An epidemic model of childhood disease dynamics with maturation delay and latent period of infection

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.