A Markov Chain Approach to the Pattern of Blood Donation Status at a Blood Service Centre in Zimbabwe

Abstract

Background: Blood donors’ behaviour towards blood donation is not easily predictable and can be considered to be a stochastic random variable. A four-state Markov chain technique was defined and adopted in this study. The transition probabilities of blood donation within the four identified states, viz: new, regular, occasional, and lapsed donor were used to make further inferences of the dynamics in blood donation in Harare, Zimbabwe. Objectives: The paper presents a four-state Discrete Time Markov Chain (DTMC) model in analysing the changes in blood donation status over the four-year study period. Methodology: A transition probabilities matrix was developed and parameters estimated using the maximum likelihood method and two other approaches, and inferences were made based on the resultant transition matrix. Results: About 56% of new donors made at least one repeat donation and become regular donors within the first year, and the numbers gradually declined with time, whilst the lapsed donors increased from 35.6% in second year to 55.6% in year 4. The long run probabilities tell the same, with 80.9% of blood donations becoming lapsed in the long run. Depending on the current state of donation, new or regular donations are likely to move to the regular donation state in the following time step (year). On the other end, occasional and lapsed donations have a higher probability of entering the lapsed donation state in the following time step (year). Conclusion: The paper provides useful insights on the Markovian transition probabilities among the blood donation states, and this has implications on future blood donors’ pool and blood bank inventory in Zimbabwe. The decline in numbers of donors who make repeat donations is a worrisome trend, since regular donations are the lifeline of any blood service centres.