10.57647/ijm2c.2026.160107

A Comprehensive Literature Review in Fuzzy Susceptible-Infected-Recovered (SIR) Model and its Applications

PDF
  • Soheil Salahshour*1,2,
  • Sankar Prasad Mondal3,
  1. Faculty of Engineering and Natural Sciences, Istanbul Okan University, Istanbul, Turkey
  2. Faculty of Engineering and Natural Sciences, Bahcesehir University, Istanbul, Turkey
  3. Department of Applied Mathematics, Maulana Abul Kalam Azad University of Technology, West Bengal, 741249, India

Received: 15-09-2025

Revised: 12-10-2025

Accepted: 06-11-2025

Published in Issue 31-03-2026

Published Online: 08-11-2025

Copyright (c) 2026 Soheil Salahshour, Sankar Prasad Mondal (Author)

Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 International License.

How to Cite

Salahshour, S., & Prasad Mondal, S. (2026). A Comprehensive Literature Review in Fuzzy Susceptible-Infected-Recovered (SIR) Model and its Applications. International Journal of Mathematical Modelling & Computations, 16(1). https://doi.org/10.57647/ijm2c.2026.160107
Crossref
Scopus
Google Scholar
Europe PMC

Abstract

Modelling the Susceptible-Infected-Recovered (SIR) for an individual is an essential tool for studying several real-life complications. When uncertainty are involves in the real-life model then its details analysis and solutions interpretations are more critical to find.   Also, it should be noted that, crisp model has some limitations to predict the actual facts. To overcome this limitation and challenges, fuzzy SIR models take an important part of fuzzy logic methodology with classical epidemiological contexts. The fuzzy logic is also permitting for imprecise and ambiguous information management system. In that context the papers motivation comes. This paper endowments a comprehensive literature review work of fuzzy SIR based models and their applications. The paper examines the key methodological developments and model-based applications. The review also recognizes the current challenges and future research prospects for theoretical and modelling perspectives. Inclusively, this study delivers an in-depth discussion of how fuzzy theory boosts the trustworthiness and applicability of SIR modelling.

Keywords

  • SIR model, Fuzzy Sets theory, Epidemic modelling
PDF

References

  1. Wang, W., Liu, Q. H., Zhong, L. F., Tang, M., Gao, H., & Stanley, H. E. (2016). Predicting the epidemic threshold of the susceptible-infected-recovered model. Scientific reports, 6(1), 24676.
  2. Ruziska, F. M., Tomé, T., & de Oliveira, M. J. (2017). Susceptible–infected–recovered model with recurrent infection. Physica A: Statistical Mechanics and its Applications, 467, 21-29.
  3. Rock, K., Brand, S., Moir, J., & Keeling, M. J. (2014). Dynamics of infectious diseases. Reports on Progress in Physics, 77(2), 026602.
  4. Keeling, M. J., & Ross, J. V. (2008). On methods for studying stochastic disease dynamics. Journal of the Royal Society Interface, 5(19), 171-181.
  5. Sun, L., He, Q., Teng, Y., Zhao, Q., Yan, X., & Wang, X. (2023). A complex network-based vaccination strategy for infectious diseases. Applied Soft Computing, 136, 110081.
  6. Willem, L., Verelst, F., Bilcke, J., Hens, N., & Beutels, P. (2017). Lessons from a decade of individual-based models for infectious disease transmission: a systematic review (2006-2015). BMC infectious diseases, 17(1), 612.
  7. Annunziata, K., Rak, A., Del Buono, H., DiBonaventura, M., & Krishnarajah, G. (2012). Vaccination rates among the general adult population and high-risk groups in the United States. PloS one, 7(11), e50553.
  8. Giladi, I., May, F., Ristow, M., Jeltsch, F., & Ziv, Y. (2014). Scale‐dependent species–area and species–isolation relationships: a review and a test study from a fragmented semi‐arid agro‐ecosystem. Journal of Biogeography, 41(6), 1055-1069.
  9. Qian, M., & Jiang, J. (2022). COVID-19 and social distancing. Journal of Public Health, 30(1), 259-261.
  10. Lin, H. H., Hsu, I. C., Lin, T. Y., Tung, L. M., & Ling, Y. (2022). After the epidemic, is the smart traffic management system a key factor in creating a green leisure and tourism environment in the move towards sustainable urban development?. Sustainability, 14(7), 3762.
  11. Jones, R. M., Bleasdale, S. C., Maita, D., Brosseau, L. M., & CDC Prevention Epicenters Program. (2020). A systematic risk-based strategy to select personal protective equipment for infectious diseases. American Journal of Infection Control, 48(1), 46-51.
  12. Juliano, S. A. (2007). Population dynamics. Journal of the American Mosquito Control Association, 23(2 Suppl), 265.
  13. Kudryashov, N. A., Chmykhov, M. A., & Vigdorowitsch, M. (2021). Analytical features of the SIR model and their applications to COVID-19. Applied Mathematical Modelling, 90, 466-473.
  14. Engle, S., Keppo, J., Kudlyak, M., Quercioli, E., Smith, L., & Wilson, A. (2021). The behavioral SIR model, with applications to the swine flu and COVID-19 pandemics. University of Wisconsin-Madison.
  15. Stolerman, L. M., Coombs, D., & Boatto, S. (2015). SIR-network model and its application to dengue fever. SIAM Journal on Applied Mathematics, 75(6), 2581-2609.
  16. Laguzet, L., & Turinici, G. (2015). Individual vaccination as Nash equilibrium in a SIR model with application to the 2009–2010 influenza A (H1N1) epidemic in France. Bulletin of mathematical biology, 77(10), 1955-1984.
  17. Zadeh, L. A. (1965). Fuzzy sets. Information and control, 8(3), 338-353.
  18. Bandemer, H., & Gottwald, S. (1995). Fuzzy sets, fuzzy logic, fuzzy methods (Vol. 341). Chichester: Wiley.
  19. Yao, Y. Y. (1998). A comparative study of fuzzy sets and rough sets. Information sciences, 109(1-4), 227-242.
  20. Zadeh, L. A. (1978). Fuzzy sets as a basis for a theory of possibility. Fuzzy sets and systems, 1(1), 3-28.
  21. Dubois, D., & Prade, H. (1989). Fuzzy sets, probability and measurement. European journal of operational research, 40(2), 135-154.
  22. Demirci, M. (2000). Fuzzy functions and their applications. Journal of Mathematical Analysis and Applications, 252(1), 495.
  23. Nemitz, W. C. (1986). Fuzzy relations and fuzzy functions. Fuzzy Sets and Systems, 19(2), 177-191.
  24. Puri, M. L., & Ralescu, D. A. (1983). Differentials of fuzzy functions. Journal of Mathematical Analysis and Applications, 91(2), 552-558.
  25. Schaible, B., & Lee, Y. C. (2002). Fuzzy logic models with improved accuracy and continuous differentiability. IEEE Transactions on Components, Packaging, and Manufacturing Technology: Part C, 19(1), 37-47.
  26. Dubois, D., & Prade, H. (1993). Fuzzy numbers: an overview. Readings in Fuzzy Sets for Intelligent Systems, 112-148.
  27. Dijkman, J. G., Van Haeringen, H., & De Lange, S. J. (1983). Fuzzy numbers. Journal of mathematical analysis and applications, 92(2), 301-341.
  28. Rahaman, M., Mondal, S. P., Algehyne, E. A., Biswas, A., & Alam, S. (2022). A method for solving linear difference equation in Gaussian fuzzy environments. Granular Computing, 7(1), 63-76.
  29. Maity, S., De, S. K., Pal, M., & Mondal, S. P. (2021). A study of an EOQ model of growing items with parabolic dense fuzzy lock demand rate. Applied System Innovation, 4(4), 81.
  30. Tudu, S., Gazi, K. H., Rahaman, M., Mondal, S. P., Chatterjee, B., & Alam, S. (2023). Type-2 fuzzy differential inclusion for solving type-2 fuzzy differential equation. Annals of fuzzy mathematics and informatics, 25(1), 33-53.
  31. Gazi, K. H., Momena, A. F., Salahshour, S., Mondal, S. P., & Ghosh, A. (2024). Synergistic strategy of sustainable hospital site selection in saudi arabia using spherical fuzzy mcdm methodology. Journal of uncertain systems, 17(03), 2450004.
  32. Mondal, S. P., & Mandal, M. (2017). Pentagonal fuzzy number, its properties and application in fuzzy equation. Future Computing and Informatics Journal, 2(2), 110-117.
  33. Maity, S., De, S. K., & Mondal, S. P. (2020). A study of a backorder EOQ model for cloud-type intuitionistic dense fuzzy demand rate. International Journal of Fuzzy Systems, 22(1), 201-211.
  34. Momena, A. F., Pakhira, R., Haque, R., Sobczak, A., & Mondal, S. P. (2025). A memory-dependent inventory model with fuzzy price-dependent demand under backlogged shortages. Journal of Uncertain Systems, 18(03), 2550003.
  35. Singh, P., Allahviranloo, T., Amirteimoori, A., Shahriari, M., Gazi, K. H., & Mondal, S. P. (2025). Fuzzy Prey–Predator Model with Holling Type II Response and Its Application in Pest Control. New Mathematics and Natural Computation, 1-26.
  36. Gazi, K. H, Salahshour, S., Mondal, S. P., Alam, S., Rahaman, M., & Alamin A. (2024). A Discussion of Newton's Law of Cooling using Difference Equations in Fuzzy Frames as an Alternative to the Traditional Continuous Dynamical System. International Journal of Mathematics in Operational Research, 1(1).
  37. Sarkar, A., Ghosh, A., Karmakar, B., Shaikh, A., & Mondal, S. P. (2020, November). Application of fuzzy topsis algorithm for selecting best family car. In 2020 International Conference on Decision Aid Sciences and Application (DASA) (pp. 59-63). IEEE.
  38. Smithson, M., & Verkuilen, J. (2006). Fuzzy set theory: Applications in the social sciences (No. 147). Sage.
  39. Bosserman, R. W., & Ragade, R. K. (1982). Ecosystem analysis using fuzzy set theory. Ecological Modelling, 16(2-4), 191-208.
  40. Shanmugam, N. S., Jayakumar, V., Pamucar, D., Pethaperumal, M., & Kannan, J. (2025). Multi-attribute decision-making technique using bipolar linear diophantine fuzzy hypersoft set. Journal of Fuzzy Extension and Applications, 6(4), 727-748.
  41. Ecer, F., Pamucar, D., & Demir, G. (2025). Decision-analytics-based electric vehicle charging station location selection: A cutting-edge fuzzy rough framework. Energy Reports, 14, 711-735.
  42. Jayakumar, V., Pethaperumal, M., Kausar, N., Pamucar, D., Simic, V., & Salman, M. A. (2025). Lattice-Based Decision Models for Green Urban Development: Insights from L_ {q} q-Rung Orthopair Multi-fuzzy Soft Set. International journal of computational intelligence systems, 18(1), 1-27.
  43. Parthasarathy, T. N., Narayanamoorthy, S., Pamucar, D., & Kang, D. (2025). Fuzzy decision-analytics based lithium-ion battery selection for maximizing the efficiency of electric vehicles. Engineering Applications of Artificial Intelligence, 159, 111709.
  44. Rahaman, M., Gazi, K. H., Rabih, M., Alamin, A., Razzaq, O. A., Khan, N. A., ... & Alam, S. (2025). Solutions of Linear Homogeneous Fuzzy Fractional Differential Equations Using the Mittag-Leffler Function. Journal of Uncertain Systems, 2550013.
  45. Rangarajan, K., Singh, P., Salahshour, S., & Mondal, S. P. (2025). Analysis of second-order linear fuzzy differential equation under an innovative fuzzy derivative approach and its application. Journal of Uncertain Systems, 18(01), 2450022.
  46. Tudu, S., Mondal, S. P., & Alam, S. (2021). Different solution strategy for solving type-2 fuzzy system of differential equations with application in arms race model. International Journal of Applied and Computational Mathematics, 7(5), 177.
  47. Rahaman, M., Mondal, S. P., Alam, S., Khan, N. A., & Biswas, A. (2021). Interpretation of exact solution for fuzzy fractional non-homogeneous differential equation under the Riemann–Liouville sense and its application on the inventory management control problem. Granular Computing, 6(4), 953-976.
  48. Mondal, S. P., & Roy, T. K. (2015). Solution of second order linear differential equation in fuzzy environment. Annals of Fuzzy Mathematics and Informatics, 10, 1-20.
  49. Mondal, S. P., & Roy, T. K. (2014). Solution of first order linear non homogeneous ordinary differential equation in fuzzy environment based on lagrange multiplier method. Journal of Uncertainty in Mathematics Science, 2014, 1-18.
  50. Zadeh, L. A. (1988). Fuzzy logic. Computer, 21(4), 83-93.
  51. Trillas, E., & Eciolaza, L. (2015). Fuzzy logic. Springer International Publishing. DOI, 10, 978-3.
  52. Hellmann, M. (2001). Fuzzy logic introduction. Université de Rennes, 1(1).
  53. Yen, J. (1999). Fuzzy logic-a modern perspective. IEEE transactions on knowledge and data engineering, 11(1), 153-165.
  54. George, Klir J., Yuan, B. (1995), Fuzzy Sets and Fuzzy Logic: Theory and Applications, Prentice Hall PTR Upper Saddle River New Jersey.
  55. Gupta, M. M. (2011). Forty-five years of fuzzy sets and fuzzy logic-A tribute to Professor Lotfi A. Zadeh (the father of fuzzy logic). Scientia Iranica. Transaction D, Computer Science & Engineering, Electrical, 18(3), 685.
  56. Perfilieva, I. (2011, August). Fuzzy function: theoretical and practical point of view. In Proceedings of the 7th conference of the European Society for Fuzzy Logic and Technology (pp. 480-486). Atlantis Press.
  57. Demirci, M. (2000). Fuzzy functions and their applications. Journal of Mathematical Analysis and Applications, 252(1), 495.
  58. Plotnikov, A. V., & Skripnik, N. V. (2014). New definition of a generalized fuzzy derivative. Journal of Advanced Research in Pure Mathematics, 6(3), 69-77.
  59. Wasques, V. F., Esmi, E., Barros, L. C., & Sussner, P. (2020). The generalized fuzzy derivative is interactive. Information Sciences, 519, 93-109.
  60. Panja, P., Mondal, S. K., & Chattopadhyay, J. (2017). Dynamical study in fuzzy threshold dynamics of a cholera epidemic model. Fuzzy Information and Engineering, 9(3), 381-401.
  61. Verma, R., Tiwari, S. P., & Upadhyay, R. K. (2017, August). Dynamical behaviors of fuzzy SIR epidemic model. In Proceedings of the Conference of the European Society for Fuzzy Logic and Technology (pp. 482-492). Cham: Springer International Publishing.
  62. Abdy, M., Side, S., Annas, S., Nur, W., & Sanusi, W. (2021). An SIR epidemic model for COVID-19 spread with fuzzy parameter: the case of Indonesia. Advances in difference equations, 2021(1), 105.
  63. Regis, S., Nuiro, S. P., Merat, W., & Doncescu, A. (2021). A data-based approach using a multi-group SIR model with fuzzy subsets: application to the COVID-19 simulation in the islands of Guadeloupe. Biology, 10(10), 991.
  64. M.Maragatham, D.Surjith Jiji and P. Mariappan, Study on spread of dengue using sir epidemic model in fuzzy environment, Advances and Applications in Mathematical Sciences Volume 21, Issue 6, April 2022, Pages 3393-3399.
  65. Youssef, I. K., Saad, M. K., Dumlu, A., & Asklany, S. A. (2024). SIR Models with Fuzzy Initial Conditions. Computer Science, 19(4), 1019-1027.
  66. Arif, M. S., Abodayeh, K., & Nawaz, Y. (2024). A Hybrid SIR-Fuzzy Model for Epidemic Dynamics: A Numerical Study. Computer Modeling in Engineering & Sciences (CMES), 139(3).
  67. P. Monisha and S. Sindu Devi, Treatment of infectious disease for tuberculosis (tb) using fuzzy mathematical model, Asia Pac. J. Math. 2024 11:16.
  68. Bhavithra, H. A., & Devi, S. S. (2024). Feasibility and stability analysis for basic measles model using fuzzy parameter. Contemporary mathematics, 897-912.
  69. Subramanian, S., Kumaran, A., Ravichandran, S., Venugopal, P., Dhahri, S., & Ramasamy, K. (2024). Fuzzy fractional Caputo derivative of susceptible-infectious-removed epidemic model for childhood diseases. Mathematics, 12(3), 466.