ghanaopendata/ghanaian-research-english huggingface dataset:
Mathematical model for the location of dumpsite in the Kumasi Metropolis

The location of dumpsite plays an important part in the waste disposal industry. In particular, a dumpsite site that is located based on minimum operational cost will further enhance efficiency in the midst of competing demands. The study aims at modelling the location of dumpsite from the economic point of view while comparing three dumpsites in the Kumasi metropolis namely: Dompoase, Amakom and Kronom. The Project involves the use of optimization techniques, specifically the transportation model, which is a special case of a linear programme. Data collected from the Kumasi Waste Management Department is used to set up and solve the transportation problem, the solution of which led to the choice of the dumpsite with the least cost. The transportation algorithm yielded a least cost for Dompoase as ¢76,266,000.00 per month, Amakom as ¢50,525,400.00 per month and Kronon of ¢77,648,000.00 per month. Amakom dumpsite has the least cost operationally amongst the three locations and therefore is the most preferred location from the economic point of view. The model when subjected to sensitivity analysis is robust within the limits of ±10% variation cost data. This model can be used not only for the location of dumpsite for a number of possible alternatives but is also recommended as a waste management tool.

Source: KNUST
A Mathematical Model of a Suspension Bridge Case Study: Adomi Bridge

The Lazer – McKenna mathematical model of a suspension bridge applied to the Adomi Bridge in Ghana is presented. Numerical methods accessible in commercially available Computer Algebraic System “MATLAB” are used to analyse the second order non-linear ordinary differential equation. Simulations are performed using an efficient SIMULINK scheme, the bridge responses are investigated by varying the various parameters of the bridge

Source: KNUST
A Mathematical Model for the Spread of Malaria Case Study: Chorkor-Accra

Malaria is an infectious disease transmitted between humans through mosquito bites that kill about two million people a year. Many infectious diseases including malaria are preventable, yet they remain endemic in many communities like Chorkor in Accra due to lack of proper, adequate and timely control policies. The main goal of this thesis is to develop a mathematical model for the transmission of malaria. It has been shown that the model has unique disease-free and endemic equilibria. A mathematical model for malaria is developed using ordinary differential equations. We analyze the existence and stability of disease-free and endemic malaria (malaria persisting in the population) equilibria. Key to our analysis is the definition of a reproductive number R_0(the number of the new infections caused by one individual in an otherwise fully susceptible population, through the duration of the infectious period. The methods for controlling any infectious disease include a rapid reduction in both the infected and susceptible populations as well as a rapid reduction in the susceptible class if a cure is available. For diseases of malaria where there are no vaccines, it is still possible to reduce the susceptible group through a variety of control measures. The disease-free equilibrium is locally asymptotically stable, if R_0≤1, and that the endemic equilibrium exist provided R_0>1. Further simulation of the model clearly shows that, with proper combination of treatment and concerted effort aimed at prevention, malaria could be eliminated from our society. In fact, effective treatment offered to about fifty percent of the infected population together with about fifty percent prevention rate is all that is required to eliminate the diseases

Source: KNUST
Mathematical Model of Cerebrospinal Meningitis in Obuasi Municipality of Ashanti Region, Ghana

Meningococcal disease is a serious health threat in the human body which begins rapidly with a relative high case fatality rate particularly in the absence of treatment and thus is a priority when it comes to prevention. Delayed treatment can lead to death or invasive meningococcal disease which causes complications such as neurologic disorder, loss of limbs, hearing loss and paralysis even in survivors. In this work, therefore the main objective is to investigate the epidemiology of meningococcal meningitis in Obuasi municipality to develop a model for predict the spreading and combating of cerebrospinal meningitis within the municipality. Using SEIR model we employed the simple Susceptible-Exposed-Infectious and Recovered (SEIR) model to compute those affected ones. The model equations are solved numerically with MatLab that employ Runge-Kutta method. Simulation and sensitivity analysis are then performed on the model equations to determine the effect of the parameter values on the spread of the disease. The simple SEIR model with and without vaccinations were used to explain the spread of the CSM in the municipality. The model has two equilibrium states: the disease-free equilibrium and the endemic equilibrium. The basic reproductive number (R_0) of CSM with and without vaccination were calculated to be 0.148 and 2.0 respectively. The model conclude that, vaccination interventions have a significant impact on the rate of transmission of CSM and other tropical diseases moreover, mode of transmission of CSM in the municipality is commonly spread through the hazardous effect of the mining waste and its operations. Finally, personal hygiene plays a major role in terms of an outbreak of an epidemic.

Source: KNUST
Mathematical model of COVID‑19 dynamics in the presence of multiple controls

The coronavirus disease 19 (COVID-19), caused by the Severe Acute Respiratory Syndrome Coronavirus 2 (SARS-COV-2), is an infectious disease constituting the most significant challenge to human and socio-economic development across the globe. Many studies have been conducted to gain more knowledge on the dynamic spread of SARS-COV-2 in the community of people. In this study, a new mathematical model made up of a system of non-linear ODEs is designed and meticulously analyzed to understand the dynamics of transmission of COVID-19. Specific necessary properties exhibited by the COVID-19 model are examined through the theory of non-negativity and boundedness of solutions. The threshold parameter measuring the invasion potential of COVID-19 in the population is worked out by employing the Next Generation Matrix approach. The model is shown to have two endemic equilibria whenever basic reproduction number R0 < 1 . The analysis ofthe endemic equilibrium stability is explored using a suitably constructed Lyapunov function. It is shown that the COVID-19 model is globally asymptotically stable whenever the associated basic reproduction number is beyond unity. The Latin Hypercube Sampling or Partial Rank Correlation Coefficient is utilized to examine how parameter changes affect the COVID-19 spread in the population. Furthermore, the study considers six optimal control interventions to flatten the curve of the coronavirus pandemic in society. Numerical experiments of the COVID-19 model are executed in MatLab to corroborate the qualitative analysis of the model.

Source: KNUST
A Mathematical Model of Project Selection under Multi-Period Capital Rationing: Case Study of Offinso Municipal Assembly Projects in Ghana

Project selection is the process of choosing a project or set of projects to be implemented by an organization. Since projects in general require a substantial investment in terms of money and resources, both of which are limited, it is of vital importance that the projects that an organization selects provide good returns on the resources and capital invested. This requirement must be balanced with the need for an organization to move forward and develop. This research work is concerned with the use of Mathematical models, specifically, Integer Programming (IP)and Linear Programming (LP) formulations, for the purpose of selecting feasible projects and maximizing the returns from the batch of projects of some District Assemblies (DAs) and Municipal Assemblies (MAs) in Ghana. The research work was a case study of Offinso Municipal Assembly‟s projects in Ghana. In these models, we maximize the Net Present Value(NPV) and maintain the net discount cash inflow for each project in each period. Sensitivity analysis on the project parameters were also carried out to test the extent to which project selection is sensitive to the changes in the parameters of the models. These facts are supposed to give the Offinso Municipal Assembly (OMA) management some guidance in their considerations of various alternatives with regards to the limited investment capital.

Source: KNUST
Mathematical model of Hepatitis B in the North Tongu District of the Volta Region of Ghana

Hepatitis B spreads in a host population through direct transmission from the parent to the offspring (vertical transmission) and also through contact with infective individuals (horizontal transmission). In this thesis, we consideedr a mathematical model for the infectious disease (Hepatitis B) and developed a model based on the Susceptible-Infected-Recovered (SIR). The North Tongu District of the Volta Region of Ghana was considered as the host population. The district was assumed to have a constant population size. A system of non-linear differential equations was used to model the spread of the disease in the district. We solveed the system numerically using the forth-order Runge-Kutta method. Simulation and sensitivity analyses were also performed on the model equations to determine the effect of different parameter values on the spread of the disease. It was shown that the global dynamics were completely determined by the basic reproductive number R_0. If R_0<1, the disease-free equilibrium is globally stable and the disease always die out. On the other hand, if R_0>1, an endemic equilibrium exists and was globally stable in the interior of the feasible region, and the disease persists at an endemic equilibrium state if it initially exists.

Source: KNUST
Mathematical modeling and optimal control: maximizing yield in submerged alcoholic fermentation

Advances in research into alternative starch sources for industrial production of alcoholic beverages, sorghum, cassava and maize are now being used as cheaper alternatives to imported barley in the brewery industry. In brewing, though involves several unit operations, the fermentation step is regarded as the heart of the entire production where a near optimal environment is desired for microorganisms to grow and produce ethanol. However, the use of fermenters is usually hampered by sub-optimal conditions in terms of yield and productivity, along with the low tolerance of strains to process stresses such as substrate and product toxicity. Attempts to improve the industrial efficacy of fermenters have been in the areas of genetic engineering to improve strain tolerance, but usually involves detailed and unfeasible mechanistic studies. Statistical design of experiments which has also been used often results in local optima due to the relatively small dimensional space covered by the experiments. Mathematical techniques have recorded great successes but proposed solutions however did not consider all degrees of freedom of the problem simultaneously (Inhibiton kinetics, temperature and pH). This thesis presents the modeling of substrate and/or product inhibtion in three different fermentation substrates: sorghum, maize and cassava extracts. At a 99% confidence interval, the pattern of these inhibtions can be described as being a linear or an exponential decrease in ethanol concentration in the case of sorghum, linear and sudden growth stop in the case of maize, linear substrate exponential product, and exponential substrate exponential product in the case of cassava. Optimal control was applied to minimize the effects of such inhibtion in sorghum extracts. Calculus of variation was introduced as a valuable tool to derive and solve the necessary conditions for optimality (optimal temperature and pH profiles). A Simulink model, developed and used for control validation shows an increase in ethanol yield by14.18%, cell growth by 71.96% and a decrease in the residual substrate by 84.77%. Since the model was developed using industrial scale fermentation data, the results obtained in the simulations can satisfactorily represent a real operation unit. From the comparative results presented in the simulations, it is concluded that the proposed strategy can be used in practice to improve the performance of industrial scale alcoholic fermentation.

Source: KNUST
A mathematical model to control the spread of malaria in Ghana

Malaria is a serious health problem in Ghana and is reported by the Ministry of Health to be responsible for more than 44 percent of outpatient visits and approximately 22 percent of deaths in children under the age of five, which means there is a lot of work to be done if the country wants to achieve the goals set by Roll Back Malaria Partnership (RBM), a global initiative that coordinates actions against malaria. The goal of this thesis is to use clinical malaria data from Ghana Health Service to develop a mathematical model to help control the spread of malaria in Ghana in order to perhaps meet the target year given by RBM programme. The model consists of seven non-linear differential equations which describe the dynamics of malaria with 4 variables for humans and 3 variables for mosquitoes. We perform stability analysis of the model and the next generation method is used to derive the basic reproduction number 〖 R〗_0. We have proved that the disease-free equilibrium is locally asymptotically stable if〖 R〗_0<1 and unstable when 〖 R〗_0>1 . The Centre Manifold theorem is used to show that the model has a unique endemic equilibrium which is locally asymptotically stable when 〖 R〗_0<1 . The basic reproduction number for Ghana is found to be R_0=0.8939 . Numerical simulation of the model suggests that the most effective strategy for controlling or eradicating malaria is to combine the use of insecticide-treated bed nets, indoor residual spraying and chemotherapy, but the best strategy is to reduce the biting rate of the female anopheles mosquito through the use of insecticide-treated bed nets and indoor residual spraying since the malaria parasite has developed resistance to some of the antimalarial drugs.

Source: KNUST
Mathematical modeling for the transmission potential of Zika virus with optimal control strategies

In this paper, we formulate a new Zika virus model in light of both mosquito and human transmission along with the human awareness in the host population. Initially, we assumed that the virus is transmitted to humans through a mosquito bite and then transmits to his or her sexual partner. Further, we investigated the mathematical results and stability analysis and proved that the model is asymptotically stable both locally and globally. We applied the Castillo-Chavez approach for establishing global stability. Similarly, we presented the existence of endemic equilibrium and demonstrate that the model is locally and globally asymptotically stable using a suitable Lyapunov function at endemic state, upon backward bifurcation analysis we proposed that no bifurcation exists for our model. The sensitivity analysis is carried out and verified that the probability per biting of the susceptible mosquito with the infected human is the most sensitive parameter. Furthermore, we developed a Zika control model and incorporated three controls. These controls are prevention through bed nets and mosquito repellents, treatment of Zika patients, and the spray of insecticides on mosquitoes. The graphical results of the model with control and without control are obtained through a numerical scheme. The infection caused by the Zika virus would be more efficiently eliminated using the new idea of human awareness and bilinear incidence presented in this paper.

Source: KNUST
Mathematical Modeling of the Epidemiology of Varicella

In this thesis a modified SIR mathematical model on the spread of Varicella (Chickenpox) in Ghana was developed. Here the population is divided into three compartments: the susceptibles, the infectives, and the recovered. The resulting system of non-linear differential equations was analysed, thus in respect of the stability of the equilibrium points. The model focuses on the spread of the disease at the initial stages of the infection when the infected persons are absent and when they are present taking into consideration birth rate and natural death rate. The study is based on the assumption that the population of Ghana is constant, and the natural death rate was assumed to be equal to the birth rate. We then determine how the various compartments react to increasing proportion of persons at the initial stages of their infection. We perform sensitivity analysis on the already estimated model parameters to determine their effect on the reproductive number and at what values of the reproductive number are the disease free and endemic equilibra stable.

Source: KNUST
Mathematical modeling of corruption practices in Ghana: a case study in KNUST campus

Abstract In this thesis, an SCR model is introduced to demonstrate how corruption practices by the workers of KNUST thrives. Based on the data, basic reproductive number was obtained to be three clearly shows that, on the average, a corrupted sta of KNUST is able to in uence three other workers to join the corruption practices in the university. We have determined the corruption-free equilibrium state and its bifurcation analysis shows that it undergoes transcritical bifurcation at where the rate of transition from susceptible into the corrupted class is the same as the sum of rates of departure from the corrupted class. This implies, if the rate of recruitment into the corrupted class from the susceptible is varied positively,then the corruption cancer rises unboundedly. The sensitivity analysis on the basic reproductive number (R0) revealed that, the number of corrupted people in KNUST increase as the rate a corrupted sta recruits from the environment of KNUST increases. The departure from corruption (recovery and departure) rates are inversely proportional to the rate at which the corruption increases, so if it is increased, corruption will decrease in KNUST.

Source: KNUST
Mathematical modeling of two strains tuberculosis and COVID-19 vaccination model: a co-infection study with cost-e􀀀ectiveness analysis

Tuberculosis and COVID-19 co-infection is currently the major issue of public health in many nations, including Ghana. Therefore, to explore the e􀀀ects of the two Tuberculosis strains on COVID-19, we suggest a Tuberculosis and COVID-19 co-infection model. The study also provides the most economical and e􀀀ective control methods to reduce the co-infection of tuberculosis and COVID-19. Based on the behavioral patterns of the two Tuberculosis strains and COVID- 19 reproduction numbers, the stability of the co-infection model is examined. We explore the sensitivity of the parameters to examine the e􀀀ect of the drug- resistant and drug-sensitive strain of Tuberculosis on the co-infection of COVID- 19. We determine the most cost-e􀀀ective and optimal treatment strategies that aim to maximize outcomes while minimizing tuberculosis and/or COVID-19 incidences, cost-e􀀀ectiveness, and optimization approaches. The outcomes of this work contribute to a better understanding of Tuberculosis and COVID-19 epidemiology and provide insights into implementing interventions needed to minimize Tuberculosis and COVID-19 burden in similar settings worldwide.

Source: KNUST
Mathematical Modeling of Transmission Dynamics with Periodic Contact Rate and Control by Different Vaccination Rates of Hepatitis B Infection in Ghana

The paper evidenced that Hepatitis B infection is the world’s deadliest liver infection and Vaccination is among the principal clinical strategies in fighting it. These have encouraged a lot of researchers to formulate mathematical models to accurately predict the mode of transmission and make deductions for better health decision-making processes. In this paper, an SEIR model is used to model the transmission of the Hepatitis B infection with periodic contact rate and examine the impact of vaccination. The model was validated using estimated data in Ghana and simulated in a MATLAB environment. The results showed that the vaccination rate has a great impact on the transmission mode of the Hepatitis B infection and the periodic contact rate may lead to a chaotic solution which could result in an uncontrolled spreading of the infection. It is concluded that even if the vaccination rate is 70%, the infection rate would reduce to the minimum barest so more newborns must be vaccinated.

Source: KNUST
Mathematical modelling of earlier stages of COVID-19 transmission dynamics in Ghana

In late 2019, a novel coronavirus, the SARS-CoV-2 outbreak was identified in Wuhan, China and later spread to every corner of the globe. Whilst the number of infection-induced deaths in Ghana, West Africa are minimal when compared with the rest of the world, the impact on the local health service is still significant. Compartmental models are a useful framework for investigating transmission of diseases in societies. To understand how the infection will spread and how to limit the outbreak. We have developed a modified SEIR compartmental model with nine compartments (CoVCom9) to describe the dynamics of SARS-CoV-2 transmission in Ghana. We have carried out a detailed mathematical analysis of the CoVCom9, including the derivation of the basic reproduction number, 0. In particular, we have shown that the disease-free equilibrium is globally asymptotically stable when 0 < 1 via a candidate Lyapunov function. Using the SARS-CoV-2 reported data for confirmed-positive cases and deaths from March 13 to August 10, 2020, we have parametrised the CoVCom9 model. The results of this fit show good agreement with data. We used Latin hypercube sampling-rank correlation coefficient (LHS-PRCC) to investigate the uncertainty and sensitivity of 0 since the results derived are significant in controlling the spread of SARS-CoV-2. We estimate that over this five month period, the basic reproduction number is given by 0 = 3.110, with the 95% confidence interval being 2.042 ≤ 0 ≤ 3.240, and the mean value being 0 = 2.623. Of the 32 parameters in the model, we find that just six have a significant influence on 0, these include the rate of testing, where an increasing testing rate contributes to the reduction of 0.

Source: KNUST
Mathematical modelling of the transmission dynamics of Marburg virus disease with optimal control and cost-effectiveness analysis based on lessons from Ebola virus disease

Marburg virus, like Ebola, causes haemorrhagic disease with high fatality rates. We developed a deterministic SEIRDVT model incorporating vaccination and treatment to study the disease dynamics. Qualitative analysis revealed a backward bifurcation when R0 = 1, meaning R0 < 1 is insufficient to eradicate the virus. Sensitivity analysis using Latin Hypercube Sampling showed that applying four control measures—screening, prevention, continuous vaccination, and treatment—significantly reduced transmission. The most cost-effective strategy combines prevention, vaccination, and treatment. These findings provide a framework for designing efficient interventions to combat Marburg virus.

Source: KNUST