A Non-Homogeneous Semi-Markov Model for the Management of Continuous Blood Glucose Level in Diabetes Patient in Nigeria

Abstract

This study develops a non-homogeneous semi-Markov model (NH-SMM) with five clinically 
defined latent states to characterize the progression and management of blood glucose levels 
in diabetic patients. The model incorporates time-dependent transition probabilities and 
variable sojourn times, allowing it to capture the effects of treatment interventions, lifestyle 
modifications, and underlying disease dynamics. Effective regulation of blood glucose is 
critical for minimizing diabetes-related complications. Simulation results indicate that 
treatment yields only marginal reductions in glycemic levels within the first day under both 
50% and 90% effectiveness scenarios. However, more substantial reductions are observed 
after approximately 40 days, particularly under higher treatment efficacy, highlighting the 
importance of sustained and intensive therapeutic interventions for improved patient 
outcomes. The interval transition probability
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n  records the largest decreases, while  
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, , n n and n    shows moderate reductions and 
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, , n n and n    
exhibit smaller long-term effects. The results further reveal that transition probabilities 
between glycemic states increase progressively over time across all modeled scenarios, with 
the most rapid escalation observed in the absence of treatment. This trend reflects the 
natural progression of uncontrolled diabetes and the associated instability in blood glucose 
dynamics. Conversely, increased treatment intensity significantly attenuates these 
transitions, promoting greater stabilization of patients’ glycemic levels. The findings 
demonstrate that both higher treatment effectiveness and sustained intervention duration 
are critical for achieving improved clinical outcomes. An illustrative application based on five 
clinically relevant glycemic states highlights the capacity of the model to support treatment 
optimization and evidence-based policy planning. Additionally, the predictive outputs enhance 
patient monitoring, surveillance, and the implementation of individualized management 
strategies in diabetes care.