Modeling and numerical simulation of control policies for co-infection Leishmaniasis-Chagas disease in Brazil via...

Vector-borne diseases have long played a significant role in human mortality and public health crises in Brazil. Among these, neglected tropical diseases such as Leishmaniasis and Chagas disease require urgent attention. This paper develops a deterministic mathematical dynamical model to study the dynamics of mono and co-infection with Leishmaniasis and Chagas disease. We begin with a rigorous mathematical analysis of the model, including the computation of the basic reproduction number R₀^LC and its sensitivity indices, which help identify key parameters driving disease dynamics. The population's equilibrium states are studied in relation to this threshold parameter. Furthermore, we incorporate four control prevention into the model to evaluate the best intervention policy. Using a reliable data set from Brazil over a specified time period, we estimate model parameters and fit the data, demonstrating strong agreement between the model predictions and the actual data. Our graphical simulations further support the findings. Additionally, we compute and analyze the controlled reproduction number, confirming that the proposed policy 5 is the most effective in reducing the disease burden in Brazil. Finally, we rewrite the fractional version of the model and perform numerical simulations for different values of α. The fractional-order model is conceptually suitable for capturing memory effects and delay response in disease transmission dynamics. This study provides valuable insights for public health stakeholders and health care centers aiming to design efficient prevention and control programs for neglected vector-borne diseases.