Mathematical Modeling and Optimal Control of Dengue Fever Using Fractional Dynamics with Exposure and Hospitalization Effects
Abstract
Dengue fever is one of the most rapidly spreading vector-borne viral diseases worldwide, constituting a significant burden on public health systems in tropical and subtropical regions. This paper develops and examines a fractional-order optimal control model for dengue transmission between human and mosquito populations, using the Caputo fractional derivative framework to incorporate memory and hereditary effects. The proposed model partitions the human population into five epidemiological classes, namely susceptible, exposed, infected, hospitalized, and recovered individuals, and the mosquito population into three classes, namely susceptible, exposed, and infected vectors. This nine-compartment SEIHR-SEI structure extends classical dengue models by accounting explicitly for the incubation period in both host and vector, as well as a dedicated compartment for hospitalized individuals requiring clinical care. Three time-varying control measures, representing personal protection, treatment and hospitalization, and insecticide-based vector suppression, are embedded in the model. Qualitative properties of the system, including positivity and boundedness of solutions, are rigorously established. A threshold parameter, the basic reproduction number, is computed via the next-generation matrix method. An optimal control problem is formulated, the existence of optimal controls is verified, and necessary optimality conditions are derived through the fractional Pontryagin Maximum Principle. Numerical experiments are conducted using a forward-backward sweep algorithm combined with an Adams-type fractional predictor-corrector scheme, covering four fractional orders. The results confirm that the combined intervention strategy offers the most substantial reduction in dengue burden, and that fractional order affects epidemic persistence in a measurable way. These outcomes provide actionable insights for the design of cost-effective dengue control policies.