Skip Navigation Links
Discontinuity, Nonlinearity, and Complexity

Dimitry Volchenkov (editor), Dumitru Baleanu (editor)

Dimitry Volchenkov(editor)

Mathematics & Statistics, Texas Tech University, 1108 Memorial Circle, Lubbock, TX 79409, USA

Email: dr.volchenkov@gmail.com

Dumitru Baleanu (editor)

Cankaya University, Ankara, Turkey; Institute of Space Sciences, Magurele-Bucharest, Romania

Email: dumitru.baleanu@gmail.com


Stability Analysis of Fractional-Order CHIKV Infection Model with Latency

Discontinuity, Nonlinearity, and Complexity 11(1) (2022) 33--48 | DOI:10.5890/DNC.2022.03.003

P. Ramesh$^1$, M. Sambath$^1$ , K. Balachandran$^2$

$^1$ Department of Mathematics, Periyar University, Salem-636 011, India

$^2$ Department of Mathematics, Bharathiar University, Coimbatore-641 046, India

Download Full Text PDF

 

Abstract

In this paper, we study the fractional order CHIKV infection model with latency. First, we establish the existence and uniqueness solutions of CHIKV model with latency. Next, we present the local and global stability of fractional order CHIKV model with latency. Finally, we produce some numerical solutions by using MATLAB software that supports the analytical results.

Acknowledgments

The first authors would like to thank the anonymous reviewers and the editors for their valuable suggestions for the improvement of the paper. The second author is thankful to UGC(BSR)-Start Up Grant (Grant No.F.30-361/2017(BSR)), University Grants Commission, New Delhi and the DST-FIST (Grant No.SR/FST/MSI-115/20\\ 16(Level-I)), DST, New Delhi for providing financial support.

References

  1. [1]  Lanciotti, R.S., Kosoy, O.L., Laven, J.J., Panella, A.J., Velez, J.O., Lambert, A.J., and Campbell, G.L. (2007), Chikungunya virus in US travelers returning from India, 2006, Emerging infectious diseases, 13(5), 764-767.
  2. [2]  Moulay, D., Aziz-Alaoui, M.A., and Cadivel, M. (2011), The chikungunya disease: modeling, vector and transmission global dynamics, Mathematical biosciences, 229(1), 50-63.
  3. [3]  Dumont, Y. and Tchuenche, J.M. (2012), Mathematical studies on the sterile insect technique for the Chikungunya disease and Aedes albopictus, Journal of mathematical Biology, 65(5), 809-854.
  4. [4]  Long, K.M. and Heise, M.T. (2015), Protective and pathogenic responses to chikungunya virus infection, Current tropical medicine reports, 2(1), 13-21.
  5. [5]  Wang, Y. and Liu, X. (2017), Stability and Hopf bifurcation of a within-host chikungunya virus infection model with two delays, Mathematics and Computers in Simulation, 138, 31-48.
  6. [6]  Elaiw, A.M., Alade, T.O., and Alsulami, S.M. (2019), Global dynamics of delayed CHIKV infection model with multitarget cells, Journal of Applied Mathematics and Computing, 60(1-2), 303-325.
  7. [7]  Kakarla, S.G., Mopuri, R., Mutheneni, S.R., Bhimala, K.R., Kumaraswamy, S., Kadiri, M.R., Gouda, K.C., and Upadhyayula, S.M. (2019), Temperature dependent transmission potential model for chikungunya in India, Science of the total environment, 647, 66-74.
  8. [8]  Feng, X., Huo, X., Tang, B., Tang, S., Wang, K., and Wu, J. (2019), Modelling and Analyzing Virus Mutation Dynamics of Chikungunya Outbreaks, Scientific reports, 9(1), 1-15.
  9. [9]  Sambath, M., Ramesh, P., and Balachandran, K. (2018), Asymptotic behavior of the fractional order three species prey-predator model, International Journal of Nonlinear Sciences and Numerical Simulation, 19(7-8), 721-733.
  10. [10]  Rihan, F.A. (2013), Numerical modeling of fractional-order biological systems, In Abstract and Applied Analysis, 2013, 1-11.
  11. [11]  Khan, M.A., Khan, A., Elsonbaty, A., and Elsadany, A.A. (2019), Modeling and simulation results of a fractional dengue model, The European Physical Journal Plus, 134(8), 379.
  12. [12]  Yousfi, N. Hattaf K. and Bachraoui, M. (2019), Global stability of a fractional order HIV infection model with cure of infected cells in eclipse stage, Revue Africaine de la Recherche en Informatique et Mathematiques Appliquees, 30, 87-101.
  13. [13]  Ucar, E., Ozdemir, N., and Altun, E. (2019), Fractional order model of immune cells influenced by cancer cells, Mathematical Modelling of Natural Phenomena, 14(3), 1-12.
  14. [14]  Ullah, S., Khan, M.A., and Farooq, M. (2018), A fractional model for the dynamics of TB virus, Chaos, Solitons and Fractals, 116, 63-71.
  15. [15]  Silva, J.G., Ribeiro, A.C., Camargo, R.F., Mancera, P.F., and Santos, F.L. (2019), Stability analysis and numerical simulations via fractional calculus for tumor dormancy models, Communications in Nonlinear Science and Numerical Simulation, 72, 528-543.
  16. [16]  Elaiw, A.M., Almalki, S.E., and Hobiny, A.D. (2019), Stability of CHIKV infection models with CHIKV-monocyte and infected-monocyte saturated incidences, AIP Advances, 9(2), 1-13.
  17. [17]  Podlubny, I. (1999), Fractional Differential Equations, Academic Press, London.
  18. [18]  Matignon, D. (1996), Stability results for fractional differential equations with applications to control processing, in Proceedings of the Computational Engineering in Systems and Application Multiconference (IMACS, IEEE-SMC), Lille, France, 2, 963-968.
  19. [19]  Li, Y., Chen, Y., and Podlubny, I. (2010), Stability of fractional-order nonlinear dynamic systems: Lyapunov direct method and generalized Mittag-Leffler stability, Computers and Mathematics with Applications, 59(5), 1810-1821.
  20. [20]  Huo, J., Zhao, H., and Zhu, L. (2015), The effect of vaccines on backward bifurcation in a fractional order HIV model, Nonlinear Analysis: Real World Applications, 26, 289-305.
  21. [21]  Mondal, S., Lahiri, A., and Bairagi, N. (2017), Analysis of a fractional order eco-epidemiological model with prey infection and type 2 functional response, Mathematical Methods in the Applied Sciences, 40(18), 6776-6789.
  22. [22]  Ahmed, E. and Elgazzar, A.S. (2007), On fractional order differential equations model for nonlocal epidemics, Physica A: Statistical Mechanics and its Applications, 379(2), 607-614.
  23. [23]  Vargas-De-Leon, C. (2015), Volterra-type Lyapunov functions for fractional-order epidemic systems, Communications in Nonlinear Science and Numerical Simulation, 24(1-3), 75-85.
  24. [24]  Diethelm, K., Ford, N.J., and Freed, A.D. (2002), A predictor-corrector approach for the numerical solution of fractional differential equations, Nonlinear Dynamics, 29(1-4), 3-22.