Discrete dynamics of an epidemic model incorporating a control strategy

Abstract

This paper proposes an epidemic model that incorporates media awareness and analyses the stability and bifurcation of the discrete-time system. It has been found that while the coefficient of media awareness m has no effect on R₀, it has a considerable impact on the infectious population portion. The centre manifold theorem and bifurcation theory have been used to investigate the existence of flip bifurcation and Hopf bifurcation in the interior of R²₊. Numerical simulations have been provided to support analytical findings. Hopf bifurcation is characterised by a smooth invariant circle that emerges from the fixed point, while flip bifurcation is characterised by a cascade of periodic doubling bifurcation in orbits of period-2, 4, 8, and chaotic orbits. The calculation of Lyapunov exponents validates the complexity of dynamical behaviour.