Author:
Jamil Saba,Bariq Abdul,Farman Muhammad,Nisar Kottakkaran Sooppy,Akgül Ali,Saleem Muhammad Umer
Abstract
AbstractRespiratory syncytial virus (RSV) is the cause of lung infection, nose, throat, and breathing issues in a population of constant humans with super-spreading infected dynamics transmission in society. This research emphasizes on examining a sustainable fractional derivative-based approach to the dynamics of this infectious disease. We proposed a fractional order to establish a set of fractional differential equations (FDEs) for the time-fractional order RSV model. The equilibrium analysis confirmed the existence and uniqueness of our proposed model solution. Both sensitivity and qualitative analysis were employed to study the fractional order. We explored the Ulam–Hyres stability of the model through functional analysis theory. To study the influence of the fractional operator and illustrate the societal implications of RSV, we employed a two-step Lagrange polynomial represented in the generalized form of the Power–Law kernel. Also, the fractional order RSV model is demonstrated with chaotic behaviors which shows the trajectory path in a stable region of the compartments. Such a study will aid in the understanding of RSV behavior and the development of prevention strategies for those who are affected. Our numerical simulations show that fractional order dynamic modeling is an excellent and suitable mathematical modeling technique for creating and researching infectious disease models.
Publisher
Springer Science and Business Media LLC
Reference31 articles.
1. Arenas, A. J., González, G. & Jódar, L. Existence of periodic solutions in a model of respiratory syncytial virus RSV. J. Math. Anal. Appl. 344(2), 969–980 (2008).
2. Weber, A., Weber, M. & Milligan, P. Modeling epidemics caused by respiratory syncytial virus (RSV). Math. Biosci. 172(2), 95–113 (2001).
3. Glezen, W. P., Taber, L. H., Frank, A. L. & Kasel, J. A. Risk of primary infection and reinfection with respiratory syncytial virus. Am. J. Dis. Child. 140(6), 543–546 (1986).
4. Rao, F., Mandal, P. S. & Kang, Y. Complicated endemics of an SIRS model with a generalized incidence under preventive vaccination and treatment controls. Appl. Math. Model. 67, 38–61 (2019).
5. Lin, J., Xu, R. & Tian, X. Global dynamics of an age-structured cholera model with both human-to-human and environment-to-human transmissions and saturation incidence. Appl. Math. Model. 63, 688–708 (2018).