Data driven mathematical models for policy making
Sammanfattning: 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?s 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.
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