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Zeb, Shah, Mohd Yatim, Siti Ainor, Kamran, Ayesha, Kausar, Rizwana, Rafiq, Muhammad. (1405). A new delayed SEIR-SEI model for dengue transmission control with sensitivity and competitive mathematical analysis. سامانه مدیریت نشریات علمی, 14(1), 470-501. doi: 10.22034/cmde.2025.67008.3176
Shah Zeb; Siti Ainor Mohd Yatim; Ayesha Kamran; Rizwana Kausar; Muhammad Rafiq. "A new delayed SEIR-SEI model for dengue transmission control with sensitivity and competitive mathematical analysis". سامانه مدیریت نشریات علمی, 14, 1, 1405, 470-501. doi: 10.22034/cmde.2025.67008.3176
Zeb, Shah, Mohd Yatim, Siti Ainor, Kamran, Ayesha, Kausar, Rizwana, Rafiq, Muhammad. (1405). 'A new delayed SEIR-SEI model for dengue transmission control with sensitivity and competitive mathematical analysis', سامانه مدیریت نشریات علمی, 14(1), pp. 470-501. doi: 10.22034/cmde.2025.67008.3176
Zeb, Shah, Mohd Yatim, Siti Ainor, Kamran, Ayesha, Kausar, Rizwana, Rafiq, Muhammad. A new delayed SEIR-SEI model for dengue transmission control with sensitivity and competitive mathematical analysis. سامانه مدیریت نشریات علمی, 1405; 14(1): 470-501. doi: 10.22034/cmde.2025.67008.3176

A new delayed SEIR-SEI model for dengue transmission control with sensitivity and competitive mathematical analysis

Computational Methods for Differential Equations
مقاله 30، دوره 14، شماره 1، فروردین 2026، صفحه 470-501    اصل مقاله (1.89 M)
نوع مقاله: Research Paper
شناسه دیجیتال (DOI): 10.22034/cmde.2025.67008.3176
نویسندگان
Shah Zeb1؛ Siti Ainor Mohd Yatim* 2؛ Ayesha Kamran3؛ Rizwana Kausar4؛ Muhammad Rafiq5
1School of Distance Education, Universiti Sains Malaysia, USM, 11800, Penang, Malaysia.
21) School of Distance Education, Universiti Sains Malaysia, USM, 11800, Penang, Malaysia. 2) School of Mathematical Sciences, Universiti Sains Malaysia, USM, 11800, Penang, Malaysia.
3Department of Mathematics, University of Management and Technology, CII Johar Town, Lahore, 54770, Punjab, Pakistan.
4School of Biological Sciences, Universiti Sains Malaysia, USM, 11800, Penang, Malaysia.
5Department of Mathematics, Namal University 30km Talagang Road, Mianwali, 42250, Pakistan.
چکیده
Dengue fever is a viral illness affecting over 129 nations and more than 50% of the global population, causing approximately 400 million cases annually. This study explores the mathematical formulation and dynamics of dengue transmission using a structured SEIR-SEI (susceptible human, exposed human, infected human, recovered human, susceptible vector, exposed vector, and infected vector) model, focusing on immunological and delay-based control strategies. An existing nonlinear delayed SEIR-SEI epidemic model is extended to evaluate the effectiveness of awareness, mosquito deterrence, and therapeutic interventions. Rather than immediately resorting to pharmacological methods, the model emphasizes analyzing delay factors due to their significant role in disease control. Since reducing mosquito populations can harm ecological balance, this new approach applies delay-based strategies on human-related factors such as hospitalization, awareness, and travel restrictions to safeguard both public health and the environment. The findings show that the reproductive number alone is insufficient to predict outbreak persistence; recruitment patterns and mosquito biting rates play a more pivotal role. We analyze the model’s mathematical properties, including the reproduction number, equilibrium points, parameter sensitivity, and both local and global stability. Our results demonstrate that model-based strategies focusing on vector control and human behavior effectively reduce dengue transmission. Additionally, we show that the non-standard finite difference scheme outperforms traditional methods like the fourth-order Runge-Kutta in terms of accuracy, stability, and predictive capability. This study offers valuable insights for public health officials and policymakers in designing sustainable strategies to control endemic dengue transmission and prevent future outbreaks.
کلیدواژه‌ها
Dengue؛ Reproductive number؛ Global stability؛ NSFD؛ Convergence analysis
مراجع
  • [1] A. Abidemi and N. A. B. Aziz, Analysis of deterministic models for dengue disease transmission dynamics with vaccination perspective in Johor, Malaysia, International Journal of Applied and Computational Mathematics, 8(1) (2022), 45.
  • [2] S. AbuBakar, S. E. W. Puteh, R. Kastner, L. Oliver, S. H. Lim, R. Hanley, and E. Gallagher, Epidemiology (2012-2019) and costs (2009-2019) of dengue in Malaysia: a systematic literature review, International Journal of Infectious Diseases, 124 (2022), 240-247.
  • [3] W. Ahmad, A. I. K. Butt, N. Akhtar, M. Rafiq, M. Gohar, Z. Idrees, and N. Ahmad, Developing computationally efficient optimal control strategies to eradicate Rubella disease, Physica Scripta, 99(3) (2024), 035202.
  • [4] W. Ahmad, M. Rafiq, A. I. K. Butt, N. Ahmad, T. Ismaeel, S. Malik, H. G. Rabbani, and Z. Asif, Analytical and numerical explorations of optimal control techniques for the bi-modal dynamics of Covid-19, Nonlinear Dynamics, 112(5) (2024), 3977-4006.
  • [5] K. A. Aldwoah, M. A. Almalahi, K. Shah, M. Awadalla, and R. H. Egami, Dynamics analysis of dengue fever model with harmonic mean type under fractal-fractional derivative, AIMS Mathematics, 9(6) (2024), 13894-13926.
  • [6] T. D. Alharbi and M. R. Hasan, Global stability and sensitivity analysis of vector-host dengue mathematical model, AIMS Mathematics, 9(11) (2024), 32797-32818.
  • [7] R. K. Alhefthi, M. A. Ur Rehman, N. Ahmed, Z. Iqbal, M. Inc, M. Iqbal, M. S. Iqbal, A. Raza, and M. Rafiq, Developing a computational framework for accurately solving a mathematical model of Streptococcus pneumonia infection, Biomedical Signal Processing and Control, 103 (2025), 107427.
  • [8] S. A. Bakar and N. Shafee, Outlook of dengue in Malaysia: a century later, Malaysian Journal of Pathology, 24(1) (2002), 23-27.
  • [9] S. Bhatter, B. Bhatia, S. Kumawat, and S. Purohit, Modeling and simulation of COVID-19 disease dynamics via Caputo Fabrizio fractional derivative, Computational Methods for Differential Equations, Online First (2024).
  • [10] O. Brathwaite Dick, J. L. San Martın, R. H. Montoya, J. del Diego, B. Zambrano, and G. H. Dayan, The history of dengue outbreaks in the Americas, The American journal of tropical medicine and hygiene, 87(4) (2012), 584-593.
  • [11] A. I. K. Butt, W. Ahmad, M. Rafiq, N. Ahmad, and M. Imran, Computationally efficient optimal control analysis for the mathematical model of Coronavirus pandemic, Expert Systems with Applications, 234 (2023), 121094.
  • [12] H. Dieng, R. G. Saifur, A. H. Ahmad, M. C. Salmah, A. T. Aziz, T. Satho, F. Miake, Z. Jaal, S. Abubakar, and R. E. Morales, Unusual developing sites of dengue vectors and potential epidemiological implications, Asian Pacific Journal of Tropical Biomedicine, 2(3) (2012), 228-232.
  • [13] Y. Dumont and J. Thuilliez, Human behaviors: A threat to mosquito control?, Mathematical Biosciences, 281 (2016), 9-23.
  • [14] C. Dye, Vectorial capacity: Must we measure all its components?, Parasitology Today, 2(8) (1986), 203-209.
  • [15] E. L. Fairbanks, M. Saeung, A. Pongsiri, E. Vajda, Y. Wang, D. J. McIver, J. H. Richardson, A. Tatarsky, N. F. Lobo, S. J. Moore, A. Ponlawat, T. Chareonviriyaphap, A. Ross, and N. Chitnis, Inference for entomological semifield experiments: Fitting a mathematical model assessing personal and community protection of vector-control interventions, Computers in Biology and Medicine, 168 (2024), 107716.
  • [16] H. Gholami, M. Gachpazan, and M. Erfanian, SEIaIsQRS epidemic model for COVID-19 by using compartmental analysis and numerical simulation, Computational Methods for Differential Equations, Online First (2024).
  • [17] K. Gosztonyi, How history of mathematics can help to face a crisis situation: the case of the polemic between Bernoulli and d’Alembert about the smallpox epidemic, Educational Studies in Mathematics, 108(1-2) (2021), 105-122.
  • [18] N. Hamdan Izzati and A. Kilicman, Local stability of dengue model using the fractional order system with different memory effect on the host and vector population, Thermal Science, 23(Suppl. 1) (2019), 327-337.
  • [19] N. Hamdan Izzati and A. Kilicman, Analysis of the fractional order dengue transmission model: a case study in Malaysia, Advances in Difference Equations, 2019(1) (2019).
  • [20] N. Hamdan Izzati and A. Kilicman, The development of a deterministic dengue epidemic model with the influence of temperature: A case study in Malaysia, Applied Mathematical Modelling, 90 (2021), 547-567.
  • [21] H. Hassan, S. Shohaimi, and N. R. Hashim, Risk mapping of dengue in Selangor and Kuala Lumpur, Malaysia, Geospatial Health, 7(1) (2012), 21.
  • [22] W. O. Kermack and A. G. McKendrick, Contributions to the mathematical theory of epidemics-I, Bulletin of Mathematical Biology, 53(1-2) (1991), 33-55.
  • [23] M. B. Khan, Z. S. Yang, C. Y. Lin, M. C. Hsu, A. N. Urbina, W. Assavalapsakul, W. H. Wang, Y. H. Chen, and S. F. Wang, Dengue overview: An updated systemic review, Journal of Infection and Public Health, 16(10) (2023), 1625-1642.
  • [24] J. L. Kyle and E. Harris, Global spread and persistence of dengue, Annual Review of Microbiology, 62(1) (2008), 71-92.
  • [25] S. Mandal, R. R. Sarkar, and S. Sinha, Mathematical models of malaria-a review, Malaria journal, 10 (2011), 1-19.
  • [26] S. B. Mohamed Siddik, F. A. Abdullah, and A. I. Md. Ismail, Mathematical model of dengue virus with predatorprey interactions, Sains Malaysiana, 49(5) (2020), 1191–1200.
  • [27] S. N. Mohd Salleh, N. Che Dom, S. Ab Rahim, E. Mohamed, N. Haron, A. S. Rambely, and S. N. Camalxaman, Dengue vector control approaches: existing options and the way forward, Journal Of Sustainability Science And Management, 17(12) (2022), 227-238.
  • [28] A. H. Mohd-Zaki, J. Brett, E. Ismail, and M. L’Azou, Epidemiology of dengue disease in Malaysia (2000–2012): a systematic literature review, PLoS Neglected Tropical Diseases, 8(11) (2014), e3159.
  • [29] M. R. Mohd Abd Razak, N. Mohmad Misnan, N. H. Md Jelas, N. A. Norahmad, A. Muhammad, T. C. D. Ho, B. Jusoh, U. R. Sastu, M. Zainol, M. I. Wasiman, H. Muhammad, R. Thayan, and A. F. Syed Mohamed, The effect of freeze-dried Carica papaya leaf juice treatment on NS1 and viremia levels in dengue fever mice model, BMC Complementary and Alternative Medicine, 18(1) (2018).
  • [30] K. Mulligan, S. J. Elliott, and C. Schuster-Wallace, The place of health and the health of place: Dengue fever and urban governance in Putrajaya, Malaysia, Health & Place, 18(3) (2012), 613-620.
  • [31] N. E. A. Murray, M. B. Quam, and A. Wilder-Smith, Epidemiology of dengue: past, present and future prospects, Clinical Epidemiology, 5 (2013), 299-309.
  • [32] M. Naveed, D. Baleanu, M. Rafiq, A. Raza, A. H. Soori, and N. Ahmed, Dynamical behavior and sensitivity analysis of a delayed coronavirus epidemic model, Computers Materials & Continua, 65(1) (2020), 225-241.
  • [33] M. Naveed, M. Rafiq, A. Raza, N. Ahmed, I. Khan, K. Sooppy Nisar, and A. Hassan Soori, Mathematical analysis of novel Coronavirus (2019-nCov) delay pandemic model, Computers Materials & Continua, 64(3) (2020), 1401– 1414.
  • [34] E. L. Pang and H. S. Loh, Current perspectives on dengue episode in Malaysia, Asian Pacific Journal of Tropical Medicine, 9(4) (2016), 395-401.
  • [35] H. J. Peng, H. B. Lai, Q. L. Zhang, B. Y. Xu, H. Zhang, W. H. Liu, W. Zhao, Y. P. Zhou, X. G. Zhong, S. Jiang, J. H. Duan, G. Y. Yan, J. F. He, and X. G. Chen, A local outbreak of dengue caused by an imported case in Dongguan, China, BMC Public Health, 12(1) (2012), 83.
  • [36] R. Prem Kumar, G. S. Mahapatra, S. Basu, and P. K. Santra, Global stability and sensitivity analysis of dengue transmission using four host and three vector classes along with control strategies, International Journal of Computer Mathematics, 1 (2024), 1-26.
  • [37] A. Raza, A. Ahmadian, M. Rafiq, S. Salahshour, M. Naveed, M. Ferrara, and A. H. Soori, Modeling the effect of delay strategy on transmission dynamics of HIV/AIDS disease, Advances in Difference Equations, 2020(1) (2020), 663.
  • [38] A. Raza, K. Ali, S. T. R. Rizvi, S. Sattar, and A. R. Seadawy, Discussion on vector control dengue epidemic model for stability analysis and numerical simulations, Brazilian Journal of Physics, 55(1) (2024).
  • [39] A. Singh and A. W. Taylor-Robinson, Vector control interventions to prevent dengue: current situation and strategies for future improvements to management of Aedes in India, Journal of Infectious Disease and Pathology, 2(1) (2017), 1-8.
  • [40] C. J. Tay, M. Fakhruddin, I. S. Fauzi, S. Y. Teh, M. Syamsuddin, N. Nuraini, and E. Soewono, Dengue epidemiological characteristic in Kuala Lumpur and Selangor, Malaysia, Mathematics and Computers in Simulation, 194 (2022), 489-504.
  • [41] P. Van Den Driessche, Reproduction numbers of infectious disease models, Infectious Disease Modelling, 2(3) (2017), 288-303.
  • [42] World Health Organization, Dengue and severe dengue, World Health Organization, (2021). Available at: https://www.who.int/westernpacific/emergencies/surveillance/dengue.
  • [43] L. P. Wong, S. M. M. Shakir, N. Atefi, and S. AbuBakar, Factors affecting dengue prevention practices: Nationwide survey of the Malaysian public, PLOS ONE, 10(4) (2015), e0122890.
  • [44] S. Zeb, S. A. Mohd Yatim, M. Rafiq, W. Ahmad, A. Kamran, and M. F. Karim, Treatment and delay control strategy for a non-linear rift valley fever epidemic model, AIP Advances, 14(11) (2024).
  • [45] S. Zeb, S. A. Mohd Yatim, A. Ahmad, A. Kamran, and M. Rafiq, Numerical modelling of SEIR on two-dose vaccination against the rubella virus, Malaysian Journal of Fundamental and Applied Sciences, 21(1) (2025), 1577-1601.
  • [46] S. Zeb, S. A. Mohd Yatim, S. Lal, A. Kamran, A. Ahmad, and M. Rafiq, Numerical analysis of the NSP epidemic model for campus drinking dynamics, Semarak International Journal of Fundamental and Applied Mathematics, 4(1) (2024), 48–60.
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