Determining Important Parameters in Ebola Epidemics

The dynamics of Ebola can best be understood using a mathematical model that determines its dynamics in the community. The model designed in this study explicitly incorporates the latency period, the different transmission compartments, and immigration and emigration effects. The steady states of the system are analysed for existence of equilibria and their stability investigated. From qualitative analysis of the model, it is established that a disease-free equilibrium exists and is stable whe

Investigating Math Self-Efficacy and Math Anxiety Regarding Gender, A-Level Math Entry Grade and Mathematics Achievement

Although mathematics is perceived as an indispensable pre-cursor to success in modern society, many students still grapple with a genuine fear of mathematics and feel anxious when engaging in mathematical tasks. One of the affective factors that can affect math anxiety is learners’ belief in their own ability which is termed self-efficacy. In this study we aimed to investigate how math anxiety and math self-efficacy varied across gender, A-level math entry grade and recent mathematics score and how math anxiety and math self-efficacy related in the context of students in Mayuge District, Uganda. We collected data from 60 advanced level (A-level) mathematics students from two secondary schools in Mayuge District. Their study of mathematics was not compulsory but rather by choice. The participants filled a Mathematics Self-Efficacy and Anxiety Questionnaire (MSEAQ). Data were analyzed using descriptive statistics, independent sample t tests, one-way ANOVA, Pearson’s Linear Correlation Coefficient (PLCC) and linear regression. Descriptive statistics indicated a high level of math self-efficacy and a low level of math anxiety among the students. Independent sample t tests revealed no gender differences in math self-efficacy and math anxiety and ANOVA suggested no differences in math self-efficacy and math anxiety for the A-level math entry grades and recent mathematics scores. PLCC revealed a strong significant negative linear correlation between math self-efficacy and math anxiety with r = -0.782. Meanwhile, regression analysis suggested that math self-efficacy explained 60% of math anxiety among A-level students in Mayuge District. A recommendation was made. Keywords: Entry Grade, Gender, Math Achievement, Math Anxiety, Math Self-Efficacy DOI: 10.7176/JEP/11-26-05 Publication date:September 30th 202

Data driven mathematical models for policy making

This thesis consists of two papers. 1. Betty Nannyonga, D.J.T. Sumpter, J.Y.T. Mugisha and L.S. Luboobi: The Dynamics,causes and possible prevention of Hepaititis E outbreaks. 2. Betty Nannyonga, D.J.T. Sumpter, andStam Nicolis: A dynamical systems approach tosocial and economic development. The first paper deals with a deterministic approach of modelling a Hepatitis E outbreak whenmalaria is endemic in a population. We design three models based on the epidemiology ofHepatitis E, malaria, and the co-infection of both diseases. We t our designed models to datathat was collected in a Hepatitis E outbreak in Kitgum district, Uganda, to estimate parameterssuch as the transmission rate, basic reproduction number and recovery rate of those aected. Inthe tting we pursue two approaches, the logistic approach when the natural mortality is zero,and a detailed tting using PottersWheel Toolbox, when natural mortality is not equal to zero.In both cases, we seek to explore how endemic malaria could aect a Hepatitis E outbreak, andsuch a disease\u92s ability to persist in a population over a long period of time. As a measure ofthe eect of malaria on Hepatitis E transmission, we use a modication parameter such thatwhen the estimated value is greater than unity, then malaria favours Hepatitis E, otherwisewe conclude that it inhibits its spread. In the same paper we attempt to estimate the levelof sanitation required to prevent future outbreaks, in terms of availability of latrines and safedrinking water.In the second paper, we look at the eects of child mortality and average child per woman(fertility rates) on economic development (demographic transition). We use data that is readilyavailable from Gapminder, to extract two dynamical systems, one for child mortality and grossdomestic product (GDP), and the second for child mortality, gross domestic product and averagechild per woman. The models obtained are analyzed numerically for existence and stability. Weuse the Gapminder data to obtain a model that comforms to the demographic transition. Ratherthan using data to justify the assumptions of our models, we use data directly to propose dynamicmodels for the economy. The major question is then, how can we use the model to determine thebest strategy to maximize development? We answer this question by setting constraints, wherewe assume that the economy can improve by 3% while the empirical value for child mortality istwice reduced. Then, we determine the time taken to reach the desired gross domestic product,set to that of a developed economy with low child mortality rates. These approximations makeit possible to draw some conclusions about the best strategy to invest: either directly into theeconomy, or indirectly through child health care. From the simulations we can also determinethe point at which to switch the investment strategy. We end this paper by including averagechild per woman and construct and study the model for the three variables

Modelling allocation of resources in prevention and control of obstetric fistula in Ugandan women

In spite of reliable and skilled healthcare resources, the prevalence rate of obstetric fistula in Uganda is high. The risk factors for obstetric fistula cut across due to high poverty rates and cultural barriers. The main objective of this study was to assess the impact of inability to access skilled healthcare at delivery and implications to the economy. The specific objective was to determine the best way of investment in getting women access to skilled healthcare before, during and after child birth. The question to be answered was whether it was more economical to invest in getting women access to skilled healthcare, or in expanding health- care. The study was conducted using data from the Uganda Demographic Health Survey 2016. The data was from 18,506 women in the age group of 15-49 in 15 regions around the country. Results show that the highest investment in providing access to skilled healthcare is required when there are few skilled healthcare centres. On the other hand, if there is little investment in providing access to skilled healthcare during child birth, many skilled health- care centres are required. Results show further that the minimum time taken to reduce fis- tula prevalence is attained when there are many women accessing skilled healthcare in the few equipped health centres. However, if there are many skilled healthcare centres but a few women treated for obstetric fistula, then it will take longer to reduce fistula prevalence. Fitting the model to data suggested that Uganda has a big backlog of women to treat for obstetric fistula as in all skilled healthcare centres, there were less women treated than expected. Although still under the expected figure, the benefit of these treatments for obstet- ric fistula is that for every one woman treated, 8 more would seek treatment for the condition. This would however cost the country a great deal in that the treatment funds would perhaps give more returns if diverted to outreach activities aimed to get women seek skilled health- care during child birth

Impact of health education on knowledge and behaviours toward obstetric fistula among women of reproductive age in Uganda

Obstetric fistula is among the most severe maternal morbidities. It is caused directly by obstructed labour, and indirectly by social, political, and economic factors. Effects of obstetric fistula include chronic urinary incontinence. Urinary incontinence often leads to isolation and death if left untreated. Death of women during childbirth is detrimental to both social economic transformation and shift of poor economies to middle income status. In this study, we estimate the burden of obstetric fistula on Ugandan women, and the effect of educating these women on its causes. We hypothesise that symptomatic women seek treatment after interactions with a treated woman. We consider one cycle of fistula and seek to determine how many women will eventually seek treatment, when one woman is treated in a population. We further assume that each treated woman becomes the educational resource for more symptomatic women. We then invest in getting women into treatment, providing treatment, or educating them about prevention and treatment of obstetric fistula. Results show that for each investment strategy, there exists a unique maximal solution that remains bounded. It is also shown from the model that high investment rates leads to high treatments rates. However, the highest treatment output is obtained when the level of investment is 44.9%. We also see from the results that for every one woman treated, 17 more seek treatment. However, as investment increases, the number of women that are eventually treated reduces due to lack of further investment into treatment and therefore no more women to treat. Results also show that educating women reduced fistula prevalence although the magnitude of reduction depended on the level of education coverage. These results show that an optimal strategy to reduce fistula prevalence would require achieving a balance between the two desirable but incompatible health outcomes. This will help maximise the total return or effectiveness under given circumstances such as continued women that develop fistula due to lack of skilled healthcare or lifetime incontinence due to lack of treatment. From this study we conclude that improving access to quality health education will contribute to the elimination of obstetric fistula in Uganda. (C) 2019 Elsevier Inc. All rights reserved.Funding Agencies|SIDA bilateral program Makerere</p

Modelling optimal allocation of resources in the context of an incurable disease.

Nodding syndrome has affected and led to the deaths of children between the ages of 5 and 15 in Northern Uganda since 2009. There is no reliable explanation of the disease, and currently the only treatment is through a nutritional programme of vitamins, combined with medication to prevent symptoms. In the absence of a proper medical treatment, we develop a dynamic compartmental model to plan the management of the syndrome and to curb its effects. We use incidence data from 2012 and 2013 from Pader, Lamwo and Kitgum regions of Uganda to parameterize the model. The model is then used to look at how to best plan the nutritional programme in terms of first getting children on to the programme through outreach, and then making sure they remain on the programme, through follow-up. For the current outbreak of nodding disease, we estimate that about half of available resources should be put into outreach. We show how to optimize the balance between outreach and follow-up in this particular example, and provide a general methodology for allocating resources in similar situations. Given the uncertainty of parameter estimates in such situations, we perform a robustness analysis to identify the best investment strategy. Our analysis offers a way of using available data to determine the best investment strategy of controlling nodding syndrome

Simulation of the steady states with <i>p</i>_<i>t</i> ∈ [0, 1].

<p>The red line is for the stunted while the blue line is for the children on treatment. Note that maximum <i>T</i> (minimum <i>R</i>) is achieved at the point <i>p</i>_<i>t</i> = 0.51. This gives The parameter values used are given in <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0172401#pone.0172401.t001" target="_blank">Table 1</a>.</p

Simulation of the model for different values of <i>p</i>_<i>t</i> ∈ [0, 1], and initial conditions <i>I</i> = 1,000, <i>T</i> = 0, and <i>R</i> = 0.

<p>Parameter values used are in <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0172401#pone.0172401.t001" target="_blank">Table 1</a>.</p

Simulation of the model for different values of <i>α</i>, <i>β</i> ∈ [0, 1].

<p>(a) Values of <i>p</i>_<i>t</i> for all <i>α</i> and <i>β</i> combinations; (b) Corresponding values of <i>R</i>. Parameter values used are in <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0172401#pone.0172401.t001" target="_blank">Table 1</a>.</p

Parameter estimates from Uganda data.

<p>Parameter estimates from Uganda data.</p