Local dynamic analysis of the covid-19 mathematical model based on discrete-time predator-prey population model

In this article, the local dynamics of a discrete-time Covid-19 pandemic model based on the Lotka Volterra model with topological classifications, bifurcation analysis and chaos control are investigated. It is shown that under some parametric conditions, the discrete-time Covid-19 pandemic model has two equilibrium points. With linear stability theory, local dynamics are investigated with topological classifications about the equilibrium points of the discrete-time Covid-19 epidemic model. In addition, the existence of a Neimark-Sacker bifurcation at the internal equilibrium point is proved and this bifurcation is analysed using explicit criteria. Furthermore, the chaos in the discrete Covid-19 pandemic model is also investigated with the OGY feedback control strategy. Lastly, illustrative examples are given to verify the theoretical findings. The parameter values of presented model were taken from Covid-19 data in Saudi Arabia between 18 November 2020 and 18 March 2020 for ensuring biological realism.