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A deterministic model was formulated and employed in the analysis of the dynamics of tuberculosis with a keen emphasis on vaccination and drug resistance as the first line of treatment. It was assumed that some of the susceptible population were vaccinated but with temporal immunity. This is due to the fact that vaccines do not confer permanent immunity. Moreover, part of the infected individual after treatment grows resistance to the drug. Infective immigrants were also considered to be part of the population. The basic reproductive number for the model is estimated using the next-generation matrix method. The equilibrium points of the TB model and their local and global stability were determined. It was established that if the basic reproductive number was less than unity R 0 < 1 , then the disease free equilibrium is stable and unstable if R 0 > 1 . Furthermore, we investigated the optimal prevention, treatment, and vaccination as control measures for the disease. As the objective functional was optimised, there have been a significant reduction in the number of infections and an increase in the number of recovery. The best control measure in combating tuberculosis infections is prevention and vaccination of the susceptible population.

Contact tracing has become one of the most useful tools for fighting the novel Corona Virus (COVID-19) pandemic worldwide. The underlining philosophy of contact tracing is determining people who have been in contact with infected persons and thus isolate them from becoming agents of onward transmission of the virus. Slow tracing of contacts and inconsistent or inaccurate information provided by patients usually leads to the spread of the virus along a trajectory at the healthcare systems' blindside. This has led to the proposal of app-based contact tracing solutions. This paper proposes an SQL-based framework that transforms simple interaction data entries into interaction graphs and applies graph theory to prioritize the contact tracing process. The framework returns nodes or individual IDs together with values called Risk_Points to enable individuals' selection for isolation and treatment. Results on simulated data show that the proposed framework can help slow the virus's rate of transmission.

A disease can be defined as an adverse change from a normally functional state of the living body usually characterized with or accompanied with some signs and symptoms which is differing in nature from physical injury. A pandemic is the worldwide spread of a new disease. COVID-19 is one of the global pandemic that emerged in Wuhan, China, in December 2019 and has since then spread over through the world. In Ghana, the first case of COVID-19 was reported in March 14, 2020 and has increased from just one case to over 29000 cases with over 150 deaths as at July 23, 2020. This study focuses on the estimation of the basic reproductive number, R0 using the Next Generation Method (NGM) approach. COVID-19 data in Ghana was collected and parameters were estimated using the Least-Squares Method. The basic reproductive number of Ghana is estimated to be 2.52 whilst the R0 ranges between 1.47 − 2.65 for transmission rates of 0.5 − 0.9.

Campylobacter genus is the bacteria responsible for campylobacteriosis infections, and it is the commonest cause of gastroenteritis in adults and infants. The disease is hyperendemic in children in most parts of developing countries. It is a zoonotic disease that can be contracted via direct contact, food, and water. In this paper, we formulated a deterministic model for Campylobacteriosis as a zoonotic disease with optimal control and to determine the best control measure. The nonstandard finite difference scheme was used for the model analysis. The disease-free equilibrium of the scheme in its explicit form was determined, and it was shown to be both locally and globally asymptotically stable. The campylobacteriosis model was extended to optimal control using prevention of susceptible humans contracting the disease and treatment of infected humans and animals. The objective function was optimised, and it was established that combining prevention of susceptible humans and treatment of infected animals was the effective control measure in combating campylobacteriosis infections. An analysis of the effects of contact between susceptible and infected animals as well susceptible and infected humans was conducted. It showed an increase in infected animals and humans whenever the contact rate increases and decreases otherwise. Biologically, it implies that campylobacteriosis infections can be controlled by ensuring that interactions among susceptible humans, infected animals, and infected humans is reduced to the barest minimum.

In microgrid operation, one of the most vital tasks of the system control is to wiselydecide between selling excess power to the local grid or charge the Battery Energy Storage System (BESS). Our study uses Mixed-Integer Linear Programming to investigate the impact of storage system on the operational cost of a microgrid. The results suggested that the presence of BESS would relieve the pressure on the utility grid but not the cost of electricity due to the expensive nature of the storage plant. In view of this, it will be more beneficial to sell excess renewable generated power to the utility grid than to invest in a storage system for larger microgrids.

Listeriosis is an illness caused by the germ Listeria monocytogenes. Generally, humans are infected with listeriosis after eating contaminated food. Listeriosis mostly affects people with weakened immune systems, pregnant women and newborns. In this paper, a model describing the dynamics of Listeriosis is developed and analysed using ordinary differential equations. The model was analysed both quantitatively and qualitatively for its local and global stability, basic reproductive number and parameter contributions to the basic reproductive number to understand the impact of each parameter on the disease spread. The Listeriosis model has been extended to include time dependent control variables such as treatment of both humans and animals, vaccination and education of humans. Pontryagin’s Maximum Principle was introduced to obtain the best optimal control strategies required for curbing Listeriosis infections. Numerical simulation was performed and the results displayed graphically and discussed. Cost effectiveness analysis was conducted using the intervention averted ratio (IAR) concepts and it was revealed that the most effective intervention strategy is the treatment of infected humans and animals.

Streptococcus pneumonia is one of the leading causes of mobility and mortality in children under 6 years and the elderly especially in developing countries in which Ghana, the study area is not an exception.In this paper, a model of the spread and control of bacterial pneumonia that include symptomatic carriers, asymptomatic carriers and vaccination is formulated and analyzed to determine the effect of the vaccination intervention.Analysis of the system show that the disease free equilibrium is stable if and only if the basic reproductive number R 0 1 . For R 0 ≥ 1 , the endemic equilibrium is globally stable and the disease persist. Numerical simulation on the system show that with effective vaccine intervention pneumonia infection can be eradicated in the long term.

Anthrax is an infection caused by bacteria and it affects both human and animal populations. The disease can be categorized under zoonotic diseases and humans can contract infections through contact with infected animals, ingest contaminated dairy and animal products. In this paper, we developed a mathematical model for anthrax transmission dynamics in both human and animal populations with optimal control. The qualitative solution of the model behaviour was analyzed by determining Rhv, equilibrium points and sensitivity analysis. A vaccination class was incorporated into the model with waning immunity. Local and global stability of the model’s equilibria was found to be locally asymptotically stable whenever Rhv Rhv. It was revealed that reducing animal and human interaction rate, would decrease Rhv. We extended the model to optimal control in order to find the best control strategy in reducing anthrax infections. It showed that the effective strategy in combating the anthrax epidemics is vaccination of animals and prevention of humans.

In Ghana, the majority of reliable electricity is generated in centralized plants. This type of electricity generation structure undoubtedly contributes to the economic rise in electricity tariffs and transmission losses due to the operational cost of such plants and their vast distances from the communities respectively. In this paper, Linear Programming was used to nd the optimal power dispatch of a decentralized grid-connected photovoltaic system in the form of a microgrid for a minimum cost of electricity. The fundamental LP problem was optimized in AMPL (A Modeling Language for Mathematical Programming) properly employing the CPLEX solver. In the case study, the involvement of microgrid in the energy sector convincingly demonstrated a daily cost of GHS63,426.23 in the rst ve years accurately representing 18% potential reduction. This cost reduction will be increased tremendously to 75% in subsequent years. This is a lower energy bill as compared to the bill of the existing electricity structure.

Ghanaian governments have made some social interventions in order to reduce risks associated with pregnancy and child delivery. However, most pregnant women do not seek maternal care. Previous studies have examined factors contributing to maternal care services utilization in Ghana using national data which limit such study applicability in some areas with specific background characteristics. These studies have mostly limited it to rural areas where the utilization is very low. This study seeks to bridge the gaps identified by exploring the factors which influence maternal care utilization in urban and rural communities in the Brong Ahafo Region of Ghana. The Chi-Square test of association and the logistic regression models are used to analyze data obtained from the 2014 Ghana Demographic and Health Survey (DHS). The data analyses were carried out using R and STATA softwares. The results revealed that women with at least 5 children were less likely (OR = 0.374, 95% CI: 0.173 - 0.796) to utilize antenatal care compared to those who had less than five live births. Educated women are three times likely (95% CI: 1.929 - 5.257) to deliver at a health facility compared to uneducated women. Women from the rich wealth quintile were nearly 16.9 times more likely (95% CI: 4.816 - 107.124) to deliver in a health facility compared to those from the poor wealth quintile. On the other hand, residing in rural communities makes it less likely (OR = 0.569, 95% CI: 0.350 - 0.913) for women to receive postnatal care within 2 months of delivery compared to living in urban communities. This study has demonstrated that maternal educational level plays a crucial role in maternal health care service utilization in the region. Therefore, government policies and programs aimed at providing more educational opportunities for girls in the region should be reinforced.

In this paper, we assessed volatility of Ghana’s inflation rates for 2000 to 2018 using the auto-regressive conditionally heteroskedasticity (ARCH), generalized ARCH (GARCH), and the exponential GARCH (EGARCH) models. The inflation data were obtained from the Ghana Statistical Service (GSS). The proposed model should be able to provide projections of inflation volatility from 2019 and beyond. The results showed that higher order models are required to properly explain Ghana’s inflation volatility and the EGARCH(12, 1) is the best fitting model for the data. The EGARCH(12, 1) model is robust to model and forecast volatility of inflation rates. Also, the results suggest that we are forecasting increasing volatility and there is increasing trend in general prices of goods and services for 2018 and beyond. The forecasts figures revealed that Ghana’s economy is likely to be unstable in 2018 and 2019. This study therefore recommends that policy makers and industry players need to put in place stringent monetary and fiscal policies that would put the anticipated increase in inflation under control. The models were implemented using R software.

The collection of solid waste from third class communities in most devel-oping countries is by skip containers, however, the location of these facilities has been done arbitrary without any mathematical considerations as to the number of customers the facility is serving, the distance one has to travel to access it and thereby making some of these residences to dump their refuse in gutters, streams and even burn them. In this paper we proposed an improved probabilistic distance, capacity clustering location model which takes into consideration the weight of solid waste from a customer and the capacity of the skip container to locate the skip container to serve a required number of customers based on the capacity constraint of the container. The model was applied on a real world situation and compared with the existing practice in terms of average distance customers had to travel to access the facility. Our results gave a well shorter average travel distance by customers, gave a number of skip containers needed in an area based on their waste generation per capita.

Students pick up the perception that mathematics is abstract and therefore, the learning of mathematics would yield to them no benefit. With their attitude towards mathematics modelled and their interest for mathematics impacted by this automatic generated perception, they may never again appreciate the beauty of mathematics. In this paper, the researchers used structural equation modeling (SEM), to investigate the variables that affect students’ interest, among the variables, students’ confidence and motivation. The foregoing variables were conceptualized to have a direct effect on students’ interest in mathematics, whilst mathematics anxiety and students’ knowledge of the usefulness of mathematics were conceptualized to have indirect effects on their interest in mathematics moderated by students’ confidence and motivation. The result showed that significantly students’ confidence directly affects students’ interest in the learning of mathematics and there is a direct relationship between confidence and motivation. A student’s knowledge about the usefulness of mathematics indirectly increases the student’s interest in mathematics.

In this paper, we employed a deterministic model in the analysis of the dynamics of Tuberculosis with a keen interest in vaccination and drug resistance as the first line of treatment. It was assumed that some of the susceptible population were vaccinated but with temporal immunity. This is due to the fact that vaccines do not confer permanent immunity. Moreover, Part of the infected individual after treatment grow resistance to the drug. Infective immigrants were also considered to be part of the population. The basic reproductive number for the model is estimated using the Next Generation Matrix method. The equilibrium points of the TB model and their local and global stability were determined. It was established that if the basic reproductive number was less than unity (R 0 1. Furthermore, we investigated the optimal prevention, treatment and vaccination as control measures for the disease. It was established that the best control measure in combating Tuberculosis infections is prevention and vaccination of susceptible population.

Tuberculosis (TB) is a major public health concern in many developing countries. Mycobacterium tuberculosis is a major cause of morbidity and mortality in Africa. Tuberculosis infection is curable but in the cases of incomplete treatment, the remains of Mycobacterium tuberculosis in the human body usually results in the bacterium developing resistant to antibiotics. In this study we developed a model that explains the dynamics of tuberculosis infection in the presence of drug resistance. The basic reproduction number of the model was computed using the next generation matrix approach. The disease free equilibrium and endemic equilibrium were obtained and their stability analysis were carried out. It revealed that they were locally and globally asymptotically stable whenever the reproductive number was less than unity. Numerical simulation of the TB model was conducted and the result revealed that contact rate can reduce or eliminate the sensitive strain and reduce drug resistant of tuberculosis.

Limited resources hinder the control and prevention of hepatitis B in some communities in Ghana and the Brong Ahafo region is no different. In this paper, we formulated a model that explains the spread of hepatitis B and suggested an intervention to minimise its effect. We analysed the local and global stability of the disease as well as the basic reproduction number. It was established that the disease is locally asymptotically stable whenever the basic reproduction number is less than unity and unstable otherwise. Optimal control theory was incorporated to determine the best control strategy in combating the spread of hepatitis B in the environment. The following control strategies were employed; treatment, vaccination and prevention. The results of the numerical simulation showed that the best optimal control strategy in combating the spread of the infection was vaccination of susceptible and treatment of the infected population.

In this paper, a deterministic model for the co-dynamics of Anthrax and Listerios diseases was formulated to investigate the qualitative and quantitative relationship of both diseases by incorporating prevention and treatment controls. The basic reproduction number, stability, existence and equilibria of each disease was investigated separately. The Anthrax-Listeriosis co-dynamics model was analysed and it the idea of backward bifurcation existed. The impact of Anthrax infection on the transmission of Listeriosis was determined. The Anthrax-Listeriosis co-dynamics model was extended and included time dependent control variables. Pontryagin’s Maximum Principle was used to obtain the optimal control strategies needed for eradication of Anthrax-Listeriosis infections. We performed the numerical simulation of the co-dynamics model in order to give the quantitative implications of the results. It was established that Anthrax infection can be attributed to increased risk of Listeriosis but Listeriosis infection is not associate with the risk of Anthrax. Effective control of Anthrax means incorporating both the intervention srategies of Anthrax and Listeriosis.

Streptococcus pneumonia is one of the leading causes of mobility and mortality in children under 6 years and the elderly especially in developing countries in which Ghana, the study area is not an exception.In this paper, a model of the spread and control of bacterial pneumonia that include symptomatic carriers, asymptomatic carriers and vaccination is formulated and analyzed to determine the effect of the vaccination intervention.Analysis of the system show that the disease free equilibrium is stable if and only if the basic reproductive number R0

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.

Assignment of jobs to workers, contract to contractors undergoing a bidding process, assigning nurses to duty post, or time tabling for teachers in school and many more have become a growing concern to both management and sector leaders alike. Hungarian algorithm has been the most successful tool for solving such problems. The authors have proposed a heuristic method for solving assignment problems with less computing time in comparison with Hungarian algorithm that gives comparable results with an added advantage of easy implementation. The proposed heuristic method is used to compute some bench mark problems.

There is a growing concern about the rise of violence on the streets and the media around the world, the possibility of an individual to be affected by violence at home is an undeniable reality facing most families around the globe. Domestic violence can take many forms including physical, psychological, sexual, and economic. It not only has devastating physical and psychological consequences on its victims, but can seriously damage the foundations of the family leading to its disintegration. There is therefore the need to find out the trend of spread in our communities, since it has the potential to slow down productivity in any society. The study used a simple continuous model for the spread of Domestic Violence, using Ordinary Differential Equations. A mathematical model is inspired from the spread of Domestic Violence in Tamale Metropolis in which the interaction of the widespread is likely to be minimized. A modeling technique of Abusive, Susceptible and Violence Victims (ASV), similar to the Susceptible, Infectious and Recovered (SIR) model in Epidemics, is used for formulating the spread of Domestic Violence as a system of Differential Equations. The system of Differential Equations is analyzed by linearization of nonlinear systems and nondimensionlization to predict the behaviour of the spread of Domestic Violence.

The poultry industry has a significant importance on national economy. It is a popular industry for the small holders with tremendous contribution to Gross Domestic Product (GDP) and employment creation. Poultry feed cost represents over sixty (60) percent of the total cost of poultry production; consequently, efficient feed formulation practice is required for a sustainable poultry industry. Many Ghanaian poultry farmers, however, employ inefficient methods like rule of thumb, experiences, and intuition to handle feed formulation problem. This paper presents a deterministic linear programming model to solve blending problem facing poultry farmers, using locally available feed ingredients from the Ghanaian poultry industry. In the model, we shall minimize cost of producing a particular diet and maintain the ingredient. Over 3% reductions in the cost of producing broiler starter and finisher feed formulation compared to the existing method on the farm was achieved.

Water is considered as a lifeline of all living things, especially humans; hence its availability is a critical component in the measurement of human wellbeing through the Human Development Index (HDI). Its production and distribution in Ghana, particularly in the Hohoe Municipality of the Volta Region is a challenge. This study seeks to identify the best-fit time series model to the water consumption data in the Hohoe Municipality and to forecast water consumption in the Municipality. This underpins the development of a time-series model for forecasting water consumption levels of the residents, institutions and businesses in the municipality. Several time series models, including AR, MA, ARMA, ARIMA and SARIMA were fitted to the data, and it emerged that the most adequate model for the data was ARIMA (2, 1, and 2). The model was then used to forecast the consumption for the next four years, to advise Ghana Water Company Limited in the municipality to meet the demand of the people.