Analyzing nonlinear dynamics of dengue epidemics: A fractional order model with alert state and optimal control strategies

Abstract

Dengue fever is a viral disease that results in numerous fatalities and considerable financial burden. Although vaccines have been developed to treat it, some countries still have endemic cases of the disease. To manage the transmission of the disease in these areas, we create a new model that includes an alert compartment to analyze the dynamics of dengue using a fractional‐order approach. We conduct a qualitative analysis of the model and use the Pontryagin principle to develop and study an optimal control problem. Since there is no definitive treatment for dengue, it is essential to prioritize measures that control or prevent the transmission of the disease. We consider control measures, including prevention efforts, insecticides, educational campaigns, and treatment for humans. We can analyze their impact on the transmission dynamics through numerical simulations. We compare our model to an existing one in two ways: with alert and without alert. We analyze the memory effect and validate the results by interpreting parameters on the reproduction number. Our results indicate that individual control measures are insufficient to eliminate the disease, and a combination of all control measures with timely alerts to the population is necessary.