Mathematical Analysis for the Influence of Seasonality on Chikungunya Virus Dynamics

Article Sidebar

PDF
DOI: https://doi.org/10.28924/2291-8639-22-2024-86
Published: May 20, 2024
Cite as:
Hanan Almuashi, Mathematical Analysis for the Influence of Seasonality on Chikungunya Virus Dynamics, Int. J. Anal. Appl., 22 (2024), 86.

Main Article Content

Hanan Almuashi

Abstract

In this article, we discuss a mathematical system modelling Chikungunya virus dynamics in a seasonal environment with general incidence rates. We establish the existence, uniqueness, positivity and boundedness of a periodic orbit. We show that the global dynamics is determined using the basic reproduction number denoted by R0 and calculated using the spectral radius of a linear integral operator. We show the global stability of the disease free periodic solution if R0<1 and we show also the persistence of the disease if R0>1 where the trajectories converge to a periodic orbit. Finally, we display some numerical examples confirming the theoretical findings.

Article Details

References

  1. M. El Hajji, Modelling and Optimal Control for Chikungunya Disease, Theory Biosci. 140 (2020), 27–44. https://doi.org/10.1007/s12064-020-00324-4.
  2. M. El Hajji, A. Zaghdani, S. Sayari, Mathematical Analysis and Optimal Control for Chikungunya Virus With Two Routes of Infection With Nonlinear Incidence Rate, Int. J. Biomath. 15 (2021), 2150088. https://doi.org/10.1142/s1793524521500881.
  3. S. Alsahafi, S. Woodcock, Mathematical Study for Chikungunya Virus with Nonlinear General Incidence Rate, Mathematics. 9 (2021) 2186. https://doi.org/10.3390/math9182186.
  4. A.M. Elaiw, T.O. Alade, S.M. Alsulami, Analysis of Latent CHIKV Dynamics Models With General Incidence Rate and Time Delays, J. Biol. Dyn. 12 (2018), 700–730. https://doi.org/10.1080/17513758.2018.1503349.
  5. A.M. Elaiw, T.O. Alade, S.M. Alsulami, Analysis of Within-Host CHIKV Dynamics Models With General Incidence Rate, Int. J. Biomath. 11 (2018), 1850062. https://doi.org/10.1142/s1793524518500626.
  6. A.M. Elaiwa, S.E. Almalkia, A. Hobiny, Global Dynamics of Chikungunya Virus With Two Routes of Infection, J. Comput. Anal. Appl. 28 (2020), 481–490.
  7. A.M. Elaiw, S.E. Almalki, A.D. Hobiny, Global Dynamics of Humoral Immunity Chikungunya Virus With Two Routes of Infection and Holling Type-II, J. Math. Computer Sci. 19 (2019), 65–73. https://doi.org/10.22436/jmcs.019.02.01.
  8. A.M. Elaiw, S.E. Almalki, A.D. Hobiny, Stability of CHIKV Infection Models With CHIKV-monocyte and InfectedMonocyte Saturated Incidences, AIP Adv. 9 (2019), 025308. https://doi.org/10.1063/1.5085804.
  9. N. Bacaër, M.G.M. Gomes, On the Final Size of Epidemics with Seasonality, Bull. Math. Biol. 71 (2009), 1954–1966. https://doi.org/10.1007/s11538-009-9433-7.
  10. J. Ma, Z. Ma, Epidemic Threshold Conditions for Seasonally Forced SEIR Models, Math. Biosci. Eng. 3 (2006), 161–172. https://doi.org/10.3934/mbe.2006.3.161.
  11. S. Guerrero-Flores, O. Osuna, C.V. de Leon, Periodic Solutions for Seasonal Siqrs Models With Nonlinear Infection Terms, Elec. J. Diff. Equ. 2019 (2019), 92.
  12. M. El Hajji, F.A.S. Alzahrani, R. Mdimagh, Impact of Infection on Honeybee Population Dynamics in a Seasonal Environment, Int. J. Anal. Appl. 22 (2024), 75. https://doi.org/10.28924/2291-8639-22-2024-75.
  13. T. Zhang, Z. Teng, On a Nonautonomous SEIRS Model in Epidemiology, Bull. Math. Biol. 69 (2007), 2537–2559. https://doi.org/10.1007/s11538-007-9231-z.
  14. Y. Nakata, T. Kuniya, Global Dynamics of a Class of SEIRS Epidemic Models in a Periodic Environment, J. Math. Anal. Appl. 363 (2010), 230–237. https://doi.org/10.1016/j.jmaa.2009.08.027.
  15. N. Bacaër, S. Guernaoui, The Epidemic Threshold of Vector-Borne Diseases With Seasonality, J. Math. Biol. 53 (2006), 421–436. https://doi.org/10.1007/s00285-006-0015-0.
  16. W. Wang, X.Q. Zhao, Threshold Dynamics for Compartmental Epidemic Models in Periodic Environments, J. Dyn. Diff. Equ. 20 (2008), 699–717. https://doi.org/10.1007/s10884-008-9111-8.
  17. M. El Hajji, D.M. Alshaikh, N.A. Almuallem, Periodic Behaviour of an Epidemic in a Seasonal Environment with Vaccination, Mathematics. 11 (2023), 2350. https://doi.org/10.3390/math11102350.
  18. M. El Hajji, R.M. Alnjrani, Periodic Trajectories for HIV Dynamics in a Seasonal Environment With a General Incidence Rate, Int. J. Anal. Appl. 21 (2023), 96. https://doi.org/10.28924/2291-8639-21-2023-96.
  19. M. El Hajji, N.S. Alharbi, M.H. Alharbi, Mathematical Modeling for a CHIKV Transmission Under the Influence of Periodic Environment, Int. J. Anal. Appl. 22 (2024), 6. https://doi.org/10.28924/2291-8639-22-2024-6.
  20. B.S. Alshammari, D.S. Mashat, F.O. Mallawi, Mathematical and Numerical Investigations for a Cholera Dynamics With a Seasonal Environment, Int. J. Anal. Appl. 21 (2023), 127. https://doi.org/10.28924/2291-8639-21-2023-127.
  21. F.A. Al Najim, Mathematical Analysis for a Zika Virus Dynamics in a Seasonal Environment, Int. J. Anal. Appl. 22 (2024), 71. https://doi.org/10.28924/2291-8639-22-2024-71.
  22. A.A. Alsolami, M. El Hajji, Mathematical Analysis of a Bacterial Competition in a Continuous Reactor in the Presence of a Virus, Mathematics. 11 (2023), 883. https://doi.org/10.3390/math11040883.
  23. A.H. Albargi, M. El Hajji, Bacterial Competition in the Presence of a Virus in a Chemostat, Mathematics. 11 (2023), 3530. https://doi.org/10.3390/math11163530.
  24. M. El Hajji, Periodic Solutions for Chikungunya Virus Dynamics in a Seasonal Environment With a General Incidence Rate, AIMS Math. 8 (2023), 24888–24913. https://doi.org/10.3934/math.20231269.
  25. M. El Hajji, R.M. Alnjrani, Periodic Behaviour of HIV Dynamics with Three Infection Routes, Mathematics. 12 (2023), 123. https://doi.org/10.3390/math12010123.
  26. M. El Hajji, Periodic Solutions for an “SVIQR" Epidemic Model in a Seasonal Environment With General Incidence Rate, Int. J. Biomath. In Press. https://doi.org/10.1142/s1793524524500335.
  27. F. Zhang, X.Q. Zhao, A Periodic Epidemic Model in a Patchy Environment, J. Math. Anal. Appl. 325 (2007), 496–516. https://doi.org/10.1016/j.jmaa.2006.01.085.
  28. X.Q. Zhao, Dynamical Systems in Population Biology, Springer, New York, 2003. https://doi.org/10.1007/978-0-387-21761-1.
  29. O. Diekmann, J. Heesterbeek, On the Definition and the Computation of the Basic Reproduction Ratio R0 in Models for Infectious Diseases in Heterogeneous Populations, J. Math. Bio. 28 (1990), 365–382. https://doi.org/10.1007/BF00178324.
  30. O. Diekmann, J.A.P. Heesterbeek, M.G. Roberts, The Construction of Next-Generation Matrices for Compartmental Epidemic Models, J. R. Soc. Interface. 7 (2009), 873–885. https://doi.org/10.1098/rsif.2009.0386.
  31. P. van den Driessche, J. Watmough, Reproduction Numbers and Sub-Threshold Endemic Equilibria for Compartmental Models of Disease Transmission, Math. Biosci. 180 (2002), 29–48. https://doi.org/10.1016/s0025-5564(02)00108-6.
  32. A.H. Albargi, M.E. Hajji, Mathematical Analysis of a Two-Tiered Microbial Food-Web Model for the Anaerobic Digestion Process, Math. Biosci. Eng. 20 (2023), 6591–6611. https://doi.org/10.3934/mbe.2023283.
  33. A. Alshehri, M. El Hajji, Mathematical Study for Zika Virus Transmission With General Incidence Rate, AIMS Math. 7 (2022), 7117–7142. https://doi.org/10.3934/math.2022397.
  34. M. El Hajji, Mathematical Modeling for Anaerobic Digestion Under the Influence of Leachate Recirculation, AIMS Math. 8 (2023), 30287–30312. https://doi.org/10.3934/math.20231547.
  35. M. El Hajji, Influence of the Presence of a Pathogen and Leachate Recirculation on a Bacterial Competition, Int. J. Biomath. In Press. https://doi.org/10.1142/s1793524524500293.
  36. M. El Hajji, A.Y. Al-Subhi, M.H. Alharbi, Mathematical Investigation for Two-Bacteria Competition in Presence of a Pathogen With Leachate Recirculation, Int. J. Anal. Appl. 22 (2024), 45. https://doi.org/10.28924/2291-8639-22-2024-45.