Modeling the progression of genetic disorders and infectious diseases with mutations by extended Markov processes on dynamic state-space: a probabilistic perspective

Abstract

Markov processes have been employed for modeling various diseases. Due to their memoryless property, existing models are predominantly constructed upon static state spaces. However, genetic disorders and infectious diseases involve random events that cause their associated cells and viruses to change over time. This research is motivated by the need to address the shortcomings of current approaches in modeling the mutation behavior of these diseases. Consequently, we propose an expanded version of the discrete Markov model that accounts for the dynamic nature of the state space when modeling mutations in genetic disorders and infectious diseases. Following model development, we investigate a probabilistic framework based on transition probabilities. Simulations have been conducted to compute transition probabilities, probability mass functions, and their statistical properties.