Fractional optimal control analysis of Covid-19 and dengue fever co-infection model with Atangana-Baleanu derivative

A co-infection with Covid-19 and dengue fever has had worse outcomes due to high mortality rates and longer stays either in isolation or at hospitals. This poses a great threat to a country's economy. To effectively deal with these threats, comprehensive approaches to prevent and control Covid-19/dengue fever co-infections are desperately needed. Thus, our focus is to formulate a new co-infection fractional model with the Atangana-Baleanu derivative to suggest effective and feasible approaches to restrict the spread of co-infection. In the first part of this paper, we present Covid-19 and dengue fever sub-models, as well as the co-infection model that is locally asymptotically stable when the respective reproduction numbers are less than unity. We establish the existence and uniqueness results for the solutions of the co-infection model. We extend the model to include a vaccination compartment for the Covid-19 vaccine to susceptible individuals and a treatment compartment to treat dengue-infected individuals as optimal control strategies for disease control. We outline the fundamental requirements for the fractional optimal control problem and illustrate the optimality system for the co-infection model using Pontraygin's principle. We implement the Toufik-Atangana approximating scheme to simulate the optimality system. The simulations show the effectiveness of the implemented strategy in determining optimal vaccination and treatment rates that decrease the cost functional to a minimum, thus significantly decreasing the number of infected humans and vectors. Additionally, we visualize a meaningful decrease in infection cases with an increase in the memory index. The findings of this study will provide reasonable disease control suggestions to regions facing Covid-19 and dengue fever co-infection.