Complexity and control in a differential-algebraic prey-predator epidemiological model with harvesting

A differential-algebraic model is proposed in this paper, which is utilized to investigate complex dynamical behavior of epidemiological system with harvesting. Especially, the periodic, quasi-periodic and chaotic phenomenon in the proposed model system is studied by virtue of Poincaré surface section, Lyapunov exponents, fractal dimension and continuous spectrum. Corresponding controller is designed to stabilize chaotic behavior to target orbit. Numerical simulations show that the chaotic behavior and quasi-periodic behavior occur due to the variation of transmission rate of the infected prey.