Stability and optimal control analysis of Zika virus with saturated incidence rate

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.

Evaluation of Vector-Borne Disease Intervention Strategies Using Compartmental Models: A Case Study of 2016 Zika Epidemic In Miami-Dade County, Florida

“…Table 1 lists the values and sources of the parameters in the baseline model. The average latent periods for humans and mosquitoes are 5.9 days and 10.5 days [51]; the recovery period for humans is 5 days [52]; the average lifespan of mosquitoes is 15 days [50]; the transmission probabilities from vector to human and from human to vector are 0.417 and 0.418 [50]. and 203 infectious (I) mosquitos using Eq.…”