Modelling the dynamics of acute and chronic hepatitis B with optimal control
Abstract This article examines hepatitis B dynamics under distinct infection phases and multiple transmissions. We formulate the epidemic problem based on the characteristics of the disease. It is shown that the epidemiological model is mathematically and biologically meaningful of its well-posednes...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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Nature Portfolio
2023-09-01
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| Series: | Scientific Reports |
| Online Access: | https://doi.org/10.1038/s41598-023-39582-9 |
| _version_ | 1797576802775859200 |
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| author | Tahir Khan Fathalla A. Rihan Hijaz Ahmad |
| author_facet | Tahir Khan Fathalla A. Rihan Hijaz Ahmad |
| author_sort | Tahir Khan |
| collection | DOAJ |
| description | Abstract This article examines hepatitis B dynamics under distinct infection phases and multiple transmissions. We formulate the epidemic problem based on the characteristics of the disease. It is shown that the epidemiological model is mathematically and biologically meaningful of its well-posedness (positivity, boundedness, and biologically feasible region). The reproductive number is then calculated to find the equilibria and the stability analysis of the epidemic model is performed. A backward bifurcation is also investigated in the proposed epidemic problem. With the help of two control measures (treatment and vaccination), we develop control strategies to minimize the infected population (acute and chronic). To solve the proposed control problem, we utilize Pontryagin’s Maximum Principle. Some simulations are conducted to illustrate the investigation of the analytical work and the effect of control analysis. |
| first_indexed | 2024-03-10T21:58:56Z |
| format | Article |
| id | doaj.art-ec16d7b4f7f9452f95006cea6de3bd97 |
| institution | Directory Open Access Journal |
| issn | 2045-2322 |
| language | English |
| last_indexed | 2024-03-10T21:58:56Z |
| publishDate | 2023-09-01 |
| publisher | Nature Portfolio |
| record_format | Article |
| series | Scientific Reports |
| spelling | doaj.art-ec16d7b4f7f9452f95006cea6de3bd972023-11-19T13:02:16ZengNature PortfolioScientific Reports2045-23222023-09-0113111510.1038/s41598-023-39582-9Modelling the dynamics of acute and chronic hepatitis B with optimal controlTahir Khan0Fathalla A. Rihan1Hijaz Ahmad2Department of Mathematical Sciences, College of Science, UAE UniversityDepartment of Mathematical Sciences, College of Science, UAE UniversityDepartment of Mathematics, Faculty of Science, Islamic University of MadinahAbstract This article examines hepatitis B dynamics under distinct infection phases and multiple transmissions. We formulate the epidemic problem based on the characteristics of the disease. It is shown that the epidemiological model is mathematically and biologically meaningful of its well-posedness (positivity, boundedness, and biologically feasible region). The reproductive number is then calculated to find the equilibria and the stability analysis of the epidemic model is performed. A backward bifurcation is also investigated in the proposed epidemic problem. With the help of two control measures (treatment and vaccination), we develop control strategies to minimize the infected population (acute and chronic). To solve the proposed control problem, we utilize Pontryagin’s Maximum Principle. Some simulations are conducted to illustrate the investigation of the analytical work and the effect of control analysis.https://doi.org/10.1038/s41598-023-39582-9 |
| spellingShingle | Tahir Khan Fathalla A. Rihan Hijaz Ahmad Modelling the dynamics of acute and chronic hepatitis B with optimal control Scientific Reports |
| title | Modelling the dynamics of acute and chronic hepatitis B with optimal control |
| title_full | Modelling the dynamics of acute and chronic hepatitis B with optimal control |
| title_fullStr | Modelling the dynamics of acute and chronic hepatitis B with optimal control |
| title_full_unstemmed | Modelling the dynamics of acute and chronic hepatitis B with optimal control |
| title_short | Modelling the dynamics of acute and chronic hepatitis B with optimal control |
| title_sort | modelling the dynamics of acute and chronic hepatitis b with optimal control |
| url | https://doi.org/10.1038/s41598-023-39582-9 |
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