The effect of social media for a Zika virus transmission with Beddington DeAngelis incidence rate: Modeling and analysis

Puji Andayani
Universitas Internasional Semen Indonesia, Gresik, Indonesia
puji.andayani@uisi.ac.id

this paper discuss a modified mathematical model of Zika virus transmission and analyzes the impact of the awareness programs on social media the modification of of Zika Virus model with saturated incidence rate. The Beddington-De Angelis functional responses used to describe the interaction between a suspected human and an infected human. The dynamics of the model were analyzed by identifying the disease-free (DFE) and endemic equilibrium (END). Next Generation Matrix (NGM) was used to determine the Basic Reproduction Number. 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. Meanwhile, 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. A sensitivity
analysis was also computed to determine the most influential parameter value of the model. In the end, the stability of DFE and END were also identified numerically depending on certain parameter values.

Keywords: Zika Virus, dynamics, social media, reproduction number, Next Generation Matrix, Beddington-De Angelis, saturated incidence rate

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