STABILITY ANALYSIS OF A DENGUE MODEL WITH AWARENESS AND REINFECTION
DOI:
https://doi.org/10.25077/jmua.15.4.565-574.2026Keywords:
dengue model, reproduction number, stability analysisAbstract
This study proposes and analyzes a mathematical model of dengue transmission incorporating awareness and reinfection effects. The human population is divided into susceptible unaware, susceptible aware, exposed, infected, and recovered compartments, while the mosquito population is classified into susceptible and infected classes. The model is formulated as a system of nonlinear ordinary differential equations.
The basic reproduction number is derived using the next-generation matrix approach to determine the threshold condition for disease transmission. The existence and stability of the disease-free equilibrium are analyzed using the Jacobian matrix. The results show that the disease-free equilibrium is locally asymptotically stable when the basic reproduction number is less than one, and unstable otherwise.
Numerical simulations are performed to illustrate the analytical findings and to examine the impact of awareness and reinfection on disease dynamics. The results indicate that increasing public awareness can significantly reduce disease transmission, while reinfection contributes to the persistence of dengue in the population.
These findings highlight the importance of awareness-based interventions in controlling dengue outbreaks.
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[1] Aguiar, M., Kooi, B. W., Stollenwerk, N., 2013, Epidemiology of dengue fever: A model with temporary cross-immunity. Journal of Theoretical Biology, 332: 70–80.
[2] Arriola, L., Hyman, J. M., 2009, Sensitivity analysis for uncertainty quantification in mathematical models. Mathematical Biosciences and Engineering, 6(3): 497–516.
[3] Asyary, A. L., 2025, Spatial vulnerability of dengue in Indonesia. Annals of Global Health, 91(1).
[4] Diekmann, O., Heesterbeek, H., Roberts, M. G., 2010, The construction of next-generation matrices for compartmental epidemic models. Journal of the Royal Society Interface, 7(47): 873–885.
[5] Esteva, L., Vargas, C., 1998, Analysis of a dengue disease transmission model. Mathematical Biosciences, 150(2): 131–151.
[6] Funk, S., Gilad, E., Watkins, C., Jansen, V. A. A., 2009, The spread of awareness and its impact on epidemic outbreaks. Proceedings of the National Academy of Sciences, 106(16): 6872–6877.
[7] Funk, S., Salathé, M., Jansen, V. A. A., 2010, Modelling the influence of human behaviour on the spread of infectious diseases. Journal of the Royal Society Interface, 7(50): 1247–1256.
[8] Harapan, H., Michie, A., Sasmono, R. T., Imrie, A., 2020, Dengue: A minireview. Viruses, 12(8): 829.
[9] Herdicho, F. F., Fatmawati, F., Alfiniyah, C., Fajrin, F. P., Bonyah, E., et al., 2025, Modeling the dynamics of dengue transmission with awareness and optimal control analysis. PLOS ONE, 20(5): e0322702.
[10] Kala, M. P., St. John, A. L., Rathore, A. P. S., 2023, Dengue: Therapeutic strategies and vaccines. Current Treatment Options in Infectious Diseases, 15(2): 27–52.
[11] Khanam, A., Gutiérrez-Barbosa, H., Lyke, K. E., Chua, J. V., 2022, Immune-mediated pathogenesis in dengue virus infection. Viruses, 14(11).
[12] Lun, X., Wang, Y., Zhao, C., Zhang, J., Liu, Q., Wu, Y., 2022, Spatiotemporal analysis of dengue cases. Infectious Diseases of Poverty, 11.
[13] Medhi, D., Sarma, G., Shyam, A., 2024, Stability analysis using Routh–Hurwitz criterion. Journal of Computational Analysis and Application, 33(8): 903–907.
[14] Naaly, B. Z., Marijani, T., Isdory, A., Ndendya, J. Z., 2024, Mathematical modeling of vector control, treatment and awareness on dengue transmission. Computer Methods and Programs in Biomedicine Update, 6.
[15] Narendran, M., Chate, S., Patil, R., 2024, Community-based dengue prevention. Clinical Epidemiology and Global Health, 30.
[16] Salim, M. F., Satoto, T. B. T., Danardono, 2025, Local determinants of dengue transmission. Tropical Medicine and Health, 53(1): 54.
[17] Sanchez, F., 2019, Hospitalization in the transmission of dengue dynamics: The impact on public health policies. arXiv preprint.
[18] Sanchez, F., Arroyo-Esquivel, J., Vásquez, P., 2020, Transmission dynamics of dengue in Costa Rica: the role of hospitalizations. Revista de Matemática: Teoría y Aplicaciones, 27(1): 241–266.
[19] Sardar, T., Rana, S., Chattopadhyay, J., 2015, A mathematical model of dengue transmission with memory. Applied Mathematics and Computation, 267: 134–146.
[20] Sharma, A., Misra, A. K., 2014, Modeling the impact of awareness on the spread of infectious diseases. Applied Mathematics and Computation, 244: 836–848.
[21] Tang, B., Wang, X., Li, Q., Bragazzi, N. L., Tang, S., Xiao, Y., Wu, J., 2020, Estimation of the transmission risk of infectious diseases. Infectious Disease Modelling, 5: 248–255.
[22] Van den Driessche, P., Watmough, J., 2002, Reproduction numbers and subthreshold endemic equilibria for compartmental models of disease transmission. Mathematical Biosciences, 180: 29–48.
[23] World Health Organization, 2024, Dengue and severe dengue. WHO.
[24] Yang, H. M., Macoris, M. L. G., Galvani, K. C., Andrighetti, M. T. M., Wanderley, D. M. V., 2009, Assessing the effects of vector control on dengue transmission. Applied Mathematics and Computation, 219(12): 7032–7042.
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