Time-optimal control strategies for tungiasis diseases with limited resources

Abstract

Tungiasis, as an epidermal parasitic skin disease, leads to long-term injury and life threats to humans in resource-limited countries. In this paper, we aim to minimize the epidemic duration of tungiasis disease with limited resources. A human-jigger parasite system with four control policies for humans and jiggers is established. We propose a time-optimal control problem, in which the eradication time and limited resources are involved. By applying the Pontryagin’s minimum principle, we prove that, only bang-bang controls are admitted for all the control policies. Furthermore, a numerical scheme combining the control parametrization scheme with the interior point algorithm is constructed. Finally, numerical simulations are carried out using actual data of humans and jiggers in Brazil. From all the results, we conclude that, there is a trade-off between the optimal eradication time and the effective funding; once the effective funding is properly used, the disease can be controlled effectively; strengthening personal protections, improving treatments for humans and making adulticiding efforts contribute to keeping humans away from the disease.