In this work, we formulated a deterministic mathematical continuous time model for the detection and elimination of a non-life threatening disease (head lice) by considering a fixed (constant) population size during the epidemic period. The formulated mathematical model was normalized for easy analysis, the model’s properties were obtained, as well as the disease free equilibrium point, the local stability and the basic reproduction number. We adopted MATLAB programing language to carry out the numerical simulation of the nonlinear ordinary differential equation, as well as simulation of different model state variables and effects of different model parameters on the state variables over time. Our result shows that early detection and treatment will lead to termination of the disease.