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Modeling and simulations of a Zika virus as a mosquito-borne transmitted disease with environmental fluctuations

  • Chellamuthu Gokila ORCID logo and Muniyagounder Sambath ORCID logo EMAIL logo
Published/Copyright: August 23, 2021
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International Journal of Nonlinear Sciences and Numerical Simulation
From the journal International Journal of Nonlinear Sciences and Numerical Simulation Volume 24 Issue 1

Abstract

This paper deals with the stochastic Zika virus model within the human and mosquito population. Firstly, we prove that there exists a global positive solution. Further, we found the condition for a viral infection to be extinct. Besides that, we discuss the existence of a unique ergodic stationary distribution through a suitable Lyapunov function. The stationary distribution validates the occurrence of infection in the population. From that, we obtain the threshold value for prevail and disappear of disease within the population. Through the numerical simulations, we have verified the reproduction ratio R 0 S as stated in our theoretical findings.

Keywords: extinction; stationary distribution; threshold; Zika virus infection model
2010 Mathematics Subject Classification: 92D30; 34F05; 34D20
Corresponding author: Muniyagounder Sambath, Department of Mathematics, Periyar University, Salem 636 011, India, E-mail:

Acknowledgment

The authors would like to thank the anonymous reviewers and the editors for their valuable suggestions for the improvement of the paper. The work of first author was supported by the DST-INSPIRE Fellowship (No. DST/INSPIRE Fellowship/2017/IF170244), Department of Science and Technology, New Delhi. 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-115/2016(Level-I)), DST, New Delhi for providing financial support.

  1. Author contribution: All the authors have accepted responsibility for the entire content of this submitted manuscript and approved submission.

  2. Research funding: None declared.

  3. Conflict of interest statement: The authors declare no conflicts of interest regarding this article.

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Received: 2020-07-05
Revised: 2020-12-29
Accepted: 2021-07-29
Published Online: 2021-08-23
Published in Print: 2023-02-23

© 2021 Walter de Gruyter GmbH, Berlin/Boston

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https://doi.org/10.1515/ijnsns-2020-0145
Keywords for this article
extinction; stationary distribution; threshold; Zika virus infection model

Articles in the same Issue

  1. Frontmatter
  2. Original Research Articles
  3. Modeling and assessment of the flow and air pollutants dispersion during chemical reactions from power plant activities
  4. Stochastic dynamics of dielectric elastomer balloon with viscoelasticity under pressure disturbance
  5. Unsteady MHD natural convection flow of a nanofluid inside an inclined square cavity containing a heated circular obstacle
  6. Fractional-order generalized Legendre wavelets and their applications to fractional Riccati differential equations
  7. Battery discharging model on fractal time sets
  8. Adaptive neural network control of second-order underactuated systems with prescribed performance constraints
  9. Optimal control for dengue eradication program under the media awareness effect
  10. Shifted Legendre spectral collocation technique for solving stochastic Volterra–Fredholm integral equations
  11. Modeling and simulations of a Zika virus as a mosquito-borne transmitted disease with environmental fluctuations
  12. Mathematical analysis of the impact of vaccination and poor sanitation on the dynamics of poliomyelitis
  13. Anti-sway method for reducing vibrations on a tower crane structure
  14. Stable soliton solutions to the time fractional evolution equations in mathematical physics via the new generalized G ′ / G -expansion method
  15. Convergence analysis of online learning algorithm with two-stage step size
  16. An estimative (warning) model for recognition of pandemic nature of virus infections
  17. Interaction among a lump, periodic waves, and kink solutions to the KP-BBM equation
  18. Global exponential stability of periodic solution of delayed discontinuous Cohen–Grossberg neural networks and its applications
  19. An efficient class of fourth-order derivative-free method for multiple-roots
  20. Numerical modeling of thermal influence to pollutant dispersion and dynamics of particles motion with various sizes in idealized street canyon
  21. Construction of breather solutions and N-soliton for the higher order dimensional Caudrey–Dodd–Gibbon–Sawada–Kotera equation arising from wave patterns
  22. Delay-dependent robust stability analysis of uncertain fractional-order neutral systems with distributed delays and nonlinear perturbations subject to input saturation
  23. Construction of complexiton-type solutions using bilinear form of Hirota-type
  24. Inverse estimation of time-varying heat transfer coefficients for a hollow cylinder by using self-learning particle swarm optimization
  25. Infinite line of equilibriums in a novel fractional map with coexisting infinitely many attractors and initial offset boosting
  26. Lump solutions to a generalized nonlinear PDE with four fourth-order terms
  27. Quantum motion control for packaging machines
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