Global Properties of Secondary DENV Infection Models with Pre-Existing CTL Immunity and Discrete/Distributed Delays

Article Sidebar

PDF
DOI: https://doi.org/10.28924/2291-8639-23-2025-88
Published: Apr 14, 2025
Cite as:
R. O. Aldubiban, A. M. Elaiw, E. A. Almohaimeed, A. D. Hobiny, Global Properties of Secondary DENV Infection Models with Pre-Existing CTL Immunity and Discrete/Distributed Delays, Int. J. Anal. Appl., 23 (2025), 88.

Main Article Content

R. O. Aldubiban, A. M. Elaiw, E. A. Almohaimeed, A. D. Hobiny

Abstract

Dengue, caused by the dengue virus (DENV), is a serious vector-borne disease mainly prevalent in tropical areas. In certain cases, it can lead to death, especially when a person is infected a second time, resulting in a secondary infection. This research begins by presenting an in-host model for secondary DENV infection under the effect of two types of cytotoxic T lymphocytes (CTLs), non-specific and strain-specific CTLs. The first model is incorporating two distinct discrete-time delays. Additionally, the model is refined by integrating two forms of distributed time delays to provide a more realistic representation of secondary DENV infection dynamics. The main objective is to examine the dynamic behavior of both models, including the non-negativity and boundedness of solutions. A qualitative stability analysis is conducted for their steady states, revealing that the uninfected steady state in both models remains globally asymptotically stable when the basic reproduction number (R0) is below one but becomes unstable when R0 exceeds this threshold. Additionally, an infected steady state emerges and is globally asymptotically stable when R0 is greater than one. The stability conditions for the two steady states are determined using the Lyapunov method. To confirm the qualitative results, comprehensive numerical simulations are conducted, offering valuable biological insights. To assess the influence of specific parameters, we conduct a sensitivity analysis on the model. The results indicate that the infection rate and viral production rate significantly impact the sensitivity of R0, ultimately affecting the dynamics of DENV. These insights could contribute to the development of antiviral treatments aimed at inhibiting viral entry and replication. Furthermore, the study explores the impact of time delays on DENV infection dynamics, highlighting that prolonged delays can mimic the effects of antiviral treatments. A sufficiently long delay slows down the virus’s progression, aiding in its control and eventual eradication. These findings suggest potential strategies for developing new treatments that could extend the viral replication or maturation.

Article Details

References

  1. P. Bhatt, S.P. Sabeena, M. Varma, G. Arunkumar, Current Understanding of the Pathogenesis of Dengue Virus Infection, Curr. Microbiol. 78 (2021), 17–32. https://doi.org/10.1007/s00284-020-02284-w.
  2. K.L. Ebi, J. Nealon, Dengue in a Changing Climate, Environ. Res. 151 (2016), 115–123. https://doi.org/10.1016/j.envres.2016.07.026.
  3. H. Lee, J.E. Kim, S. Lee, C.H. Lee, Potential Effects of Climate Change on Dengue Transmission Dynamics in Korea, PLOS ONE 13 (2018), e0199205. https://doi.org/10.1371/journal.pone.0199205.
  4. European Centre for Disease Prevention and Control, Dengue Worldwide Overview, (2024). https://www.ecdc.europa.eu/en/dengue-monthly, Retrieved February 15, 2025.
  5. World Health Organization, Dengue and Severe Dengue, https://www.who.int/news-room/fact-sheets/detail/dengue-and-severe-dengue, Retrieved February 15, 2025.
  6. J. Ding, D. Mairiang, D. Prayongkul, et al. In-host Modeling of Dengue Virus and Non-structural Protein 1 and the Effects of Ivermectin in Patients with Acute Dengue Fever, CPT: Pharmacomet. Syst. Pharmacol. 13 (2024), 2196–2209. https://doi.org/10.1002/psp4.13233.
  7. M. Adimy, P.F.A. Mancera, D.S. Rodrigues, F.L.P. Santos, C.P. Ferreira, Maternal Passive Immunity and Dengue Hemorrhagic Fever in Infants, Bull. Math. Biol. 82 (2020), 24. https://doi.org/10.1007/s11538-020-00699-x.
  8. R. Da Silva Carvalho, J. Gustavo Machado Miranda, R. Melo Lima, et al. Immunogenomics of Dengue Fever and Association to Physiopathology and Disease Control, in: Mosquito-Borne Tropical Diseases, IntechOpen, 2025. https://doi.org/10.5772/intechopen.1008488.
  9. S.K. Sasmal, Y. Dong, Y. Takeuchi, Mathematical Modeling on T-Cell Mediated Adaptive Immunity in Primary Dengue Infections, J. Theor. Biol. 429 (2017), 229–240. https://doi.org/10.1016/j.jtbi.2017.06.035.
  10. M.G. Guzmán, G. Kouri, Dengue: An Update, Lancet Infect. Dis. 2 (2002), 33–42. https://doi.org/10.1016/S1473-3099(01)00171-2.
  11. M.H. Islam, M.A. Masud, E. Kim, Stochastic Behavior of Within-Host Progression in Primary Dengue Infection, J. Appl. Math. Comput. 70 (2024), 1499–1521. https://doi.org/10.1007/s12190-024-02015-5.
  12. V. Anam, B.V. Guerrero, A.K. Srivastav, N. Stollenwerk, M. Aguiar, Within-Host Models Unravelling the Dynamics of Dengue Reinfections, Infect. Dis. Model. 9 (2024), 458–473. https://doi.org/10.1016/j.idm.2024.02.004.
  13. S. Perera, S.S.N. Perera, Mathematical Modeling and Analysis of Innate and Humoral Immune Responses to Dengue Infections, Int. J. Biomath. 12 (2019), 1950077. https://doi.org/10.1142/S1793524519500773.
  14. R. Nikin-Beers, S.M. Ciupe, Modelling Original Antigenic Sin in Dengue Viral Infection, Math. Med. Biol. 35 (2018), 257–272. https://doi.org/10.1093/imammb/dqx002.
  15. N. Nuraini, H. Tasman, E. Soewono, K.A. Sidarto, A With-in Host Dengue Infection Model with Immune Response, Math. Comput. Model. 49 (2009), 1148–1155. https://doi.org/10.1016/j.mcm.2008.06.016.
  16. H. Ansari, M. Hesaaraki, A With-In Host Dengue Infection Model with Immune Response and BeddingtonDeAngelis Incidence Rate, Appl. Math. 03 (2012), 177–184. https://doi.org/10.4236/am.2012.32028.
  17. S. Perera, S.S.N. Perera, Impact of Innate and Cell Mediated Immune Responses on Dengue Virus Dynamics, Int. J. Pure Appl. Math. 118 (2018), 353-360.
  18. J.J. Thibodeaux, D. Nuñez, A. Rivera, A Generalized Within-Host Model of Dengue Infection with a Non-Constant Monocyte Production Rate, J. Biol. Dyn. 14 (2020), 143–161. https://doi.org/10.1080/17513758.2020.1733678.
  19. R. Nikin-Beers, S.M. Ciupe, The Role of Antibody in Enhancing Dengue Virus Infection, Math. Biosci. 263 (2015), 83–92. https://doi.org/10.1016/j.mbs.2015.02.004.
  20. R. Ben-Shachar, K. Koelle, Minimal Within-Host Dengue Models Highlight the Specific Roles of the Immune Response in Primary and Secondary Dengue Infections, J. R. Soc. Interface 12 (2015), 20140886. https://doi.org/10.1098/rsif.2014.0886.
  21. A. Mishra, AWithin-Host Model of Dengue Viral Infection Dynamics, in: J.M. Cushing, M. Saleem, H.M. Srivastava, M.A. Khan, M. Merajuddin (Eds.), Applied Analysis in Biological and Physical Sciences, Springer India, New Delhi, 2016: pp. 165–176. https://doi.org/10.1007/978-81-322-3640-5_9.
  22. M.C. Gómez, H.M. Yang, Mathematical Model of the Immune Response to Dengue Virus, J. Appl. Math. Comput. 63 (2020), 455–478. https://doi.org/10.1007/s12190-020-01325-8.
  23. A. Mishra, AWithin-Host Model of Dengue Viral Infection Dynamics, in: J.M. Cushing, M. Saleem, H.M. Srivastava, M.A. Khan, M. Merajuddin (Eds.), Applied Analysis in Biological and Physical Sciences, Springer India, New Delhi, 2016: pp. 165–176. https://doi.org/10.1007/978-81-322-3640-5_9.
  24. T.P. Gujarati, G. Ambika, Virus Antibody Dynamics in Primary and Secondary Dengue Infections, J. Math. Biol. 69 (2014), 1773–1800. https://doi.org/10.1007/s00285-013-0749-4.
  25. M. Cerón Gómez, H.M. Yang, A Simple Mathematical Model to Describe Antibody-Dependent Enhancement in Heterologous Secondary Infection in Dengue, Math. Med. Biol. 36 (2019), 411–438. https://doi.org/10.1093/imammb/dqy016.
  26. F. De A. Camargo, M. Adimy, L. Esteva, C. Métayer, C.P. Ferreira, Modeling the Relationship Between AntibodyDependent Enhancement and Disease Severity in Secondary Dengue Infection, Bull. Math. Biol. 83 (2021), 85. https://doi.org/10.1007/s11538-021-00919-y.
  27. S.K. Sasmal, Y. Takeuchi, S. Nakaoka, T-Cell Mediated Adaptive Immunity and Antibody-Dependent Enhancement in Secondary Dengue Infection, J. Theor. Biol. 470 (2019), 50–63. https://doi.org/10.1016/j.jtbi.2019.03.010.
  28. S. Rashid, F. Jarad, S.A.A. El-Marouf, S.K. Elagan, Global Dynamics of Deterministic-Stochastic Dengue Infection Model Including Multi Specific Receptors via Crossover Effects, AIMS Math. 8 (2023), 6466–6503. https://doi.org/10.3934/math.2023327.
  29. M. Borisov, G. Dimitriu, P. Rashkov, Modelling the Host Immune Response to Mature and Immature Dengue Viruses, Bull. Math. Biol. 81 (2019), 4951–4976. https://doi.org/10.1007/s11538-019-00664-3.
  30. A. Mishra, S. Gakkhar, A Micro-Epidemic Model for Primary Dengue Infection, Commun. Nonlinear Sci. Numer. Simul. 47 (2017), 426–437. https://doi.org/10.1016/j.cnsns.2016.12.001.
  31. Q. Liu, D. Jiang, T. Hayat, A. Alsaedi, Stationary Distribution of a Stochastic Within-Host Dengue Infection Model with Immune Response and Regime Switching, Physica A 526 (2019), 121057. https://doi.org/10.1016/j.physa.2019.121057.
  32. A.L. Rothman, Immunity to Dengue Virus: A Tale of Original Antigenic Sin and Tropical Cytokine Storms, Nat. Rev. Immunol. 11 (2011), 532–543. https://doi.org/10.1038/nri3014.
  33. A.A. Raezah, A.M. Elaiw, M.A. Alshaikh, Global Stability of Secondary DENV Infection Models with Non-Specific and Strain-Specific CTLs, Heliyon 10 (2024), e25391. https://doi.org/10.1016/j.heliyon.2024.e25391.
  34. J.K. Hale, S.M. Verduyn Lunel, Introduction to Functional Differential Equations, Springer, New York, 1993.
  35. Y. Kuang, Delay Differential Equations: With Applications in Population Dynamics, Academic Press, 1993.
  36. R. Cologna, R. Rico-Hesse, American Genotype Structures Decrease Dengue Virus Output from Human Monocytes and Dendritic Cells, J. Virol. 77 (2003), 3929–3938. https://doi.org/10.1128/JVI.77.7.3929-3938.2003.
  37. S.M. Ciupe, R.M. Ribeiro, P.W. Nelson, G. Dusheiko, A.S. Perelson, The Role of Cells Refractory to Productive Infection in Acute Hepatitis B Viral Dynamics, Proc. Nat. Acad. Sci. 104 (2007), 5050–5055. https://doi.org/10.1073/pnas.0603626104.
  38. G. Huang, Y. Takeuchi, W. Ma, Lyapunov Functionals for Delay Differential Equations Model of Viral Infections, SIAM J. Appl. Math. 70 (2010), 2693–2708. https://doi.org/10.1137/090780821.
  39. A. Korobeinikov, Global Properties of Basic Virus Dynamics Models, Bull. Math. Biol. 66 (2004), 879–883. https://doi.org/10.1016/j.bulm.2004.02.001.
  40. E.A. Barbashin, Introduction to the Theory of Stability, Wolters-Noordhoff, Groningen, 1970.
  41. J. P. LaSalle, The Stability of Dynamical Systems, SIAM, Philadelphia, 1976.
  42. A.M. Ljapunov, A.T. Fuller, A.M. Ljapunov, The General Problem of the Stability of Motion, Taylor & Francis, London, 1992.
  43. M.Y. Li, H. Shu, Impact of Intracellular Delays and Target-Cell Dynamics on In Vivo Viral Infections, SIAM J. Appl. Math. 70 (2010), 2434–2448. https://doi.org/10.1137/090779322.