Stability and Bifurcation Analysis of a Bird Flu Model with Vaccination in Poultry Farm

arrival rince putri (Departemen Matematika Dan Sains Data, FMIPA Universitas Andalas)
Bala Muhammad Muhammad (Departemen Matematika Dan Sains Data, FMIPA Universitas Andalas)
Mahdhivan Syafwan (Departemen Matematika Dan Sains Data, FMIPA Universitas Andalas)

JURNAL MATEMATIKA STATISTIKA DAN KOMPUTASI
Vol. 22 No. 3 (2026): May 2026

We analyze a nonlinear compartmental model describing bird flu transmission dynamics within a poultry farm, incorporating susceptible, infectious, and removed compartments with vaccination. The basic reproduction number R0 is derived, and the local stability of the disease-free and endemic equilibrium is investigated using linearization techniques. Bifurcation analysis based on standard bifurcation theory is conducted to identify parameter leading to qualitative changes in disease dynamics, revealing the occurrence of a forward transcritical bifurcation. Numerical simulations are used to illustrate threshold behavior and assess the impact of vaccination as a mitigation strategy on outbreak persistence. The results provide insights into control thresholds and the design of effective on-farm intervention strategies