Semi-Markov model for evaluating the HIV patient treatment cost

The aim of this study is to model the progression of HIV/AIDS disease and evaluate the cost of the anti-retroviral therapy for an HIV infected patient under ART follow-up using Non homogeneous semi-Markov processes. States of the Markov process are defined by the seriousness of the sickness based on the clinical scores. The five states considered are: Asymptomatic (CD$^{+}_{4}$ count > 500 cells/microliter); Symptomatic 1 (350 < CD$^{+}_{4}$ count ≤ 500 cells/microliter); Symptomatic 2 (200 < CD$^{+}_{4}$ count ≤ 350 cells/microliter); AIDS (CD$^{+}_{4}$ count ≤ 200 cells/microliter) and Death (Absorbing state). The first four states are named as good or alive states. The models formulated can be used to gain insights on the transition dynamics of the HIV patient given the follow-up time. The transition probability Model, when fitted with data will give insights on the conditional probability of a patient moving from one disease state to another, given the current state and the follow-up time. This model will also give the probability of survival for the HIV patient under treatment given the current state and follow-up time. The total Lifetime Treatment Cost model obtained, when applied to real data will give the cost of managing an HIV patient given the starting state, the treatment combination which incurs minimum cost and which treatment combination is most effective at each state. The treatment reward model also when applied to real data will give the state, which a patient should be maintained so that they remain healthy, noninfectious and productive to the society. Also the model will show the optimal/effective time to initiate treatment, which can be used to give advice on how to handle the HIV infecteds given their states.
HIV evolution, Therapeutic intervention, Non homogeneity, Treatment Cost, Semi-Markov model, transition probabilities, reward model.