A Mathematical Model of a Zika Virus Transmission with Impact of Awareness by Media

Abstract

This paper has studied the transmission of Zika Virus with the impact of media. We analyzed the impact of the awareness programs on social media for the Zika Virus transmission model with saturated incidence rate. The Beddington-De Angelis functional responses used to explain the interaction between a suspected human and an infected human. The dynamical analysis identified by computing the disease-free equilibrium(DFE) and endemic equilibrium(END). The Basic Reproduction Number was identified by Next Generation Matrix(NGM) method. Then the stability of DFE and END were analyzed locally by computing the determinant of Jacobian. The DFE was identified as locally stable when the basic reproduction number was less than unity and was identified as unstable otherwise. Otherwise, the END was identified as existents when the basic reproduction number was greater than unity. The Routh-Hurwitz Criterion showed that the END was locally stable under a specific condition. In the last, the stability of the equilibrium point was also identified numerically depending on certain parameter values.

Keywords

• Zika Virus,dynamical analysis,social media,next generation matriks,routh hurwitz

References

1. [1] U. D. of Health and H. Services, Zika transmission, (from Center for Disease Control and Prevention:https://www.cdc.gov/zika/transmission/index.html).
2. [2] P. P. Padmanabhan and C.Castillo-Chavez., Letters in Biomathematics 4, 148–166 (2017).
3. [3] A. A. Ishaku, B.S.Musa and A.M.Bakoji, IOSR Journal of Mathematics 4, 72–79 (2018).
4. [4] R. A.K.Misra and Y.Takeuchi, Mathematical Biosciennces and Engineering 15, 1315–1343 (2018).
5. [5] S. Collinson and J.M.Heernan, BMC Public Health 14, 1–10 (2014).
6. [6] A. P. Andayani, L.R.Sari and I.Darti, Far East Journal of Mathematical Sciences(FJMS) 11, 145–157 (2019).
7. [7] R. P. Andayani and L.R.Sari, J. Exp. Life Sci. 8, 161–164 (2019).
8. [8] X. Yang, Applied Mathematics Letters 15, 615–621 (2002).

9. [9] P. Andayani, Jurnal Matematika dan Sains 24, 19–23 (2019).
10. [10] S. Kemp, Digital 2019: Global digital overview, Https://datareportal.com/reports/digital-2019-global-digitaloverview.
11. [11] P. Andayani, “The eect of social media for a zika virus transmission with beddington de angelis incidencerate: Modeling and analysis,” (American Institute of Physics, 2019).