Complex dynamics of COVID-19 mathematical model on Erdős–Rényi network

Abstract

In this study, a conformable fractional order Lotka–Volterra predator-prey model that describes the COVID-19 dynamics is considered. By using a piecewise constant approximation, a discretization method, which transforms the conformable fractional-order differential equation into a difference equation, is introduced. Algebraic conditions for ensuring the stability of the equilibrium points of the discrete system are determined by using Schur–Cohn criterion. Bifurcation analysis shows that the discrete system exhibits Neimark–Sacker bifurcation around the positive equilibrium point with respect to changing the parameter d and e. Maximum Lyapunov exponents show the complex dynamics of the discrete model. In addition, the COVID-19 mathematical model consisting of healthy and infected populations is also studied on the Erdős Rényi network. If the coupling strength reaches the critical value, then transition from nonchaotic to chaotic state is observed in complex dynamical networks. Finally, it has been observed that the dynamical network tends to exhibit chaotic behavior earlier when the number of nodes and edges increases. All these theoretical results are interpreted biologically and supported by numerical simulations.