No abstract

Clinical study of malaria presents a modeling challenge as patients disease status and progress is partially observed and assessed at discrete clinic visit times. Since patients initiate visits based on symptoms, intense research has focused on identication of reliable prediction for exposure, susceptibility to infection and development of severe malaria complications. Despite detailed literature on malaria infection and transmission, very little has been documented in the existing literature on malaria symptoms modeling, yet these symptoms are common. Furthermore, imperfect diagnostic tests may yield misclassication of observed symptoms. Place and Duration of Study: The main objective of this study is to develop a Bayesian Hidden Markov Model of Malaria symptoms in Masinde Muliro University of Science and Technology student population. An expression of Hidden Markov Model is developed and the parameters estimated through the forward-backward algorithm.

Aims/ objectives: To develop a state-transition model for malaria symptoms. Study design: Longitudinal study.  Place and Duration of Study: Department of Mathematics Masinde Muliro University of Science and Technology between January 2015 and December 2015.  Methodology: We included 300 students (patients) with liver malaria disease, with or without the medical history of malaria disease, physical examination for signs and symptoms for both specific and non-specific symptom, investigation of the disease through laboratory test (BS test) and diagnostic test results. the focus of this study was to develop state-transition model for malaria symptoms. Bayesian method using Markov Chain Monte Carlo via Gibbs sampling algorithm was implemented for obtaining the parameter estimates.  Results: The results of the study showed a significant association between malaria disease and observed symptoms  Conclusion: The study findings provides a useful information that can be used for predicting malaria disease in areas where Blood slide test and rapid diagnostic test for malaria disease is not possible.

The mathematical study of waiting lines is mainly concerned with queue performance measures where several applications have been drawn in past studies. Among the vast uses and applications of the theory of queuing system in banking halls, is the main focus of this study where the theory has been used to solve the problem of long queues as witnessed in banks leads to resource waste. The study aims to model the waiting times for queues in selected banks within Eldoret town, Kenya. The latter component was put under D/D/1 framework and therein its mean derived while the stochastic component was put under the M/M/c framework. Harmonization of the moments of the deterministic and the stochastic components was done to come up with the mean of the overall bank queue traffic delay. The simulation was performed using MATLAB for traffic intensities ranging from 0.1 to 1.9. The results reveal that both deterministic and the stochastic delay components are compatible in modelling waiting time. The models also are applicable to real-time bank queue data whereupon simulation, both models depict fairly equal waiting times for server utilisation factors below 1 and an infinitely increasing delay at rho greater than 1. In conclusion, the models that estimate waiting time were developed and applied on real bank queue data. The models need to be implemented by the banks in their systems so that customers are in a position to know the expected waiting time to be served as soon as they get the ticket from the ticket dispenser.

Malaria remains a major infectious disease that affects millions of people. Once infected with Plasmodium parasites, a host can develop a broad range of clinical presentations, which result from complex interactions between factors derived from the host, the parasite and the environment. Malaria has historically been a very serious health problem and currently poses the most significant threat to the health of Masinde Muliro University of Science and Technology students, data shows that more than 70% percent of pediatric cases are due to malaria. Methodology: Hence, the study aimed to fit malaria incidences dataset for the period 1st January, 2013 to 31st December, 2015. Data on monthly malaria incidence was obtained from the Masinde Muliro University of Science and Technology health service. Gamma, Weibull and Lognormal Distributions were employed to fit the malaria incidence dataset using R-software. Results: High malaria incidences were observed in the months of August, September and November. AIC values results showed that lognormal distribution had the lowest AIC value of 185.9875 followed by the Gamma distribution with a value of 187.8815 and then the Weibull distribution with a value of 188.7271. This confirmed the lognormal distribution to be the best fitting distribution for the malaria incidence dataset Conclusion: The Poisson regression model did not accurately fit the data on malaria incidences due to over dispersion in the data but lognormal distribution was a better fit compared to gamma and Weibull distribution.