In the present study, an epidemic model is proposed with maturation delay and latent period of infection, keeping in view the childhood disease dynamics and studied the asymptotic behavior of the model for all the feasible equilibrium states. The criterion for local stability of the system around steady states are established in terms of delay, latent period and system parameters. Further explored the possibility of Hopf bifurcation at the endemic equilibrium state and threshold is determined. We also performed the sensitivity analysis of the state variables at the endemic equilibrium state with respect to the model parameters and identified the respective sensitive indices. Further numerical simulations have been carried out to justify our analytic findings.

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In the present study, keeping in view of Leslie-Gower prey-predator model, the stability and bifurcation analysis of discrete-time prey-predator system with generalized predator (i.e., predator partially dependent on prey) is examined. Global stability of the system at the fixed points has been discussed. The specific conditions for existence of flip bifurcation and Neimark-Sacker bifurcation in the interior of R 2 + have been derived by using center manifold theorem and bifurcation theory. Numerical simulation results show consistency with theoretical analysis. In the case of a flip bifurcation, numerical simulations display orbits of period 2, 4, 8 and chaotic sets; whereas in the case of a Neimark-Sacker bifurcation, a smooth invariant circle bifurcates from the fixed point and stable period 16, 26 windows appear within the chaotic area. The complexity of the dynamical behavior is confirmed by a computation of the Lyapunov exponents.

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