Modeling the Effects of Human Awareness and Use of Insecticides on the Spread of Human African Trypanosomiasis: A Fractional-Order Model Approach

In this research work, we proposed and studied a fractional-order model for Human African Trypanosomiasis (HAT) disease transmission, incorporating three control strategies: health education campaigns, prevention measures, and use of insecticides. The theoretical analysis of the model was presented, including the computation of disease-free equilibrium and basic reproduction number. We performed the stability analysis of the model and the results showed that the disease-free equilibrium point was locally asymptotically stable whenever R0<1 and unstable when R0>1. Furthermore, we performed parameter estimation of the model using HAT-reported cases in Tanzania. The results showed that fractional-order model had a better fit to the real data compared to the classical integer-order model. Sensitivity analysis of the basic reproduction number was performed using computed partial rank correlation coefficients to assess the effects of parameters on HAT transmission. Additionally, we performed numerical simulations of the model to assess the impact of memory effects on the spread of HAT. Overall, we observed that the order of derivatives significantly influences the dynamics of HAT transmission in the population. Moreover, we simulated the model to assess the effectiveness of proposed control strategies. We observed that the use of insecticides and prevention measures have the potential to significantly reduce the spread of HAT within the population.