Robust bi-objective optimal control of tungiasis diseases

Tungiasis, a neglected seasonal disease, leads to long-term injury and life threats to humans in developing countries. In this paper, we investigate the optimal control of tungiasis disease with an uncertain parameter, where both epidemic prevention and economic concerns are considered. Based on the life cycle of jiggers and propagation process of the disease, a human-jigger parasite model with control schemes for humans and jiggers is established. The effect of controls on the control reproduction number is discussed. A robust bi-objective optimal control problem is proposed, in which the accumulated number of infected humans and control cost, and their sensitivities to the uncertain parameter are all in the vector objective. Since the objective vector contains non-standard sensitivity terms, it is difficult to solve this problem using conventional optimization techniques. By introducing an auxiliary initial value system, we transform this problem into a standard form. Furthermore, a numerical method which combines a modified normal boundary intersection scheme with the interior point scheme is constructed. Finally, numerical simulations for different seasons are carried out using actual data of humans and jiggers in Nigeria. From all results, we conclude that enhancing the jigger adulticiding effort can significantly reduce the control reproduction number; the intervention control measures should be carried out in time, especially in the dry season; the obtained Pareto points can provide decision-makers with a trade-off between the two goals and choose an appropriate policy to implement.