Optimal Control and Cost-Effective Analysis of a Scabies Model with Direct and Indirect Transmissions

Scabies is caused by sarcoptes scabiei var. hominis, which is also referred to as itch mice. The disease is transmitted through direct contact with an infected person, or from contact with infested bedding or clothing. In this paper, a mathematical model for the spread of scabies was proposed and analyzed. Sensitivity analysis of the model parameters was carried out. Optimal control theory was applied to our proposed model, with the controls representing treatment and vaccination. Our aim was to minimize cumulative infectious cases and susceptible individuals through treatment and vaccination, respectively. Pontryagin’s maximum principle was utilized to characterize the optimal levels of the two controls. The resulting optimality system was then solved numerically. The optimal control result was further highlighted by applying the results realized from the cost objective functional, the IAR, and the ICER.