Continuous-time Markov model with application to leprosy transmission dynamics

Leprosy is a public problem because of its latency, diagnosis, treatments and its transmission potential. It is considered as one of the neglected tropical diseases. Although remarkable effort has been made towards the control of leprosy, the burden of leprosy is still severe among population. A number of leprosy models exist but could not account for the proper transmission dynamics of leprosy. This study develops a Continuous-Time Markov Model to enhance the understanding of leprosy transmission dynamics, addressing limitations in prior models by integrating retreatment of relapse cases, undetected case detection, and disability progression. Extending the existing model framework, new compartments for diagnosed exposed individuals (Ed) and disabled populations (D) are introduced, alongside parameters such as case finding rates, treatment adherence, and relapse probabilities sourced from epidemiological data. We carried out a numerical simulation on the model where we obtained our sample paths/stochastic realization using Gillespie Algorithms with “Adaptivetau” package in R. The results of the sample paths reveal a decline in a population of Susceptible with an incline and decline among population of Exposed, Infected with Multibacillary, Infected with Paucibacillary, Exposed/detected diagnosed, Treated, Disable, Relapsed to Multibacillary and Relapse to Paucibacillary by varying the levels of leprosy interventions transmission parameters at fixed population. The model was also successfully fitted into data obtained from National Tuberculosis and Leprosy Control Programme for North East, Nigeria capturing the impact of control strategies for the transmission dynamics of leprosy.