Markov Chain Modelling of Pneumonia Cases in the Builsa North Municipality of the Upper East Region of Ghana

Abdulai Jafar¹ and Alhassan Faisal^1,

¹Department of Statistics, Faculty of Physical Sciences, University for Development Studies, Tamale, Ghana

Cite this paper:
Abdulai Jafar and Alhassan Faisal. Markov Chain Modelling of Pneumonia Cases in the Builsa North Municipality of the Upper East Region of Ghana. American Journal of Applied Mathematics and Statistics. 2025; 13(3):47-56. doi: 10.12691/ajams-13-3-1

Abstract

The aim of the study is to model pneumonia cases using Markov Chain. Secondary data on monthly pneumonia cases spanning January, 2015 to December, 2020 was obtained from Builsa North Municipal hospital. Descriptive statistics of the data revealed the minimum and maximum number of pneumonia cases were 9 and 370 respectively with an approximate mean of 121. The data was classified into Low, Moderate and High states based on quartiles of the dataset. The analysis with the aid of R software revealed that, the transition probability of remaining in the low, moderate and high states were 61.10%, 62.9% and 50% respectively, but the probability of transitioning from the low state to the moderate and high states were 33.30% and 5.60% respectively. Also, in the long-run there will be higher chances of recording moderate pneumonia cases with a probability of approximately 51% as compared to 26% and 23% for low and high states respectively. Again, the estimates for Mean Recurrence Time for the low, moderate and high states were 4, 2 and 4 months, respectively and their respective sojourn times were 3, 3 and 2 months. The estimated first passage time probabilities also revealed that when low pneumonia cases are observed in the first month, there is higher probability of low pneumonia cases being observed in the next month. The analysis also revealed that it will take the states twenty-eight (28) months to be in equilibrium and in the long-run the municipality will record, on average, approximately 117 pneumonia cases monthly.

Keywords:
Steady state probabilities first-order Markov Chain transition probability mean recurrence time sojourn time first passage time probabilities

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