Threshold dynamics of stochastic cholera epidemic model with direct transmission
This paper extends the cholera human-to-human direct transmission model from a deterministic to a stochastic framework. This is expressed as mixed system of stochastic and deterministic differential equations. A Lyapunov function is created to investigate the global stability of the stochastic chole...
| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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AIMS Press
2023-09-01
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| Series: | AIMS Mathematics |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/math.20231375?viewType=HTML |
| _version_ | 1827796604701114368 |
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| author | Roshan Ara Saeed Ahmad Zareen A. Khan Mostafa Zahri |
| author_facet | Roshan Ara Saeed Ahmad Zareen A. Khan Mostafa Zahri |
| author_sort | Roshan Ara |
| collection | DOAJ |
| description | This paper extends the cholera human-to-human direct transmission model from a deterministic to a stochastic framework. This is expressed as mixed system of stochastic and deterministic differential equations. A Lyapunov function is created to investigate the global stability of the stochastic cholera epidemic, which shows the existence of global positivity of the solution using the theory of stopping time. We then find the threshold quantity of the extended stochastic cholera epidemic model. We derive a parametric condition $ \widetilde{R}_0 $, and for additive white noise, we establish sufficient conditions for the extinction and the persistence of the cholera infection. Finally, for a suitable choice of the parameter of the system for $ \widetilde{R}_0 $, we perform numerical simulations for both scenarios of extinction and persistence of the dynamic of the cholera infection. |
| first_indexed | 2024-03-11T19:08:24Z |
| format | Article |
| id | doaj.art-93fbb38933314b6db42ce7279d1847c7 |
| institution | Directory Open Access Journal |
| issn | 2473-6988 |
| language | English |
| last_indexed | 2024-03-11T19:08:24Z |
| publishDate | 2023-09-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | AIMS Mathematics |
| spelling | doaj.art-93fbb38933314b6db42ce7279d1847c72023-10-10T01:35:22ZengAIMS PressAIMS Mathematics2473-69882023-09-01811268632688110.3934/math.20231375Threshold dynamics of stochastic cholera epidemic model with direct transmissionRoshan Ara0Saeed Ahmad 1Zareen A. Khan2Mostafa Zahri 31. Department of Mathematics University of Malakand Chakdara Dir (L), Pakistan1. Department of Mathematics University of Malakand Chakdara Dir (L), Pakistan2. Department of Mathematical Sciences, College of Science, Princess Nourah bint Abdulrahman University, P.O. Box 84428, Riyadh 11671, Saudi Arabia3. Department of Mathematics, Research Groups MASEP and Bioinformatics FG, University of Sharjah, United Arab EmiratesThis paper extends the cholera human-to-human direct transmission model from a deterministic to a stochastic framework. This is expressed as mixed system of stochastic and deterministic differential equations. A Lyapunov function is created to investigate the global stability of the stochastic cholera epidemic, which shows the existence of global positivity of the solution using the theory of stopping time. We then find the threshold quantity of the extended stochastic cholera epidemic model. We derive a parametric condition $ \widetilde{R}_0 $, and for additive white noise, we establish sufficient conditions for the extinction and the persistence of the cholera infection. Finally, for a suitable choice of the parameter of the system for $ \widetilde{R}_0 $, we perform numerical simulations for both scenarios of extinction and persistence of the dynamic of the cholera infection.https://www.aimspress.com/article/doi/10.3934/math.20231375?viewType=HTMLstochastic cholera epidemic systemextinctionpersistenceglobal positivitylyapunov function |
| spellingShingle | Roshan Ara Saeed Ahmad Zareen A. Khan Mostafa Zahri Threshold dynamics of stochastic cholera epidemic model with direct transmission AIMS Mathematics stochastic cholera epidemic system extinction persistence global positivity lyapunov function |
| title | Threshold dynamics of stochastic cholera epidemic model with direct transmission |
| title_full | Threshold dynamics of stochastic cholera epidemic model with direct transmission |
| title_fullStr | Threshold dynamics of stochastic cholera epidemic model with direct transmission |
| title_full_unstemmed | Threshold dynamics of stochastic cholera epidemic model with direct transmission |
| title_short | Threshold dynamics of stochastic cholera epidemic model with direct transmission |
| title_sort | threshold dynamics of stochastic cholera epidemic model with direct transmission |
| topic | stochastic cholera epidemic system extinction persistence global positivity lyapunov function |
| url | https://www.aimspress.com/article/doi/10.3934/math.20231375?viewType=HTML |
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