Fractional-order brucellosis transmission model between interspecies with a saturated incidence rate
DOI:
https://doi.org/10.59292/bulletinbiomath.2024005Keywords:
Atangana-Baleanu derivative, brucellosis, existence and uniqueness, fixed point theory, mathematical modelingAbstract
In this study, brucellosis dynamics between interspecies are discussed with the Atangana-Baleanu fractional derivative to examine the transmission of brucellosis by its behavior. The recovered compartment, recruitment, and natural death rate for humans are considered for the fractional order model to analyze the transmission dynamics in more detail from an epidemiological point of view. Additionally, the saturated incidence rate is suggested for brucellosis as indirectly transmitted to individuals from the environment. By fixed point theory, it is verified that developed fractional transmission dynamics have a unique solution. The model under consideration employs the Adams-type predictor-corrector method for numerical solution. All comparative results are plotted by MATLAB.
References
Pappas, G., Akritidis, N., Bosilkovski, M. and Tsianos, E. Brucellosis. The New England Journal of Medicine, 352, 2325-2336, (2005).
Doganay, M. and Aygen, B. Human brucellosis: an overview. International Journal of Infectious Diseases, 7(3), 173-182, (2003).
Roth, F., Zinsstag, J., Orkhon, D., Chimed-Ochir, G., Hutton, G., Cosivi, O. et al. Human health benefits from livestock vaccination for brucellosis: case study. Bulletin of the World Health Organization, 81, 867-876, (2003).
Moreno, E. Retrospective and prospective perspectives on zoonotic brucellosis. Frontiers in Microbiology, 5, 213, (2014).
Li, M.T., Sun, G.Q., Wu, Y.F., Zhang, J. and Jin, Z. Transmission dynamics of a multi-group brucellosis model with mixed cross infection in public farm. Applied Mathematics and Computation, 237, 582-594, (2014).
Bonyah, E., Khan, M.A., Okosun, K.O. and Gómez-Aguilar, J.F. On the co-infection of dengue fever and Zika virus. Optimal Control Applications and Methods, 40(3), 394-421, (2019).
Ghaffari, P., Silva, C.J. and Torres, D.F.M. Mathematical models and optimal control in mosquito transmitted diseases. In Bio-Mathematics, Statistics, and Nano-Technologies: Mosquito Control Strategies (pp. 143-156). New York, USA: Chapman and Hall/CRC, (2023).
Yapışkan, D., Yurtoğlu, M., Avcı, D., Eroğlu, B.B.İ. and Bonyah, E. A novel model for Monkeypox disease: system analysis and optimal preventive strategies. Iranian Journal of Science, 47, 1665-1677, (2023).
Tajani, A., El Alaoui, F.Z. and Boutoulout, A. Regional boundary controllability of semilinear subdiffusion Caputo fractional systems. Mathematics and Computers in Simulation, 193, 481-496, (2022).
Özaltun, G., Konuralp, A. and Gümgüm, S. Gegenbauer wavelet solutions of fractional integro-differential equations. Journal of Computational and Applied Mathematics, 420, 114830, (2023).
Tunç, O. and Tunç, C. Ulam stabilities of nonlinear iterative integro-differential equations. Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas, 117(3), 118, (2023).
Wanassi, O.K. and Torres, D.F.M. An integral boundary fractional model to the world population growth. Chaos, Solitons & Fractals, 168, 113151, (2023).
Goyal, M., Baskonus, H.M. and Prakash, A. Regarding new positive, bounded and convergent numerical solution of nonlinear time fractional HIV/AIDS transmission model. Chaos, Solitons & Fractals, 139, 110096, (2020).
Veeresha, P., Malagi, N.S., Prakasha, D.G. and Baskonus, H.M. An efficient technique to analyze the fractional model of vector-borne diseases. Physica Scripta, 97(5), 054004, (2022).
Zaitri, M.A., Zitane, H. and Torres, D.F.M. Pharmacokinetic/Pharmacodynamic anesthesia model incorporating psi-Caputo fractional derivatives. Computers in Biology and Medicine, 167, 107679, (2023).
Eroğlu, B.B.İ and Yapışkan, D. Optimal strategies to prevent COVID-19 from becoming a pandemic. In Mathematical Modeling and Intelligent Control for Combating Pandemics, Springer Optimization and Its Applications (pp. 39-55). Cham, Switzerland: Springer, (2023).
Hussain, S., Tunç, O., ur Rahman, G., Khan, H. and Nadia, E. Mathematical analysis of stochastic epidemic model of MERS-corona & application of ergodic theory. Mathematics and Computers in Simulation, 207, 130-150, (2023).
Yapışkan, D. and Eroğlu, B.B.İ. Fractional optimal control of a generalized SIR epidemic model with vaccination and treatment. In Fractional Dynamics in Natural Phenomena and Advanced Technologies (pp. 131-150). Newcastle upon Tyne, UK: Cambridge Scholars Publishing, (2024).
Yurtoğlu, M. and Avcı, D. Optimal antivirus strategies for a virus propagation modelled with Mittag-Leffler Kernel. In Fractional Dynamics in Natural Phenomena and Advanced Technologies (pp. 113-130). Newcastle upon Tyne, UK: Cambridge Scholars Publishing, (2024).
Musafir, R.R., Suryanto, A. and Darti, I. Optimal control of a fractional-order Monkeypox epidemic model with vaccination and rodents culling. Results in Control and Optimization, 14, 100381, (2024).
Li, M., Sun, G., Zhang, J., Jin, Z., Sun, X., Wang, Y. et al. Transmission dynamics and control for a brucellosis model in Hinggan League of Inner Mongolia, China. Mathematical Biosciences and Engineering, 11(5), 1115-1137, (2014).
Li, M.T., Sun, G.Q., Zhang, W.Y. and Jin, Z. Model-based evaluation of strategies to control brucellosis in China. International Journal of Environmental Research and Public Health, 14(3), 295, (2017).
Lolika, P.O., Mushayabasa, S., Bhunu, C.P., Modnak, C. and Wang, J. Modeling and analyzing the effects of seasonality on brucellosis infection. Chaos, Solitons & Fractals, 104, 338-349, (2017).
Nyerere, N., Luboobi, L.S., Mpeshe, S.C. and Shirima, G.M. Modeling the impact of seasonal weather variations on the infectiology of brucellosis. Computational and Mathematical Methods in Medicine, 2020, 8972063, (2020).
Nyerere, N., Luboobi, L.S., Mpeshe, S.C. and Shirima, G.M. Mathematical model for brucellosis transmission dynamics in livestock and human populations. Communications in Mathematical Biology and Neuroscience, 2020(3), 1-29, (2020).
Sun, G.Q., Li, M.T., Zhang, J., Zhang, W., Pei, X. and Jin, Z. Transmission dynamics of brucellosis: mathematical modelling and applications in China. Computational and Structural Biotechnology Journal, 18, 3843-3860, (2020).
Lolika, P.O. and Helikumi, M. An intrinsic analysis of human brucellosis dynamics in Africa. Asian Research Journal of Mathematics, 18(11), 1-26, (2022).
Ma, X., Sun, G.Q., Wang, Z.H., Chu, Y.M., Jin, Z. and Li, B.L. Transmission dynamics of brucellosis in Jilin province, China: Effects of different control measures. Communications in Nonlinear Science and Numerical Simulation, 114, 106702, (2022).
Abagna, S., Seidu, B. and Bornaa, C.S. A mathematical model of the transmission Dynamics and control of bovine brucellosis in cattle. Abstract and Applied Analysis, 2022, 9658567, (2022).
Thongtha, A. and Modnak, C. The bison–human–environment dynamics of brucellosis infection with prevention and control studies. International Journal of Dynamics and Control, 12, 551-570, (2024).
Peter, O.J. Transmission dynamics of fractional order brucellosis model using Caputo-Fabrizio operator. International Journal of Differential Equations, 2020, 2791380, (2020).
Lolika, P.O. and Helikumi, M. Dynamics and analysis of chronic brucellosis in sheep. Journal of Advances in Mathematics and Computer Science, 37(7), 61-81, (2022).
Guan, P., Wu, W. and Huang, D. Trends of reported human brucellosis cases in mainland China from 2007 to 2017: an exponential smoothing time series analysis. Environmental Health and Preventive Medicine, 23, 23, (2018).
Jajarmi, A., Yusuf, A., Baleanu, D. and Inc, M. A new fractional HRSV model and its optimal control: a non-singular operator approach. Physica A: Statistical Mechanics and its Applications, 547, 123860, (2020).
Biswas, A.S., Aslam, B.H. and Tiwari, P.K. Mathematical modeling of a novel fractional-order Monkeypox model using the Atangana-Baleanu derivative. Physics of Fluids, 35(11), (2023).
Slimane, I., Nieto, J.J. and Ahmad, S. A fractional-order bovine babesiosis epidemic transmission model with nonsingular Mittag-Leffler law. Fractals, 31(02), 2340033, (2023).
Hussain, G., Khan, A., Zahri, M. and Zaman, G. Stochastic permanence of an epidemic model with a saturated incidence rate. Chaos, Solitons & Fractals, 139, 110005, (2020).
Capasso, V. and Serio, G. A generalization of the Kermack-Mckendrick deterministic epidemic model. Mathematical Biosciences, 42(1-2), 43-61, (1978).
Mwasa, A. and Tchuenche, J.M. Mathematical analysis of a cholera model with public health interventions. Biosystems, 105(3), 190-200, (2011).
Lemos-Paião, A.P., Silva, C.J. and Torres D.F.M. An epidemic model for cholera with optimal control treatment. Journal of Computational and Applied Mathematics, 318, 168-180, (2017).
Zhang, J., Jin, Z., Li, L. and Sun, X.D. Cost assessment of control measure for brucellosis in Jilin province, China. Chaos, Solitons & Fractals, 104, 798-805, (2017).
Hou, Q., Sun, X., Zhang, J., Liu, Y., Wang, Y. and Jin, Z. Modeling the transmission dynamics of sheep brucellosis in Inner Mongolia Autonomous Region, China. Mathematical Biosciences, 242(1), 51-58, (2013).
Atangana, A. and Baleanu, D. New fractional derivatives with nonlocal and non-singular kernel: theory and application to heat transfer model. Thermal Science, (20)2, 763-769, (2016).
Kermack, W.O. and McKendrick, A.G. A contribution to the mathematical theory of epidemics. Proceedings of the Royal Society of London. Series A, 115(772), 700-721, (1927).
Gómez-Aguilar, J.F., Rosales-García, J.J., Bernal-Alvarado, J.J., Córdova-Fraga, T. and Guzmán- Cabrera, R. Fractional mechanical oscillators. Revista Mexicana de Física, 58(4), 348-352, (2012).
Baleanu, D., Jajarmi, A., Sajjadi, S.S. and Mozyrska, D. A new fractional model and optimal control of a tumor-immune surveillance with non-singular derivative operator. Chaos: An Interdisciplinary Journal of Nonlinear Science, 29(8), 083127, (2019).
Ma, J. National Bureau of Statistics of China. In China Statistical Yearbook. Beijing, China: China Statistics Press, (2010).
Bosilkovski, M., Keramat, F. and Arapovi ́c, J. The current therapeutical strategies in human brucellosis. Infection, 49, 823-832, (2021).
Downloads
Published
How to Cite
Issue
Section
License
Copyright (c) 2024 Dilara Yapışkan, Beyza Billur İskender Eroğlu
This work is licensed under a Creative Commons Attribution 4.0 International License.
Articles published in the Bulletin of Biomathematics are made freely available online immediately upon publication, without subscription barriers to access. All articles published in this journal are licensed under the Creative Commons Attribution 4.0 International License (click here to read the full-text legal code). This broad license was developed to facilitate open access to, and free use of, original works of all types. Applying this standard license to your work will ensure your right to make your work freely and openly available.
Under the Creative Commons Attribution 4.0 International License, authors retain ownership of the copyright for their article, but authors allow anyone to download, reuse, reprint, modify, distribute, and/or copy articles in the Bulletin of Biomathematics, so long as the original authors and source are credited.
The readers are free to:
- Share — copy and redistribute the material in any medium or format
- Adapt — remix, transform, and build upon the material for any purpose, even commercially.
- The licensor cannot revoke these freedoms as long as you follow the license terms.
under the following terms:
- Attribution — You must give appropriate credit, provide a link to the license, and indicate if changes were made. You may do so in any reasonable manner, but not in any way that suggests the licensor endorses you or your use.
- No additional restrictions — You may not apply legal terms or technological measures that legally restrict others from doing anything the license permits.
