Enhanced Modelling of Listeriosis Disease Transmission Using Fractal-Fractional Differential Equations with Fuzzy Logic
Tamil Vizhi Mariappan
1
(
Department of Mathematics, Alagappa University, Karaikudi, India.
)
Vimala Jayakumar
2
(
Department of Mathematics, Alagappa University, Karaikudi, India.
)
Jeevitha Kannan
3
(
Department of Mathematics, Alagappa University, Karaikudi, India.
)
کلید واژه: Listeriosis disease, Ulam-Hyers stable, Riemann-Liouville fractal-fractional derivative, Lagrange piecewise interpolation, fuzzy number.,
چکیده مقاله :
Listeriosis, caused by Listeria monocytogenes, presents significant public health risks, especially to vulnerable groups such as the elderly, immunocompromised individuals, and pregnant women. Despite advancements in food safety measures, the bacteria’s resilience across various environments makes their complete eradication challenging. This study addresses this challenge by incorporating uncertainty and memory effects into the disease modelling process. This study offers an advanced mathematical framework to analyse listeriosis dynamics using fractal-fractional differential equations and a fuzzy fractal-fractional approach. The integration of fractal calculus allows for a detailed examination of complex, multi-scale behaviours of real-world disease spread, while the incorporation of fuzzy logic accounts for inherent uncertainties in initial conditions and parameter values. Ensuring the mathematical validity of the proposed models, the research explores key properties such as existence, uniqueness, and Ulam-Hyers stability, which confirm the robustness and reliability of the solutions. A computational approach is utilized to solve the model, revealing the dynamics of susceptible, infected, and recovered populations, as well as the bacterial class and the progression of spoiled and unspoiled food packages over time. The importance of fractal dimensions in the Listeriosis model is emphasized by variation maps that depict changes over time. The extension of the model to include fuzzy initial conditions enhances predictive capabilities and supports decision-making by accommodating uncertainty. The findings underscore the importance of applying sophisticated mathematical tools, such as fractal-fractional and fuzzy differential equations, to improve the understanding and management of listeriosis and similar public health challenges, enabling more effective prevention and control strategies.
چکیده انگلیسی :
Listeriosis, caused by Listeria monocytogenes, presents significant public health risks, especially to vulnerable groups such as the elderly, immunocompromised individuals, and pregnant women. Despite advancements in food safety measures, the bacteria’s resilience across various environments makes their complete eradication challenging. This study addresses this challenge by incorporating uncertainty and memory effects into the disease modelling process. This study offers an advanced mathematical framework to analyse listeriosis dynamics using fractal-fractional differential equations and a fuzzy fractal-fractional approach. The integration of fractal calculus allows for a detailed examination of complex, multi-scale behaviours of real-world disease spread, while the incorporation of fuzzy logic accounts for inherent uncertainties in initial conditions and parameter values. Ensuring the mathematical validity of the proposed models, the research explores key properties such as existence, uniqueness, and Ulam-Hyers stability, which confirm the robustness and reliability of the solutions. A computational approach is utilized to solve the model, revealing the dynamics of susceptible, infected, and recovered populations, as well as the bacterial class and the progression of spoiled and unspoiled food packages over time. The importance of fractal dimensions in the Listeriosis model is emphasized by variation maps that depict changes over time. The extension of the model to include fuzzy initial conditions enhances predictive capabilities and supports decision-making by accommodating uncertainty. The findings underscore the importance of applying sophisticated mathematical tools, such as fractal-fractional and fuzzy differential equations, to improve the understanding and management of listeriosis and similar public health challenges, enabling more effective prevention and control strategies.
[1] Koopmans MM, Brouwer MC, Vázquez-Boland JA, van de Beek D. Human listeriosis. Clinical Microbiology Reviews. 2023; 36(1): e00060-19. https://doi.org/10.1128/cmr.00060-19
[2] World Health Organization. International travel and health. https://www.who.int/ith/diseases/Listeriosis [Accessed 26th July 2020]
[3] Riaz R, Shaheen R. Listeriosis in pregnancy: an important cause of febrile illness Listeriosis in pregnancy: an important cause of febrile illness. Journal of University Medical & Dental College. 2022; 13(1): 351- 353. https://doi.org/10.37723/jumdc.v13i1.709
[4] Ivanek R, Gröhn YT, Wiedmann M. Listeria monocytogenes in multiple habitats and host populations: review of available data for mathematical modeling. Foodbourne Pathogens & Disease. 2006; 3(4): 319- 336. https://doi.org/10.1089/fpd.2006.3.319
[5] Swaminathan B, Gerner-Smidt P. The epidemiology of human listeriosis. Microbes and Infection. 2007; 9(10): 1236-1243. https://doi.org/10.1016/j.micinf.2007.05.011
[6] Hernandez-Milian A, Payeras-Cifre A. What is new in listeriosis?. BioMed Research International. 2014; 2014(1): 358051. https://doi.org/10.1155/2014/358051
[7] Bennion JR, Sorvillo F, Wise ME, Krishna S, Mascola L. Decreasing listeriosis mortality in the United States, 1990-2005. Clinical Infectious Diseases. 2008; 47(7): 867-874. https://doi.org/10.1086/591131
[8] Bongiovanni M, Cavallo C, Barda B, Strulak L, Bernasconi E, Cardia A. Clinical findings of listeria monocytogenes infections with a sSpecial focus on bone localizations. Microorganisms. 2024; 12(1): 178. https://doi.org/10.3390/microorganisms12010178
[9] Duarte F, Pinto SM, et al. A rare presentation of Listeria monocytogenes infection: perianal abscess associated with lumbar spine osteitis. IDCases. 2019; 15: e00488. https://doi.org/10.1016/j.idcr.2019.e00488
[10] Centers for disease Control and Prevention. [Accessed 26 May 2020] https://www.cdc.gov/Listeria/prevention.html
[11] Roh SH, Oh YJ, Lee SY, Kang JH, Min SC. Inactivation of Escherichia coli O157: H7, Salmonella, Listeria monocytogenes, and Tulane virus in processed chicken breast via atmospheric in-package cold plasma treatment. LWT 2020; 127: 109429. http://doi.org/10.1016/j.lwt.2020.109429
[12] Ryser ET, Marth EH. Listeria, listeriosis, and food safety. 3rd ed. Boca Raton: CRC Press; 2007. https://doi.org/10.1201/9781420015188
[13] Shi C, Lv D, Zhou K, Jin T, Wang G, Wang B, Li Y, Xu Y. Clinical and laboratory characteristics of patients infected by Listeria monocytogenes at a Tertiary hospital in Hefei City, China. Infection and Drug Resistance. 2021; 2021: 4409-4419. https://doi.org/10.2147/IDR.S334929
[14] Kaptchouang Tchatchouang CD, Fri J, De Santi M, Brandi G, Schiavano GF, Amagliani G, Ateba CN. Listeriosis outbreak in South Africa: a comparative analysis with previously reported cases worldwide. Microorganisms. 2020; 8(1): 135. https://doi.org/10.3390/microorganisms8010135
[15] Sulieman AME, Abu Zeid IM, Abdalla EM, Ed-Dra A. New discoveries in toxins from Gram-Positive Bacteria, Listeria monocytogenes. In: Moneim Elhadi Sulieman, A., Alshammari, N.I. (eds.) Microbial toxins in food systems: causes, mechanisms, complications, and metabolism. Cham: Springer; 2024. p. 303-318. https://doi.org/10.1007/978-3-031-62839-9 23
[16] Chukwu CW, Nyabadza F, Asamoah JKK. A mathematical model and optimal control for Listeriosis disease from ready-to-eat food products. International Journal of Computing Science and Mathematics. 2023; 17(1): 39-49. https://doi.org/10.1504/IJCSM.2023.130421
[17] Lanzas C, Lu Z, Gröhn YT. Mathematical modeling of the transmission and control of foodborne pathogens and antimicrobial resistance at preharvest. Foodborne Pathogens and Disease. 2011; 8(1): 1-0. https://doi.org/10.1089/fpd.2010.0643
[18] Osman S, Makinde OD. A mathematical model for coinfection of listeriosis and anthrax diseases. International Journal of Mathematics and Mathematical Sciences. 2018; 2018(1): 1725671. https://doi.org/10.1155/2018/1725671
[19] Osman S, Otoo D, Sebil C. Analysis of listeriosis transmission dynamics with optimal control. Applied Mathematics. 2020; 11(7): 712-737. https://doi.org/10.4236/am.2020.117048
[20] Osman S, Makinde OD, Theuri DM. Stability analysis and modelling of listeriosis dynamics in human and animal populations. Global Journal of Pure and Applied Mathematics. 2018; 14(1): 115-137.
[21] Bonyah E, Yavuz M, Baleanu D, Kumar S. A robust study on the listeriosis disease by adopting fractal-fractional operators. Alexandria Engineering Journal. 2022; 61(3): 2016-2028. https://doi.org/10.1016/j.aej.2021.07.010
[22] Chukwu CW, Nyabadza F. A theoretical model of listeriosis driven by cross contamination of readyto-eat food products. International Journal of Mathematics and Mathematical Sciences. 2020; 2020(1): 9207403. https://doi.org/10.1155/2020/9207403
[23] Tchoumi SY, Chukwu CW, Windarto AP. A multi-population approach to epidemiological modeling of listeriosis transmission dynamics incorporating food and environmental contamination. Healthcare Analytics. 2024; 5: 100344. https://doi.org/10.1016/j.health.2024.100344
[24] Osman S, Makinde OD, Theuri DM. Mathematical modelling of Listeriosis Epidemics in Animal and Human Population with Optimal Control. Tamkang Journal of Mathematics. 2020; 51(4): 261-287.
https://doi.org/10.5556/j.tkjm.51.2020.2860
[25] Chauhan JP, Khirsariya SR, Yeolekar BM, Yeolekar MA. Fractional mathematical model of Listeria infection caused by pre-cooked package food. Results in Control and Optimization. 2024; 14: 100371. https://doi.org/10.1016/j.rico.2024.100371
[26] Asamoah JKK, Addai E, Arthur YD, Okyere E. A fractional mathematical model for listeriosis infection using two kernels. Decision Analytics Journal. 2023; 6:100191. https://doi.org/10.1016/j.dajour.2023.100191
[27] Atangana A. Fractal-fractional differentiation and integration: connecting fractal calculus and fractional calculus to predict complex system. Chaos, Solitons & Fractals. 2017; 102: 396-406. https://doi.org/10.1016/j.chaos.2017.04.027
[28] Kubra KT, Gulshan S, Ali R. An Atangana-Baleanu derivative-based fractal-fractional order model for the monkey pox virus: A case study of USA. Partial Differential Equations in Applied Mathematics. 2024; 9: 100623. https://doi.org/10.1016/j.padiff.2024.100623
[29] Atangana A, Qureshi S. Modeling attractors of chaotic dynamical systems with fractalfractional operators. Chaos, Solitons & Factals. 2019; 123: 320-337. https://doi.org/10.1016/j.chaos.2019.04.020
[30] Qureshi S, Atangana A. Fractal-fractional differentiation for the modeling and mathematical analysis of nonlinear diarrhea transmission dynamics under the use of real data. Chaos, Solitons & Fractals. 2020; 136: 109812. https://doi.org/10.1016/j.chaos.2020.109812
[31] Kubra KT, Ali R, Alqahtani RT, Gulshan S, Iqbal Z. Author Correction: analysis and comparative study of a deterministic mathematical model of SARS-COV-2 with fractal-fractional operators: a case study. Scientific Reports. 2024; 14(1): 6431. https://doi.org/10.1038/s41598-024-58414-y
[32] Nisar KS, Ahmad S, Ullah A, Shah K, Alrabaiah H, Arfan M. Mathematical analysis of SIRD model of COVID-19 with Caputo fractional derivative based on real data. Results in Physics. 2021; 21: 103772. https://doi.org/10.1016/j.rinp.2020.103772
[33] Qureshi S, Yusuf A. Modeling chickenpox disease with fractional derivatives: from Caputo to AtanganaBaleanu. Chaos, Solitons & Fractals. 2019; 122: 111-118. https://doi.org/10.1016/j.chaos.2019.03.020
[34] Singh HK, Pandey DN. Analysis of the Chickenpox Disease Evolution in an MSEIR Model Using Fractal-Fractional Differential Operator. Differential Equations and Dynamical Systems. 2024; 4: 1-21. https://doi.org/10.1007/s12591-024-00690-1
[35] Allahviranloo, T. Fuzzy fractional differential operators and equations. Cham: Springer; 2021. https://doi.org/10.1007/978-3-030-51272-9
[36] Babakordi F, Allahviranloo T. Application of fuzzy ABC fractional differential equations in infectious diseases. Computational Methods for Differential Equations. 2024; 12(1): 1-15. https://doi.org/10.22034/cmde.2023.47768.2000
[37] Subramanian S, Kumaran A, Ravichandran S, Venugopal P, Dhahri S, Ramasamy K. Fuzzy fractional Caputo derivative of susceptible-infectious-removed epidemic model for childhood diseases. Mathematics. 2024; 12(3): 466. https://doi.org/10.3390/math12030466
[38] Babakordi F. An efficient method for solving the fuzzy AH1N1/09 influenza model using the fuzzy Atangana-Baleanu-Caputo fractional derivative. Fuzzy Optimization and Modeling Journal. 2023; 4(2): 27-38. https://doi.org/10.30495/fomj.2023.1988760.1096
[39] Khaliq R, Iqbal P, Bhat SA, Sheergojri AR. A fuzzy mathematical model for tumor growth pattern using generalized Hukuhara derivative and its numerical analysis. Applied Soft Computing. 2022; 118: 108467. https://doi.org/10.1016/j.asoc.2022.108467
[40] Granas A, Dugundji J. Fixed point theory. New York: Springer Monographs in Mathematics/SpringerVerlag; 2003. https://doi.org/10.1007/978-0-387-21593-8
