Optimal control interventions for the prevention of bluetongue virus transmission in dairy cattle

Bluetongue virus is a vector-borne infection of ruminants, spread by Culicoides midges, that threatens dairy cattle production on a global scale. In this study, we formulate and analyze an optimal control problem for a deterministic hostvector model that describes the transmission dynamics of bluetongue virus in dairy cattle populations. Three time-dependent control strategies are incorporated into the model: vaccination of susceptible cattle, insecticide-based control of adult vectors, and treatment of infected cattle. A cost functional is proposed to minimize the number of exposed and infected hosts and vectors while balancing the implementation costs of the control measures. The necessary optimality conditions are obtained via Pontryagin’s maximum principle, yielding the corresponding adjoint system together with explicit expressions for the optimal controls. Numerical simulations using the forward–backward sweep method demonstrate that the combined implementation of the proposed control strategies leads to a substantial reduction in bluetongue virus transmission and effectively mitigates disease spread.