Periodic transmission and vaccination effects in epidemic dynamics: a study using the SIVIS model

This work explores the dynamics of an epidemic considering an SIVIS (susceptible-infected-vaccinated-infected-susceptible) epidemiological model, accounting for heterogeneous susceptibility, governmental interventions, social behavioral dynamics and public reactions in both of autonomous and nonautonomous aspects. The study frames the system as an optimal control problem, considering time-dependent control strategies for strength of social behavior of public and pharmaceutical treatments. The emergence of a coexistence steady state is analyzed based on the basic reproduction number. The impact of model parameters on disease propagation is assessed through sensitivity analysis. Transcritical bifurcation-induced stability alteration is explored, and numerical simulations illustrate theoretical findings. The proposed system investigates the dynamical behavior in case of periodic transmission rate. It vividly highlights the profound impact of factors such as vaccination rates, frequency and amplitude of transmission on the enduring and evolving dynamic patterns exhibited by the disease.