Optimal Control and Levenberg-Marquardt Backpropagation Neural Network Approaches for Managing Rift Valley Fever Transmission Dynamics

Rift Valley fever (RVF) is a zoonotic vector-borne disease that can cause severe illness in humans, livestock mortality and abortion, and substantial economic losses in livestock production and trade. To manage RVF effectively, interventions should reduce transmission within a cost-conscious control framework. This study develops a deterministic host–vector–environment model to examine the dynamics of RVF transmission among humans, cattle, mosquitoes, and contaminated animal tissues. Cattle vaccination and environmental sanitation are incorporated as time-dependent control measures, and limited treatment capacity is represented by saturated recovery functions. The vaccination-adjusted reproduction number is derived using the next-generation matrix method, and optimal intervention strategies are characterised using Pontryagin's maximum principle. For the parameter set used in this study, the threshold value is R 0 = 2.1077, indicating that transmission can persist under the baseline vaccination assumptions. The resulting optimality system is solved numerically using a forward–backward fourth-order Runge–Kutta scheme. Four intervention scenarios (vaccination alone, environmental sanitation alone, combined control, and no control) are investigated to assess their impact on disease transmission. The numerical simulations show that vaccination primarily suppresses the cattle–mosquito transmission cycle, whereas environmental sanitation reduces the persistence of infectious animal tissues in the environment. The combined intervention produces a greater reduction in infections than either intervention alone. Furthermore, a feed-forward artificial neural network (ANN) trained using the Levenberg–Marquardt algorithm is employed as a supervised surrogate to approximate the model-generated state trajectories and optimal-control profiles obtained from the mechanistic model. The principal contribution of this study is an integrated framework for RVF decision support that combines optimal-control analysis with a neural-network surrogate. The proposed framework may support rapid scenario evaluation and intervention planning and could subsequently be calibrated and validated using epidemiological observations for data-informed applications.