Background: Tuberculosis (TB) is a deadly infectious disease caused by Mycobacteria tuberculosis. Tuberculosis as a chronic and highly infectious disease is prevalent in almost every part of the globe. More than 95% of TB mortality occurs in low/middle income countries. In 2014, approximately 10 million people were diagnosed with active TB and two million died from the disease. In this study, our aim is to compare the predictive powers of the seasonal autoregressive integrated moving average (SARIMA) and neural network auto-regression (SARIMA-NNAR) models of TB incidence and analyse its seasonality in South Africa. Methods: TB incidence cases data from January 2010 to December 2015 were extracted from the Eastern Cape Health facility report of the electronic Tuberculosis Register (ERT.Net). A SARIMA model and a combined model of SARIMA model and a neural network auto-regression (SARIMA-NNAR) model were used in analysing and predicting the TB data from 2010 to 2015. Simulation performance parameters of mean square error (MSE), root mean square error (RMSE), mean absolute error (MAE), mean percent error (MPE), mean absolute scaled error (MASE) and mean absolute percentage error (MAPE) were applied to assess the better performance of prediction between the models. Results: Though practically, both models could predict TB incidence, the combined model displayed better performance. For the combined model, the Akaike information criterion (AIC), second-order AIC (AICc) and Bayesian information criterion (BIC) are 288.56, 308.31 and 299.09 respectively, which were lower than the SARIMA model with corresponding values of 329.02, 327.20 and 341.99, respectively. The seasonality trend of TB incidence was forecast to have a slightly increased seasonal TB incidence trend from the SARIMA-NNAR model compared to the single model. Conclusions: The combined model indicated a better TB incidence forecasting with a lower AICc. The model also indicates the need for resolute intervention to reduce infectious disease transmission with co-infection with HIV and other concomitant diseases, and also at festival peak periods.

Aim This is an applied study to investigate the association of selected socio-economic and demographic factors with the relative risk of tuberculosis (TB) prevalence in the Eastern Cape Province of South Africa and to produce disease maps for the spatial outlines of the disease in the province. Subjects and methods This is an ecological spatial study of TB prevalence in the Eastern Cape, a province in South Africa, during the year 2014. Three socio-economic indicators and three demographic factors, all calculated per sub-district, were used to assess their relationship with tuberculosis prevalence, using a Poisson regression model. Results From the analysis, the best model included all the selected covariates of the proximal model with the spatial random effects. The improvement in the goodness-of-fit statistic when the spatial structure was included confirms the spatial pattern of population density and average household size. Conclusion The idea of assessing both the impact of covariates at the ecological level and spatial outlines in the same context should be encouraged in epidemiology to help with creating epidemiological surveillance systems (ESS) on a provincial basis for planning interventions and improvement of control programme efficiency.

The basic model usually used in disease mapping is the Besag, York and Mollie (BYM) model, which combines two random effects, a spatially structured and a spatially unstructured random effect. Bayesian Conditional Autoregressive (CAR) model is a disease mapping method that is commonly used for smoothening the relative risk of any disease as used in the Besag, York and Mollie (BYM) model. This model (CAR), which is also usually assigned as a prior to one of the spatial random effects in the BYM model, successfully uses information from adjacent sites to improve estimates for individual sites. However, it has been pointed out that there exist some unrealistic or counterintuitive consequences on the posterior covariance matrix of the CAR prior for the spatial random effects. In the conventional BYM (Besag, York and Mollie) model, the spatially structured and the unstructured random components cannot be seen independently, and which challenges the prior definitions for the hyperparameters of the two random effects. Therefore, the main objective of this study is to utilize some spatial CAR models for flexibility as applied to tuberculosis (TB) disease mapping. The extended Bayesian spatial CAR model is proved to be a useful and a little robust tool for disease modeling and as a prior for the structured spatial random effects because of the inclusion of an extra hyperparameter. A Bayesian modeling approach by the Integrated Nested Laplace Approximation method (INLA) is used to estimate model parameters and comparison was made by the deviance information criterion (DIC).

We investigated the finite properties as well as the goodness of fit test for the cubic smoothing spline selection methods like the Generalized Maximum Likelihood (GML), Generalized Cross-Validation (GCV) and Mallow CP criterion (MCP) estimators for time-series observation when there is the presence of Autocorrelation in the error term of the model. The Monte-Carlo study considered 1,000 replication with six sample sizes: 30; 60; 120; 240; 480 and 960, four degree of autocorrelations; 0.1; 0.3; 0.5; and 0.9 and three smoothing parameters; lambdaGML= 0.07271685, lambdaGCV= 0.005146929, lambdaMCP= 0.7095105. The cubic smoothing spline selection methods were also applied to a real-life dataset. The Predictive mean square error, R-square, and adjusted R-square criteria for assessing finite properties and goodness of fit among competing models discovered that the performance of the estimators is affected by changes in the sample sizes and autocorrelation levels of the simulated and real-life data set. The study concluded that the Generalized Cross-Validation estimator provides a better fit for Autocorrelated time series observation. It is recommended that the GCV works well at the four autocorrelation levels and provides the best fit for time-series observations at all sample sizes considered. This study can be applied to; non –parametric regression, non –parametric forecasting, spatial, survival and econometric observations.

Introduction: The need to model the impact of some demographic indicators on the frequency of household visits to healthcare centres in Nigeria's community is very important for preventing and spreading community diseases. This study aimed to investigate the effect of the patents' age, gender, marital status, type of illness and amount spent on the frequency of visits to community health care centres in Nigeria and to compared Negative Binomial Regression (NBR) and Generalized Poisson Regression (GPR) models to determine the preferred count regression model for the number of household visits to health centres in some communities in Nigeria. Methods: Survey of 132640 households in some Nigeria communities obtained from the 2018/2019 Nigeria Living Standard Survey (NLSS) were extracted from the National Bureau of Statistics (NBS) in collaboration with the World Bank. The Negative Binomial and Generalised Poisson regression models were used to investigate the five demographic variables on the frequency of visit to the community health centres. The performance of the count regression model was assessed using the Chi-square -2log Likelihood Statistic (2logL), Akaike Information Criterion (AIC) and Bayesian Information Criterion (BIC) selection criteria. Results: Findings from the study showed that the type of illness and amount spent has a significantly positive effect on the number of household members' visits to the community health care centres in Nigeria while age, gender, and marital status was discovered to have a negative effect on the number of household members' visits to the community health care centres in Nigeria. Conclusion: The Nigeria Government, health centre management and community healthcare service providers' need to be aware that the amount spent and the nature of illness determines the level of health care services utilisation in the Nigeria community, hence the need for the drastic reduction in charges to encourage a household visit to the community health centres whenever the need arises.