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.
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.
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.
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.
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 hv R , 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 1 hv R < and unstable otherwise. Analysis of parameter contribution was conducted to determine the contribution of each to hv R. It was revealed that reducing animal and human interaction rate, would decrease hv R. 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.
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. Keywords: Abusive, domestic violence, epidemic model, infectious and recovered susceptible and violence victims.
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