Co-Dynamics of COVID-19 and Viral Hepatitis B Using a Mathematical Model of Non-Integer Order: Impact of Vaccination
The modeling of biological processes has increasingly been based on fractional calculus. In this paper, a novel fractional-order model is used to investigate the epidemiological impact of vaccination measures on the co-dynamics of viral hepatitis B and COVID-19. To investigate the existence and stab...
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MDPI AG
2023-07-01
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| Series: | Fractal and Fractional |
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| Online Access: | https://www.mdpi.com/2504-3110/7/7/544 |
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| author | Andrew Omame Ifeoma P. Onyenegecha Aeshah A. Raezah Fathalla A. Rihan |
| author_facet | Andrew Omame Ifeoma P. Onyenegecha Aeshah A. Raezah Fathalla A. Rihan |
| author_sort | Andrew Omame |
| collection | DOAJ |
| description | The modeling of biological processes has increasingly been based on fractional calculus. In this paper, a novel fractional-order model is used to investigate the epidemiological impact of vaccination measures on the co-dynamics of viral hepatitis B and COVID-19. To investigate the existence and stability of the new model, we use some fixed point theory results. The COVID-19 and viral hepatitis B thresholds are estimated using the model fitting. The vaccine parameters are plotted against transmission coefficients. The effect of non-integer derivatives on the solution paths for each epidemiological state and the trajectory diagram for infected classes are also examined numerically. An infection-free steady state and an infection-present equilibrium are achieved when <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mi mathvariant="script">R</mi><mn>0</mn></msub><mo><</mo><mn>1</mn></mrow></semantics></math></inline-formula> and <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mi mathvariant="script">R</mi><mn>0</mn></msub><mo>></mo><mn>1</mn></mrow></semantics></math></inline-formula>, respectively. Similarly, phase portraits confirm the behaviour of the infected components, showing that, regardless of the order of the fractional derivative, the trajectories of the disease classes always converge toward infection-free steady states over time, no matter what initial conditions are assumed for the diseases. The model has been verified using real observations. |
| first_indexed | 2024-03-11T01:03:23Z |
| format | Article |
| id | doaj.art-182b3487417d48a2ae62a576304f6ec7 |
| institution | Directory Open Access Journal |
| issn | 2504-3110 |
| language | English |
| last_indexed | 2024-03-11T01:03:23Z |
| publishDate | 2023-07-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Fractal and Fractional |
| spelling | doaj.art-182b3487417d48a2ae62a576304f6ec72023-11-18T19:26:17ZengMDPI AGFractal and Fractional2504-31102023-07-017754410.3390/fractalfract7070544Co-Dynamics of COVID-19 and Viral Hepatitis B Using a Mathematical Model of Non-Integer Order: Impact of VaccinationAndrew Omame0Ifeoma P. Onyenegecha1Aeshah A. Raezah2Fathalla A. Rihan3Abdus Salam School of Mathematical Sciences, Government College University, Katchery Road, Lahore 54000, PakistanFaculty of Communication and Media Studies, Cyprus International University, 99258 Nicosia, TurkeyDepartment of Mathematics, Faculty of Science, King Khalid University, Abha 62529, Saudi ArabiaDepartment of Mathematical Sciences, College of Science, UAE University, Al Ain 15551, United Arab EmiratesThe modeling of biological processes has increasingly been based on fractional calculus. In this paper, a novel fractional-order model is used to investigate the epidemiological impact of vaccination measures on the co-dynamics of viral hepatitis B and COVID-19. To investigate the existence and stability of the new model, we use some fixed point theory results. The COVID-19 and viral hepatitis B thresholds are estimated using the model fitting. The vaccine parameters are plotted against transmission coefficients. The effect of non-integer derivatives on the solution paths for each epidemiological state and the trajectory diagram for infected classes are also examined numerically. An infection-free steady state and an infection-present equilibrium are achieved when <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mi mathvariant="script">R</mi><mn>0</mn></msub><mo><</mo><mn>1</mn></mrow></semantics></math></inline-formula> and <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mi mathvariant="script">R</mi><mn>0</mn></msub><mo>></mo><mn>1</mn></mrow></semantics></math></inline-formula>, respectively. Similarly, phase portraits confirm the behaviour of the infected components, showing that, regardless of the order of the fractional derivative, the trajectories of the disease classes always converge toward infection-free steady states over time, no matter what initial conditions are assumed for the diseases. The model has been verified using real observations.https://www.mdpi.com/2504-3110/7/7/544mathematical modelfractional calculusexistence and uniqueness of solutionstabilitydata fitting |
| spellingShingle | Andrew Omame Ifeoma P. Onyenegecha Aeshah A. Raezah Fathalla A. Rihan Co-Dynamics of COVID-19 and Viral Hepatitis B Using a Mathematical Model of Non-Integer Order: Impact of Vaccination Fractal and Fractional mathematical model fractional calculus existence and uniqueness of solution stability data fitting |
| title | Co-Dynamics of COVID-19 and Viral Hepatitis B Using a Mathematical Model of Non-Integer Order: Impact of Vaccination |
| title_full | Co-Dynamics of COVID-19 and Viral Hepatitis B Using a Mathematical Model of Non-Integer Order: Impact of Vaccination |
| title_fullStr | Co-Dynamics of COVID-19 and Viral Hepatitis B Using a Mathematical Model of Non-Integer Order: Impact of Vaccination |
| title_full_unstemmed | Co-Dynamics of COVID-19 and Viral Hepatitis B Using a Mathematical Model of Non-Integer Order: Impact of Vaccination |
| title_short | Co-Dynamics of COVID-19 and Viral Hepatitis B Using a Mathematical Model of Non-Integer Order: Impact of Vaccination |
| title_sort | co dynamics of covid 19 and viral hepatitis b using a mathematical model of non integer order impact of vaccination |
| topic | mathematical model fractional calculus existence and uniqueness of solution stability data fitting |
| url | https://www.mdpi.com/2504-3110/7/7/544 |
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