Journal
FRACTAL AND FRACTIONAL
Volume 7, Issue 7, Pages -Publisher
MDPI
DOI: 10.3390/fractalfract7070544
Keywords
mathematical model; fractional calculus; existence and uniqueness of solution; stability; data fitting
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In this study, 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. The existence and stability of the new model are investigated using fixed point theory results. The COVID-19 and viral hepatitis B thresholds are estimated using the model fitting and the effect of non-integer derivatives on the solution paths and trajectory diagram are examined numerically.
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 R-0<1 and R-0>1, 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.
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