Global dynamics and optimal control of a nonlinear fractional-order cholera model
In this article, a fractional-order epidemic model for cholera is proposed and analyzed. Two transmission routes for cholera are considered to develop the compartmental epidemic model. The basic biological properties of the solutions of the fractional-order model are investigated. The global asympt...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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Vilnius University Press
2024-01-01
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| Series: | Nonlinear Analysis |
| Subjects: | |
| Online Access: | https://www.journals.vu.lt/nonlinear-analysis/article/view/34220 |
| _version_ | 1797326623908823040 |
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| author | Anupam Khatua Tapan Kumar Kar Soovoojeet Jana |
| author_facet | Anupam Khatua Tapan Kumar Kar Soovoojeet Jana |
| author_sort | Anupam Khatua |
| collection | DOAJ |
| description |
In this article, a fractional-order epidemic model for cholera is proposed and analyzed. Two transmission routes for cholera are considered to develop the compartmental epidemic model. The basic biological properties of the solutions of the fractional-order model are investigated. The global asymptotic stability of the equilibrium points have been established using appropriate Lyapunov functional. Moreover, a fractional-order control problem is presented, and its analytical solution is derived using Pontryagin’s maximum principle. Also, some graphical visualizations of the theoretical results are provided. It is found that the factional-order derivative only affect the time to reach the stationary states. Sensitivity analysis reveals that by reducing the rates of new recruitment and both the disease transmission rates, it may be possible to reduce the value of the basic reproduction number.
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| first_indexed | 2024-03-08T06:26:55Z |
| format | Article |
| id | doaj.art-014223d6228f492089f124e1c6210419 |
| institution | Directory Open Access Journal |
| issn | 1392-5113 2335-8963 |
| language | English |
| last_indexed | 2024-03-08T06:26:55Z |
| publishDate | 2024-01-01 |
| publisher | Vilnius University Press |
| record_format | Article |
| series | Nonlinear Analysis |
| spelling | doaj.art-014223d6228f492089f124e1c62104192024-02-03T14:14:16ZengVilnius University PressNonlinear Analysis1392-51132335-89632024-01-0129210.15388/2024.29.34220Global dynamics and optimal control of a nonlinear fractional-order cholera modelAnupam Khatua0Tapan Kumar Kar1https://orcid.org/0000-0001-7723-1489Soovoojeet Jana2https://orcid.org/0000-0002-0123-9940National Institute of Advanced Manufacturing TechnologyIndian Institute of Engineering Science and TechnologyRamsaday College In this article, a fractional-order epidemic model for cholera is proposed and analyzed. Two transmission routes for cholera are considered to develop the compartmental epidemic model. The basic biological properties of the solutions of the fractional-order model are investigated. The global asymptotic stability of the equilibrium points have been established using appropriate Lyapunov functional. Moreover, a fractional-order control problem is presented, and its analytical solution is derived using Pontryagin’s maximum principle. Also, some graphical visualizations of the theoretical results are provided. It is found that the factional-order derivative only affect the time to reach the stationary states. Sensitivity analysis reveals that by reducing the rates of new recruitment and both the disease transmission rates, it may be possible to reduce the value of the basic reproduction number. https://www.journals.vu.lt/nonlinear-analysis/article/view/34220cholera modelfractional-order derivativeglobal stabilityLyapunov functionalfractional optimal control |
| spellingShingle | Anupam Khatua Tapan Kumar Kar Soovoojeet Jana Global dynamics and optimal control of a nonlinear fractional-order cholera model Nonlinear Analysis cholera model fractional-order derivative global stability Lyapunov functional fractional optimal control |
| title | Global dynamics and optimal control of a nonlinear fractional-order cholera model |
| title_full | Global dynamics and optimal control of a nonlinear fractional-order cholera model |
| title_fullStr | Global dynamics and optimal control of a nonlinear fractional-order cholera model |
| title_full_unstemmed | Global dynamics and optimal control of a nonlinear fractional-order cholera model |
| title_short | Global dynamics and optimal control of a nonlinear fractional-order cholera model |
| title_sort | global dynamics and optimal control of a nonlinear fractional order cholera model |
| topic | cholera model fractional-order derivative global stability Lyapunov functional fractional optimal control |
| url | https://www.journals.vu.lt/nonlinear-analysis/article/view/34220 |
| work_keys_str_mv | AT anupamkhatua globaldynamicsandoptimalcontrolofanonlinearfractionalordercholeramodel AT tapankumarkar globaldynamicsandoptimalcontrolofanonlinearfractionalordercholeramodel AT soovoojeetjana globaldynamicsandoptimalcontrolofanonlinearfractionalordercholeramodel |