Discrete (q,τ)-nabla fractional modeling of Dengue dynamics with stability and optimal control
Utilizing the (q, τ)-nabla fractional operator, we develop a discrete-time Dengue transmission model incorporating memory and time-scale deformation effects. Stability, endemic equilibrium, and bifurcation behavior are analyzed through Jacobian eigenvalue methods and fractional threshold conditions. A Lyapunovbased feedback strategy and a memory-weighted optimal control framework are introduced to regulate infected and hospitalized populations. Necessary optimality conditions are derived using a generalized Pontryagin maximum principle adapted to the (q, τ)-fractional setting. Numerical simulations confirm the theoretical results and demonstrate the influence of the parameters q, τ, and α on memory dynamics and intervention efficiency. The proposed framework provides a flexible approach for modeling and controlling epidemic systems with nonlocal memory effects.
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