Stability and optimal control analysis of Zika virus with saturated incidence rate
Authors :
Naba Kumar Goswami 1 * and B. Shanmukha 2
Author Address :
1 Department of Mathematics, PET Research Centre,University of Mysore, Karnataka, India.
2 Department of Mathematics, PES College of Engineering, Mandya, Karnataka, India.
*Corresponding author.
Abstract :
Stability analysis of a non-linear mathematical model is studied and analyzed the transmission dynamics of the Zika virus disease. In our model, the human to human sexual transmission of Zika virus is modeled by considering the saturated incidence rate. This assumption is reasonable as it incorporates the behavioral change of the susceptible individuals and the crowding effect of the infective individuals. The equilibria of the proposed model are obtained and the basic reproduction number $(R_0)$ is computed. The model also exhibits backward bifurcation where the stable disease-free equilibrium coexists with a stable endemic equilibrium, which suggests that the $R_0<1$ is not enough to eradicate the disease. The sensitivity analysis of the parameters of the basic reproduction number of the model is presented. The sensitivity analysis is performed to distinguish the main variables that affect the basic reproduction number, which can be regulated to control the transmission dynamics of the Zika. Finally, the optimal control strategies are incorporated into the model and performed a numerical simulation to support our analytical findings.
Keywords :
Zika virus, basic reproduction number, bifurcation analysis, stability analysis, sensitivity Analysis.
DOI :
Article Info :
Received : November 17, 2019; Accepted : February 22, 2020.
