Asian Journal of Probability and Statistics

This study analysed the monthly incidence of malaria diagnosed among students who visited a university clinic for medical check-ups over a five-year period (2019-2023). The data were examined using graphical methods and a discrete-time Markov chain model. Monthly totals were classified into five discrete incidence states, and the transition probabilities between pairs of states were estimated. The Chapman-Kolmogorov equations were used to obtain n-step transition probabilities, while steady-state probabilities were determined using both repeated matrix multiplication and steady-state equations. The model was then used to predict future monthly malaria incidence levels among students attending the clinic. The results showed that the highest annual incidence of diagnosed malaria during the study period occurred in 2023. The findings also indicated a higher likelihood of increased malaria incidence from October to January of the following year. The first incidence state, representing 1-50 diagnosed students per month, was the most likely to dominate in the long run if prevailing conditions remained unchanged, accounting for approximately 57% of monthly diagnosed malaria totals at steady state. The analysis further suggested that the Markov process would most likely reach steady state after 41 months. These findings provide an incidence-level forecasting framework for clinic-based malaria planning within the study setting.