Chaotic Analysis with Lyapunov Exponent of five-dimensional Influenza Model with Vaccination
DOI:
https://doi.org/10.5269/bspm.78895Resumen
We analyse here a model of influenza infectious disease in the presence of vaccination strategies using different parameter coefficients. The Lyapunov exponent is computed using various parameter inputs, and the model’s chaos is determined using the exponent’s values. This article uses concepts from chaos theory to examine the dynamics of the influenza virus from a chaotic viewpoint. The model has been analysed for different parameters, and it has been tried to control the chaos in the dynamical system.
Referencias
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N., Anam, V., Shrivastava, A., Aguiar, M.: Seasonally forced sir systems applied
to respiratory infectious diseases, bifurcations, and chaos. Computational and Mathematical Methods 2022(1), 3556043 (2022)
[21] O’Regan, S.M., Kelly, T.C., Korobeinikov, A., O’Callaghan, M.J., Pokrovskii,
A.V., Rachinskii, D.: Chaos in a seasonally perturbed SIR model: avian influenza
in a seabird colony as a paradigm. Journal of Mathematical Biology 67, 293–327
(2013)
[22] Thornley, J.H., France, J.: Dynamics of Single-City influenza with Seasonal Forcing: From Regularity to Chaos. International Scholarly Research Notices 2012(1),
471653 (2012)
[23] Jonnalagadda, J.M.: Epidemic Analysis and Mathematical Modelling of H1N1
(A) with Vaccination. Nonautonomous Dynamical Systems 9(1), 1–10 (2022)
[24] Alimi, M., Rhif, A., Rebai, A., Vaidyanathan, S., Azar, A.T.: Optimal adaptive
backstepping control for chaos synchronization of nonlinear dynamical systems.
In: Vaidyanathan, S., Azar, A.T. (eds.) Backstepping Control of Nonlinear
Dynamical Systems. Elsevier, Bengaluru (2020)
[25] Ramasubramanian, K., Sriram, M.S.: A comparative study of computation of
Lyapunov spectra with different algorithms. Physica D: Nonlinear Phenomena
139(1-2), 72–86 (2000)
H.E., Cox, N.J.: Surveillance for influenza—United states, 1994–95, 1995–96, and
1996–97 seasons. MORBIDITY AND MORTALITY WEEKLY REPORT: CDC
Surveillance Summaries, 13–28 (2000)
[2] Chatterjee, A., Ambrose, K., Canaday, D.H., Delair, S., Ezike, N., Huber, V.C.,
Jhaveri, R., Nyquist, A.-C., Sporer, A., Varman, M., et al.: The association
between influenza vaccine effectiveness and egg-based manufacturing technology:
literature review and US expert consensus. Current medical research and opinion
40(2), 335–343 (2024)
[3] Malosh, R.E., McGovern, I., Monto, A.S.: Influenza during the 2010–2020 decade
in the united states: seasonal outbreaks and vaccine interventions. Clinical
Infectious Diseases 76(3), 540–549 (2023)
[4] Sabu-Kurian, A., Shrestha, K., Dissanaike, S.: The reduction in influenza rates in
the United States during the COVID-19 pandemic. The Southwest Respiratory
and Critical Care Chronicles 9(39), 22–24 (2021)
[5] Leuba, S.I., Yaesoubi, R., Antillon, M., Cohen, T., Zimmer, C.: Tracking and
predicting US influenza activity with a real-time surveillance network. PLoS
computational biology 16(11), 1008180 (2020)
[6] Konty, K.J., Bradshaw, B., Ramirez, E., Lee, W.-N., Signorini, A., Foschini, L.:
Influenza surveillance using wearable mobile health devices. Online Journal of
Public Health Informatics 11(1), 62425 (2019)
[7] Kim, S., Lee, J., Jung, E.: Mathematical model of transmission dynamics and
optimal control strategies for 2009 A/H1N1 influenza in the Republic of Korea.
Journal of theoretical biology 412, 74–85 (2017)
[8] Mossong, J., Hens, N., Jit, M., Beutels, P., Auranen, K., Mikolajczyk, R., Massari,
M., Salmaso, S., Tomba, G.S., Wallinga, J., et al.: Social contacts and mixing patterns relevant to the spread of infectious diseases. PLoS medicine 5(3), 74
(2008)
[9] Pedro, S., Rwezaura, H., Mandipezar, A., Tchuenche, J.: Qualitative analysis of
an influenza model with biomedical interventions. Chaos, Solitons & Fractals 146,
110852 (2021)
[10] Ainslie, K.E., Riley, S.: Is annual vaccination best? A modelling study of influenza
vaccination strategies in children. Vaccine 40(21), 2940–2948 (2022)
[11] Sabir, Z., Botmart, T., Raja, M.A.Z., Sadat, R., Ali, M.R., Alsulami, A.A.,
Alghamdi, A., et al.: Artificial neural network scheme to solve the nonlinear
influenza disease model. Biomedical Signal Processing and Control 75, 103594
(2022)
[12] Li, L., Jiang, Y., Huang, B.: Long-term prediction for temporal propagation
of seasonal influenza using Transformer-based model. Journal of biomedical
informatics 122, 103894 (2021)
[13] Guan, X., Yang, F., Cai, Y., Wang, W.: Global stability of an influenza A model
with vaccination. Applied Mathematics Letters 134, 108322 (2022)
[14] Bhowmick, S., Sokolov, I.M., Lentz, H.H.: Decoding the double trouble: A mathematical modelling of co-infection dynamics of SARS-CoV-2 and influenza-like
illness. Biosystems 224, 104827 (2023)
[15] Abdoon, M.A., Saadeh, R., Berir, M., Guma, F.E., et al.: Analysis, modeling and
simulation of a fractional-order influenza model. Alexandria Engineering Journal
74, 231–240 (2023)
[16] Pongsumpun, P.: Influenza Transmission Model by Dynamical Analysis and
Cellular Automata. In: Proceedings of the 7th International Conference on
Bioinformatics Research and Applications, pp. 44–48 (2020)
[17] Seroussi, I., Levy, N., Paolotti, D., Sochen, N., Yom-Tov, E.: On the use of multiple compartment epidemiological models to describe the dynamics of influenza
in Europe. arXiv preprint arXiv:1906.08631 (2019)
[18] Kadhim, M.S.: Controlling Influenza A (H1N1) Through the Fractional SIR
Model With Time Delay. Basrah Journal of Sciences 40(3), 588–601 (2022)
[19] Roberts, M., Hickson, R.I., McCaw, J.M., Talarmain, L.: A simple influenza model
with complicated dynamics. Journal of mathematical biology 78, 607–624 (2019)
[20] Stollenwerk, N., Spaziani, S., Mar, J., Arrizabalaga, I.E., Knopoff, D., Cusimano,
N., Anam, V., Shrivastava, A., Aguiar, M.: Seasonally forced sir systems applied
to respiratory infectious diseases, bifurcations, and chaos. Computational and Mathematical Methods 2022(1), 3556043 (2022)
[21] O’Regan, S.M., Kelly, T.C., Korobeinikov, A., O’Callaghan, M.J., Pokrovskii,
A.V., Rachinskii, D.: Chaos in a seasonally perturbed SIR model: avian influenza
in a seabird colony as a paradigm. Journal of Mathematical Biology 67, 293–327
(2013)
[22] Thornley, J.H., France, J.: Dynamics of Single-City influenza with Seasonal Forcing: From Regularity to Chaos. International Scholarly Research Notices 2012(1),
471653 (2012)
[23] Jonnalagadda, J.M.: Epidemic Analysis and Mathematical Modelling of H1N1
(A) with Vaccination. Nonautonomous Dynamical Systems 9(1), 1–10 (2022)
[24] Alimi, M., Rhif, A., Rebai, A., Vaidyanathan, S., Azar, A.T.: Optimal adaptive
backstepping control for chaos synchronization of nonlinear dynamical systems.
In: Vaidyanathan, S., Azar, A.T. (eds.) Backstepping Control of Nonlinear
Dynamical Systems. Elsevier, Bengaluru (2020)
[25] Ramasubramanian, K., Sriram, M.S.: A comparative study of computation of
Lyapunov spectra with different algorithms. Physica D: Nonlinear Phenomena
139(1-2), 72–86 (2000)
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Publicado
2026-06-03
Número
Sección
Special Issue: Advanced Computational Methods for Fractional Calculus
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Derechos de autor 2026 Boletim da Sociedade Paranaense de Matemática
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