FRACTIONAL-ORDER DENGUE VIRUS MODEL WITH VECTOR AND NON-VECTOR TRANSMISSION: BIFURCATION ANALYSIS AND MEMORY EFFECTS
Abstract
Dengue fever, a major mosquito-borne disease, poses significant global health challenges, particularly in tropical and subtropical regions. Traditional epidemiological models often fail to capture the memory-dependent dynamics and complexities of disease transmission, limiting their effectiveness in informing public health strategies. This study introduces a novel fractional-order dengue transmission model using the Caputo fractional derivative to incorporate memory effects. The model considers both vector and non-vector transmission pathways, along with mosquito-to-mosquito transmission. The basic reproduction number was derived using the next-generation matrix method. Stability analyses were performed to explore the conditions under which backward bifurcation occurs, with a particular focus on the influence of mosquito-to-mosquito transmission dynamics. Stability analysis revealed that backward bifurcation arises when the reproduction number associated with mosquito-to-mosquito transmission exceeds one, highlighting its critical role in dengue dynamics. Numerical simulations demonstrated that fractional-order models effectively delay epidemic peaks and extend the transition period of exposed populations, providing extended windows for timely interventions. Sensitivity analysis identified mosquito-to-human and mosquito-to-mosquito transmission rates as key drivers of emphasizing the need for targeted control measures, including vector control and vaccination campaigns. This study demonstrates that fractional-order models are superior to traditional integer-order models in capturing the complex dynamics of dengue transmission. By integrating memory effects and analyzing critical transmission pathways, the model offers a more realistic framework for understanding dengue spread. These findings provide valuable insights for optimizing public health interventions, emphasizing the transformative potential of fractional-order models in sustainable dengue control and future research.
References
Adel, W., Elsonbaty, A., & Mahdy, A. M. S. (2024). On some recent advances in fractional order modeling in engineering and science. Computation and Modeling for Fractional Order Systems, 169197. DOI: https://doi.org/10.1016/B978-0-44-315404-1.00016-3
Alshehry, A. S., Yasmin, H., Khammash, A. A., & Shah, R. (2024). Numerical analysis of dengue transmission model using CaputoFabrizio fractional derivative. Open Physics, 22(1), 20230169. DOI: https://doi.org/10.1515/phys-2023-0169
Asaduzzaman, M., Kilicman, A., Al-Mamun, A., & Hossain, M. D. (2024). Analysis of a novel conformable fractional order ASIR dengue transmission model in the perspective of Bangladesh. Mathematical Models and Computer Simulations, 16(3), 431456. DOI: https://doi.org/10.1134/S2070048224700157
Atokolo, W., Aja, R. O., Omale, D., Ahman, Q. O., Acheneje, G. O., & Amos, J. (2024). Fractional mathematical model for the transmission dynamics and control of Lassa fever. Franklin Open, 7(15), 27731863. DOI: https://doi.org/10.1016/j.fraope.2024.100110
Chitnis, N., Smith, T., & Schapira, A. (2021). The role of vertical transmission in the spread of mosquito-borne diseases: Insights from a dengue model. Journal of Theoretical Biology, 523, 110713. https://doi.org/10.1016/j.jtbi.2021.110713. DOI: https://doi.org/10.1016/j.jtbi.2021.110713
El-Shenawy, A., El-Gamel, M., & Teba, A. (2024). Simulation of the SIR dengue fever nonlinear model: A numerical approach. Partial Differential Equations in Applied Mathematics, 11, 100891. DOI: https://doi.org/10.1016/j.padiff.2024.100891
Islam, N., Borhan, J. R. M., & Prodhan, R. (2024). Application of mathematical modeling: A mathematical model for dengue disease in Bangladesh. International Journal of Mathematical Sciences and Computing, 10(1), 1930. DOI: https://doi.org/10.5815/ijmsc.2024.01.03
Kumar, R., Saxena, B., Shrivastava, R., & Bhardwaj, R. (2024). Mathematical modeling of dengue disease transmission dynamics. Indian Journal of Science and Technology, 17(39), 41014110. DOI: https://doi.org/10.17485/IJST/v17i39.1526
Meena, M., & Purohit, M. (2024). Mathematical analysis using fractional operator to study the dynamics of dengue fever. Physica Scripta, 99(9), 095206. DOI: https://doi.org/10.1088/1402-4896/ad671b
Meetei, M. Z., Zafar, S., Zaagan, A. A., Mahnashi, A. M., & Idrees, M. (2024). Dengue transmission dynamics: A fractional-order approach with compartmental modeling. Fractal and Fractional, 8(4), 207. DOI: https://doi.org/10.3390/fractalfract8040207
Mohammed, A., Abdulfatai, A., Abimbola, N. G. A., & Ali, I. M. (2022). Mathematical modelling of dengue fever incorporating vaccination as control. Abacus (Mathematics Science Series, 49(1).
Naaly, B. Z., Marijani, T., Isdory, A., & Ndendya, J. Z. (2024). Mathematical modeling of the effects of vector control, treatment and mass awareness on the transmission dynamics of dengue fever. Computer Methods and Programs in Biomedicine Update, 6, 100159. DOI: https://doi.org/10.1016/j.cmpbup.2024.100159
Nisar, K. S., Farman, M., Abdel-Aty, M., & Ravichandran, C. (2024). A review of fractional order epidemic models for life sciences problems: Past, present and future. Alexandria Engineering Journal, 95, 283305. DOI: https://doi.org/10.1016/j.aej.2024.03.059
Olayiwola, M. O., & Alaje, A. I. (2024). Mathematical analysis of intrahost spread and control of dengue virus: Unraveling the crucial role of antigenic immunity. Franklin Open, 100117. DOI: https://doi.org/10.1016/j.fraope.2024.100117
Olayiwola, M. O., & Yunus, A. O. (2024). Mathematical analysis of a within-host dengue virus dynamics model with adaptive immunity using Caputo fractional-order derivatives. Journal of Umm Al-Qura University for Applied Sciences, 120. DOI: https://doi.org/10.1007/s43994-024-00151-z
Pandey, H. R., & Phaijoo, G. R. (2024). Dengue dynamics in Nepal: A Caputo fractional model with optimal control strategies. Heliyon, 10(13). DOI: https://doi.org/10.1016/j.heliyon.2024.e33822
Rahman, A., Khan, M., & Islam, S. (2022). Modeling rare human-to-human transmission routes in dengue dynamics. Journal of Infectious Diseases and Epidemiology, 10(3), 5665. https://doi.org/10.1016/j.jide.2022.05.003.
Shanmugam, S. N., & Byeon, H. (2024). Comprehending symmetry in epidemiology: A review of analytical methods and insights from models of COVID-19, Ebola, dengue, and monkeypox. Medicine, 103(41), e40063. DOI: https://doi.org/10.1097/MD.0000000000040063
Sk, T., Bal, K., Biswas, S., & Sardar, T. (2024). Global stability and optimal control in a single-strain dengue model with fractional-order transmission and recovery process. arXiv preprint, arXiv:2402.11974.
Usman, M., Abbas, M., Khan, S. H., & Omame, A. (2024). Analysis of a fractional-order model for dengue transmission dynamics with quarantine and vaccination measures. Scientific Reports, 14(1), 11954. DOI: https://doi.org/10.1038/s41598-024-62767-9
Vellappandi, M., Govindaraj, V., Kumar, P., & Nisar, K. S. (2024). An optimal control problem for dengue fever model using Caputo fractional derivatives. Progress in Fractional Differentiation, 10(1), 115. DOI: https://doi.org/10.18576/pfda/100101
Vijayalakshmi, G. M., Ariyanatchi, M., Cepova, L., & Karthik, K. (2024). Advanced optimal control approaches for immune boosting and clinical treatment to enhance dengue viremia models using ABC fractional-order analysis. Frontiers in Public Health, 12, 1398325. DOI: https://doi.org/10.3389/fpubh.2024.1398325
World Health Organization (WHO). (2022). Dengue and severe dengue. WHO Fact Sheets. Retrieved from https://www.who.int/newsroom/fact-sheets/detail/dengue-and-severe-dengue.
Xu, Z., Zhang, H., Yang, D., Wei, D., Demongeot, J., & Zeng, Q. (2024). The mathematical modeling of the hostvirus interaction in dengue virus infection: A quantitative study. Viruses, 16(2), 216. DOI: https://doi.org/10.3390/v16020216
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