In biology and life sciences, fractal theory and fractional calculus have significant applications in simulating and understanding complex problems. In this paper, a compartmental model employing Caputo-type fractional and fractal-fractional operators is presented to analyze Nipah virus (NiV) dynamics and transmission. Initially, the model includes nine nonlinear ordinary differential equations that consider viral concentration, flying fox, and human populations simultaneously. The model is reconstructed using fractional calculus and fractal theory to better understand NiV transmission dynamics. We analyze the model's existence and uniqueness in both contexts and instigate the equilibrium points. The clinical epidemiology of Bangladesh is used to estimate model parameters. The fractional model's stability is examined using Ulam-Hyers and Ulam-Hyers-Rassias stabilities. Moreover, interpolation methods are used to construct computational techniques to simulate the NiV model in fractional and fractal-fractional cases. Simulations are performed to validate the stable behavior of the model for different fractal and fractional orders. The present findings will be beneficial in employing advanced computational approaches in modeling and control of NiV outbreaks.

Department of Computer Science and Mathematics Lebanese American University Byblos Lebanon

Department of Mathematics University of Peshawar Peshawar Khyber Pakhtunkhwa Pakistan

IT4Innovations VSB Technical University of Ostrava Ostrava Czech Republic

School of Mathematics and Data Sciences Changji University Changji Xinjiang China

Zobrazit více v PubMed

Tan C, Wong K. Nipah encephalitis outbreak in Malaysia. Annals of the Academy of Medicine, Singapore. 2003;32(1):112–117. doi: 10.47102/annals-acadmedsg.V32N1p112 PubMed DOI

World Health Organization. https://www.who.int/news-room/fact-sheets/detail/nipah-virus.;.

Yadav PD, Sahay RR, Balakrishnan A, Mohandas S, Radhakrishnan C, Gokhale MD, et al.. Nipah virus outbreak in Kerala State, India amidst of COVID-19 pandemic. Frontiers in Public Health. 2022;10:818545. doi: 10.3389/fpubh.2022.818545 PubMed DOI PMC

Nipah virus (CDC). https://www.cdc.gov/vhf/nipah/index.html;.

Ullah S, Khan MA, Farooq M, Gul T. Modeling and analysis of tuberculosis (TB) in Khyber Pakhtunkhwa, Pakistan. Mathematics and Computers in Simulation. 2019;165:181–199. doi: 10.1016/j.matcom.2019.03.012 DOI

Chukwu C, Nyabadza F, Asamoah J. 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. doi: 10.1504/IJCSM.2023.10055620 DOI

Khan AA, Ullah S, Altanji M, Amin R, Haider N, Alshehri A, et al.. A numerical study of spatio-temporal COVID-19 vaccine model via finite-difference operator-splitting and meshless techniques. Scientific Reports. 2023;13(1):12108. doi: 10.1038/s41598-023-38925-w PubMed DOI PMC

Din A. Bifurcation analysis of a delayed stochastic HBV epidemic model: Cell-to-cell transmission. Chaos, Solitons & Fractals. 2024;181:114714. doi: 10.1016/j.chaos.2024.114714 DOI

Adu IK, Wireko FA, Nana-Kyere S, Appiagyei E, Osman MA, Asamoah JKK. Modelling the dynamics of Ebola disease transmission with optimal control analysis. Modeling Earth Systems and Environment. 2024;p. 1–27.

Din A, Li Y, Yusuf A. Delayed hepatitis B epidemic model with stochastic analysis. Chaos, Solitons & Fractals. 2021;146:110839. doi: 10.1016/j.chaos.2021.110839 DOI

Khan A, Ikram R, Din A, Humphries UW, Akgul A. Stochastic COVID-19 SEIQ epidemic model with time-delay. Results in Physics. 2021;30:104775. doi: 10.1016/j.rinp.2021.104775 PubMed DOI PMC

Sultana J, Podder CN, et al.. Mathematical analysis of nipah virus infections using optimal control theory. Journal of Applied Mathematics and Physics. 2016;4(06):1099. doi: 10.4236/jamp.2016.46114 DOI

Zewdie AD, Gakkhar S. A mathematical model for Nipah virus infection. Journal of Applied Mathematics. 2020;2020:1–10. doi: 10.1155/2020/6050834 DOI

Barua S, Dénes A. Global dynamics of a compartmental model for the spread of Nipah virus. Heliyon. 2023;9:e19682. doi: 10.1016/j.heliyon.2023.e19682 PubMed DOI PMC

Zewdie AD, Gakkhar S, Gupta SK. Human–animal Nipah virus transmission: model analysis and optimal control. International Journal of Dynamics and Control. 2023;11(4):1974–1994. doi: 10.1007/s40435-022-01089-y DOI

Biswas M. Optimal control of Nipah virus (NiV) infections: a Bangladesh scenario. Journal of Pure and Applied Mathematics: Advances and Applications. 2014;12(1):77–104.

Biswas MHA, Haque MM, Duvvuru G. A mathematical model for understanding the spread of nipah fever epidemic in Bangladesh. In: 2015 International Conference on Industrial Engineering and Operations Management (IEOM). IEEE; 2015. p. 1–8.

Khan FM, Khan ZU, et al.. Numerical analysis of fractional order drinking mathematical model. Journal of Mathematical Techniques in Modeling. 2024;1(1):11–24.

Liu X, Ullah S, Alshehri A, Altanji M. Mathematical assessment of the dynamics of novel coronavirus infection with treatment: A fractional study. Chaos, Solitons & Fractals. 2021;153:111534. doi: 10.1016/j.chaos.2021.111534 PubMed DOI PMC

Khan WA, Zarin R, Zeb A, Khan Y, Khan A. Navigating food allergy dynamics via a novel fractional mathematical model for antacid-induced allergies. Journal of Mathematical Techniques in Modeling. 2024;1(1):25–51.

Podlubny I. Fractional differential equations: an introduction to fractional derivatives, fractional differential equations, to methods of their solution and some of their applications. vol. 198. Elsevier; 1998.

Caputo M, Fabrizio M. A new definition of fractional derivative without singular kernel. Progr Fract Differ Appl. 2015;1(2):1–13.

Atangana A, Baleanu D. New fractional derivatives with nonlocal and non-singular kernel: theory and application to heat transfer model. Therm Sci;p. 763–769.

Atangana A. Fractal-fractional differentiation and integration: Connecting fractal calculus and fractional calculus to predict complex system. Chaos, Solitons & Fractals. 2017;102:396–406. doi: 10.1016/j.chaos.2017.04.027 DOI

Li XP, Ullah S, Zahir H, Alshehri A, Riaz MB, Al Alwan B. Modeling the dynamics of coronavirus with super-spreader class: A fractal-fractional approach. Results in Physics. 2022;34:105179. doi: 10.1016/j.rinp.2022.105179 PubMed DOI PMC

Alzubaidi AM, Othman HA, Ullah S, Ahmad N, Mahtab M. Analysis of Monkeypox viral infection with human to animal transmission via a fractional and Fractal-fractional operators with power law kernel. Mathematical Biosciences and Engineering. 2023;20(4):6666–6690. doi: 10.3934/mbe.2023287 PubMed DOI

Ullah S, Nawaz R, AlQahtani SA, Li S, Hassan AM, et al.. A mathematical study unfolding the transmission and control of deadly Nipah virus infection under optimized preventive measures: New insights using fractional calculus. Results in Physics. 2023;51:106629. doi: 10.1016/j.rinp.2023.106629 DOI

Ali A, Yousef A, Ullah A, Ahmad S, Naz H, Al-Mdallal QM. Analysis Of The Transmission Of Nipah Virus Under Fractional Operator With Non-Singular And Nonlocal Kernel. Fractals. 2022;30(10):2240193. doi: 10.1142/S0218348X22401934 DOI

Li S, Ullah S, Samreen S, Khan IU, AlQahtani SA, Riaz MB. A robust computational study for assessing the dynamics and control of emerging zoonotic viral infection with a case study: A novel epidemic modeling approach. AIP Advances. 2024;14(1). doi: 10.1063/5.0188703 DOI

Khan MY, Ullah S, Farooq M, Al Alwan B, Saqib AB. Optimal control analysis for the Nipah infection with constant and time-varying vaccination and treatment under real data application. Scientific Reports. 2024;14(1):17532. doi: 10.1038/s41598-024-68091-6 PubMed DOI PMC

Worldometers Bangladesh Population (LIVE). https://www.worldometers.info/world-population/bangladesh-population/;.

Rahman M, Chakraborty A. Nipah virus outbreaks in Bangladesh: a deadly infectious disease. WHO South-East Asia Journal of Public Health. 2012;1(2):208–212. doi: 10.4103/2224-3151.206933 PubMed DOI

Sharma V, Kaushik S, Kumar R, Yadav JP, Kaushik S. Emerging trends of Nipah virus: A review. Reviews in medical virology. 2019;29(1):e2010. doi: 10.1002/rmv.2010 PubMed DOI PMC

Mondal MK, Hanif M, Biswas MHA. A mathematical analysis for controlling the spread of Nipah virus infection. International Journal of Modelling and Simulation. 2017;37(3):185–197. doi: 10.1080/02286203.2017.1320820 DOI

Khan MA, Ullah S, Kumar S. A robust study on 2019-nCOV outbreaks through non-singular derivative. The European Physical Journal Plus. 2021;136:1–20. doi: 10.1140/epjp/s13360-021-01159-8 PubMed DOI PMC

Odibat ZM, Shawagfeh NT. Generalized Taylor?s formula. Applied Mathematics and Computation. 2007;186(1):286–293. doi: 10.1016/j.amc.2006.07.102 DOI

Lin W. Global existence theory and chaos control of fractional differential equations. Journal of Mathematical Analysis and Applications. 2007;332(1):709–726. doi: 10.1016/j.jmaa.2006.10.040 DOI

Van den Driessche P, Watmough J. Reproduction numbers and sub-threshold endemic equilibria for compartmental models of disease transmission. Mathematical biosciences. 2002;180(1-2):29–48. doi: 10.1016/S0025-5564(02)00108-6 PubMed DOI

Hyers DH. On the stability of the linear functional equation. Proceedings of the National Academy of Sciences. 1941;27(4):222–224. doi: 10.1073/pnas.27.4.222 PubMed DOI PMC

Rassias TM. On the stability of the linear mapping in Banach spaces. Proceedings of the American mathematical society. 1978;72(2):297–300. doi: 10.1090/S0002-9939-1978-0507327-1 DOI

Rezapour S, Asamoah JKK, Hussain A, Ahmad H, Banerjee R, Etemad S, et al.. A theoretical and numerical analysis of a fractal–fractional two-strain model of meningitis. Results in Physics. 2022;39:105775. doi: 10.1016/j.rinp.2022.105775 DOI

Ackora-Prah J, Seidu B, Okyere E, Asamoah JK. Fractal-Fractional Caputo Maize Streak Virus Disease Model. Fractal and Fractional. 2023;7(2):189. doi: 10.3390/fractalfract7020189 DOI

Li C, Zeng F. Numerical methods for fractional calculus. Chapman and Hall/CRC; 2015.

Sinha D, Sinha A. Mathematical model of zoonotic nipah virus in south-east asia region. Acta Scientific Microbiology. 2019;2(9):82–89.

Zewdie AD, Gakkhar S, Gupta SK. Human–animal Nipah virus transmission: model analysis and optimal control. International Journal of Dynamics and Control. 2022;p. 1–21.

Atangana A, Qureshi S. Modeling attractors of chaotic dynamical systems with fractal–fractional operators. Chaos, Solitons & Fractals. 2019;123:320–337. doi: 10.1016/j.chaos.2019.04.020 DOI