A. J.  Ademola, M. Gbadegeshin(2018). Modeling Tuberculosis (TB) Using Higher Order Markov Model. Covenant Journal of Physical & Life Sciences (CJPL), 6(2): 21-30.

http://journals.covenantuniversity.edu.ng/index.php/cjpls/article/view/1238

 

In Ademola et al (2018), the authors considered the problem of applying Directly Observed Treatment short course (DOTS) in the treatment of tuberculosis health problem. They propose to higher-order Markov model on the application of DOTS with state of the patients (success, failure). They claim it will help to determine the future condition of patients and the efficient control of Tuberculosis (TB) by concentrating on the initial conditions of TB patients and focus on other factors that can improve the condition of patients because the conditional probability of being in the current state depends on the previous state. They also claim it will help in reducing cost and making a decision on policies on DOTS.

 

In the higher-order Markov model of Ademola et al. (2018), the original categorical sequence is the state of application of DOTS (success, failure) on the patient. The parsimonious high-order Markov chain model along with the parameter estimation method in Ching et al. (2004, 2008) are then applied in the data prediction. This helps reducing the increasing rate of parameter number and reduce the parameter estimation problem to a linear programming problem which is much easier to be handled.

 

The authors in Ademola et al. (2018) conducted an experiment with the data from a survey on “Appraisal of Directly Observed Treatment Short-course (DOTS) and Tuberculosis Eradication in Secondary Healthcare facility in Southwest, Nigeria” at West African Post Graduate College of Pharmacist, Yaba, Lagos. The data collected from 250 patients suffering from Tuberculosis were used. It shows the second order Markov model has a promising result with Akaike information criterion (AIC) (132.649) and Bayesian information criterion (BIC) (134.219).

 

W. Ching, M. Ng and K. Wong (2004) Hidden Markov Models and their Applications to Customer Relationship Management.  IMA Journal of Management Mathematics. 15(I): 13-24.

https://doi.org/10.1093/imaman/15.1.13

 

W. Ching, M. Ng and E. Fung (2008). Higher-order Multivariate Markov Chains and Their Applications, Linear Algebra and Its Applications, 428(2–3):492-507.

 

https://www.sciencedirect.com/science/article/pii/S0024379507002169