Markov Chain Modeling Hepatitis B Virus Infection with Liver Microstructure

Abstract

Based on the special blood supply system and microscopic structure of the liver, a series of novel Markov chain models is constructed to mimic the entire dynamic process of hepatitis B virus colonization, diffusion and evolution in liver, named as colonization Markov chain, diffusion Markov chain and evolution Markov chain. Theoretically, the colonization probability and infection distribution in hepatic lobules are first obtained. Then, the likelihood of sustained chronicity risk and the expected recovery time for chronic hepatitis B patients undergoing antiviral therapy are also derived. Numerical simulations validate the feasibility of models and the theoretical results. Especially, the model of evolutionary Markov chain with immune saturation may be suitable to simulate the clinically observed complex kinetic patterns of biomarkers, which has potential clinical application prospects.