| Abstract: |
| This work develops and analyzes a prey--predator model in which the prey population exhibits Smith-type growth, group-defense behavior, and continuous external replenishment. A forward--Euler discretization produces a two-dimensional map whose positivity, boundedness, and equilibrium stability are established. Bifurcation analysis shows that the coexistence equilibrium may lose stability through Neimark--Sacker or period-doubling bifurcations, leading to quasiperiodic or chaotic dynamics. Numerical simulations, including bifurcation diagrams, phase portraits, and Lyapunov exponents, reveal rich dynamical behaviors. A global sensitivity analysis using partial rank correlation coefficients identifies parameters that most strongly influence long-term species densities. Finally, calibration with COVID-19 and tuberculosis surveillance data demonstrates the potential applicability of the framework under a phenomenological interpretation. |
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