Bifurcation Analysis in a Discrete SIRS Epidemic Model with Non-Monotonic Incidence Rates

In this study, we investigate a discrete SIRS epidemic model with non-monotonic incidence rates. Employing bifurcation theory and critical normal form analysis, we study the existence of three codimension-two bifurcations, including 1:1 strong resonance, 1:2 strong resonance, and fold-flip bifurcation. To verify theoretical results, we provide a series of numerical simulations, including bifurcation diagrams, phase portraits, and maximum Lyapunov exponent diagrams. We further investigate the influence of initial conditions through two-parameter space plots.