Abstract
An infectious disease called dengue is a significant health concern nowadays. The dengue outbreak occurred with a single serotype all over Nepal in 2023. In the tropical and subtropical regions, dengue fever is a leading cause of sickness and death. Currently, there is no specified treatment for dengue fever. Avoiding mosquito bites is strongly advised to reduce the likelihood of controlling this disease. In underdeveloped countries like Nepal, the implementation of appropriate control measures is the most important factor in preventing and controlling the spread of dengue illness. The Caputo fractional dengue model with optimum control variables, including mosquito repellent and insecticide use, investigates the impact of alternative control strategies to minimize dengue prevalence. Using the fixed point theorem, the existence and uniqueness of a solution will be demonstrated for the problem. Ulam-Hyers stability, disease-free equilibrium point stability, and basic reproduction number are studied for the proposed model. The model is simulated using a two-step Lagrange interpolation technique, and the least squares method is used to estimate parameter values using real monthly infected data. We then analyze the sensitivity analysis to determine influencing parameters and the control measure effects on the basic reproduction number. The Pontryagin Maximum Principle is used to determine the optimal control variable in the dengue model for control strategies. The present study suggests that the deployment of control measures is extremely successful in lowering infectious disease incidences. Which facilitates the decision-makers to practice rigorous evaluation of such an epidemiological scenario while implementing appropriate control measures to prevent dengue disease transmission in Nepal.