joydev Chattopadhyay Global Analysis and Optimal Control of a Periodic Visceral Leishmaniasis Model Mathematics visceral leishmaniasis non-autonomous system periodic solutions global stability analysis optimal control |
| title | Global Analysis and Optimal Control of a Periodic Visceral Leishmaniasis Model |
| title_full | Global Analysis and Optimal Control of a Periodic Visceral Leishmaniasis Model |
| title_fullStr | Global Analysis and Optimal Control of a Periodic Visceral Leishmaniasis Model |
| title_full_unstemmed | Global Analysis and Optimal Control of a Periodic Visceral Leishmaniasis Model |
| title_short | Global Analysis and Optimal Control of a Periodic Visceral Leishmaniasis Model |
| title_sort | global analysis and optimal control of a periodic visceral leishmaniasis model |
| topic | visceral leishmaniasis non-autonomous system periodic solutions global stability analysis optimal control |
| url | https://www.mdpi.com/2227-7390/5/4/80 |
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