Dynamics and optimal control in transmission of tungiasis diseases

This paper aims to model the transmission of tungiasis disease and assess the optimal control schemes to stop its occurrence. Based on the development stage of fleas and propagation process of diseases, we propose a human-flea model without control, in which the susceptible-infected in latent stage-infectious populations and the egg-larva-pupa-adult stage of fleas are all in involved. In the light of the Lyapunov function method, we prove global stability of equilibria. The model is extended by reformulating it as an optimal control problem, with the use of four time-dependent controls, to assess the impact of individual protection, treatment and two flea control strategies (killing adult fleas and reduction of eggs and larvae). By using Pontryagin's maximum principle, we characterize the optimal control. Using the data of human and flea in Brazil and Nigeri, numerical simulations are performed. The numerical results show that enhancing the protection and treatment of people and increasing the killing efficacy of flea adults would contribute to prevent and control the spread of the disease appreciably.