Mathematical analysis of Zika virus transmission: exploring semi-analytical solutions and effective controls

Abstract

This paper examined the mathematical model of Zika virus transmission, focusing on the impact of the virus on humans and mosquitoes. Human and mosquito populations involved in Zika virus transmission are divided into two categories: susceptible and infected. In addressing the nonlinear differential equation that governing Zika virus transmission, the Taylor series method (TSM) and the new Homotopy perturbation method (NHPM) were employed to derive semi-analytical solutions. Furthermore, for a comprehensive assessment of the nonlinear system behavior and the accuracy of the obtained solutions, a comparative analysis was performed using numerical simulations. This comparative analysis enabled us to validate the results and to gain valuable insights into the behavior of the Zika virus transmission model under different conditions. Moreover, to decrease the number of infected human population, we analyzed the contact rate of Zika virus transmission between humans and mosquitoes, as well as between humans and humans.