This paper focused on the higher-Order Markov Model whose number of states and parameters are linear with respect to the order of the model and as well as classifying it. Model for Efficient estimation methods of the parameters was developed and the model was applied to solve the application of DOTS in the treatment of tuberculosis health problem. Numerical examples with applications are given to illustrate the power of our proposed model. It was discovered that the second order Markov model was best fit base on the values of the AIC and BIC result obtained.Â