Mathematical models for chemically reacting systems have high degrees of freedom (very large) and are computationally expensive to analyse. In this discussion, we present and analyse a model reduction method that is based on stoichiometry and mass balances. This method can significantly reduce the high degrees of freedom of such systems. Numerical simulations are undertaken to validate and establish efficiency of the method. A practical example of acid mine drainage is used as a test case to demonstrate the efficacy of the procedure. Analytical results show that the stoichiometrically-reduced model is consistent with the original large model, and numerical simulations demonstrate that the method can accelerate convergence of the numerical schemes in some cases.
Background: Coronavirus disease 2019 (COVID-19) is a pandemic that has affected the daily life, governments and economies of many countries all over the globe. Ghana is currently experiencing a surge in the number of cases with a corresponding increase in the cumulative confirmed cases and deaths. The surge in cases and deaths clearly shows that the preventive and management measures are ineffective and that policy makers lack a complete understanding of the dynamics of the disease. Most of the deaths in Ghana are due to lack of adequate health equipment and facilities for managing the disease. Knowledge of the number of cases in advance would aid policy makers in allocating sufficient resources for the effective management of the cases. Methods: A predictive tool is necessary for the effective management and prevention of cases. This study presents a predictive tool that has the ability to accurately forecast the number of cumulative cases. The study applied polynomial and spline models on the COVID-19 data for Ghana, to develop a generalized additive model (GAM) that accurately captures the growth pattern of the cumulative cases. Results: The spline model and the GAM provide accurate forecast values. Conclusion: Cumulative cases of COVID-19 in Ghana are expected to continue to increase if appropriate preventive measures are not enforced. Vaccination against the virus is ongoing in Ghana, thus, future research would consider evaluating the impact of the vaccine.
Background: Recent global reports show that the number of Tuberculosis (TB) cases or deaths is declining, however, the rate of decline is not adequate to meet the World Health Organization's (WHO's) mitigation. TB remains a public health problem in Ghana with a significant economic and health burden on citizens and health infrastructure. Aims: Consequently, there is a need for further studies about the disease aimed at accelerating the rate of decline in cases. Methods: In this article, we study the spatio-temporal characteristics of TB in Ghana, using data obtained from Ghana National Tuberculosis Programme (NTP) for the 10 regions of Ghana, collected over a six-year period. Bayesian spatial and space-time regression models are used to map the risk of TB infections across the nation, in time and space. The study also examines some baseline predictors of TB infections to ascertain their effects on the TB risk. Results: Our study results showed that hot-spots of TB cases are observed in the Upper East, Upper West, Volta, Western, and Central regions and low risk in the Northern, Ashanti, Greater Accra, Brong Ahafo, Eastern and Western regions. We observed clustering of risk between neighboring regions. TB cure rate, TB success rate, knowledge about TB, awareness that TB is airborne, HIV prevalence, percentage of literacy, high income are important predictors of TB detection across the 10 regions of Ghana. Conclusions: Most regions in Ghana have similar TB risk. Efforts for more TB cases detection should be encouraged to increase TB success and cure rate which will lead to substantial decrease in TB spread. There is the need for provision of adequate health facilities with easy access to these facilities irrespective of your income status to bridge the gap between TB cases among the poor and the rich. TB cases are expected to grow exponentially in countries with low success and cure rate. Finally, for a substantial TB cases reduction, there is the need to adopt measures that will increase TB cases detection, TB success and cure rates, TB awareness, knowledge about how TB spread as well adequate health facilities with easy access.
Background: The number of Tuberculosis (TB) cases or deaths is declining, however, the rate of decline is not adequate to meet the World Health Organization's (WHO's) mitigation. TB remains a public health problem in Ghana with a significant economic and health burden on its citizens and health care system. Consequently, there is a need for further studies about the disease aimed at accelerating the rate of decline in cases. Methods: The spatio-temporal characteristics of TB in Ghana using Bayesian spatial and spatio-temporal regression models was analysed in this study. Data were obtained from Ghana National Tuberculosis Programme (NTP) for the 10 regions of Ghana, collected over a six-year period. The study also examines some baseline predictors of TB infections to ascertain their effects on the TB risk across the ten regions in Ghana. Results: Hot-spots of TB cases are observed in the Upper East, Upper West, Volta, Western, and Central regions and low risk in the Northern, Ashanti, Greater Accra, Brong Ahafo, Eastern and Western regions. The results indicated a clustering of risk between neighboring regions. TB cure rate, TB success rate, knowledge about TB, awareness that TB is airborne, HIV prevalence, percentage of literacy, and high income are important predictors of detection for this disease across the ten regions of Ghana. Conclusion: Most regions in Ghana have similar TB risks. A substantial reduction in TB cases requires measures that will increase detection, success and cure rates, awareness, knowledge about how this disease spreads as well adequate health facilities with easy access.
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