Dynamical Behavior of a Fractional Order Delay SIR Model with Stability Analysis - Paul, Subrata; Mahata, Animesh; Mukherjee, Supriya; Mali, Prakash Chandra; Roy, Banamali (Discontinuity, Nonlinearity, and Complexity, 2026)
A nonlinear delayed fractional order SIR compartmental model with a Holling type II saturated incidence rate and treatment rate are explored in this manuscript in the Caputo order fractional derivative approach. A few findings for the new model’s existence and uniqueness criterion, as well as non-negativity and boundedness of the solution, have been established. The stability analysis of the model shows that the system is locally as well as globally asymptotically stable at disease-free equilibrium point E_0 when R_0< 1 and at epidemic equilibrium E_1 when R_0 >1. We have studied forward bifurcation at E_0 and Hopf bifurcation at E_1 theoretically as well as numerically of our proposed model. The stability behavior of the endemic equilibrium is also discussed, revealing that oscillatory and periodic solutions may appear via Hopf bifurcation when regarding delay as the bifurcation parameter. Analytical correlations between delay and other system characteristics are built to ensure the presence of stability situations. Additionally, the suggested model’s solution is approximated using the fractional-order Taylor’s technique. Both graphical presentations and numerical simulations might be carried out with the help of MATLAB.