Thesis (MSc)--University of Stellenbosch, 2007. / ENGLISH ABSTRACT: While research and population surveys in HIV/AIDS are well established in developed countries, Sub-Saharan Africa is still experiencing scarce HIV/AIDS information. Hence it depends on results obtained from models. Due to this dependence, it is important to understand the strengths and limitations of these models very well. In this study, a simple mathematical model is formulated and then extended to incorporate various features such as stages of HIV development, time delay in AIDS death occurrence, and risk groups. The analysis is neither purely mathematical nor does it concentrate on data but it is rather an exploratory approach, in which both mathematical methods and numerical simulations are used. It was found that the presence of stages leads to higher prevalence levels in a short term with an implication that the primary stage is the driver of the disease. Furthermore, it was found that time delay changed the mortality curves considerably, but it had less effect on the proportion of infectives. It was also shown that the characteristic behaviour of curves valid for most epidemics, namely that there is an initial increase, then a peak, and then a decrease occurs as a function of time, is possible in HIV only if low risk groups are present. It is concluded that reasonable or quality predictions from mathematical models are expected to require the inclusion of stages, risk groups, time delay, and other related properties with reasonable parameter values. / AFRIKAANSE OPSOMMING: Terwyl navorsing en bevolkingsopnames oor MIV/VIGS in ontwikkelde lande goed gevestig is, is daar in Afrika suid van die Sahara slegs beperkte inligting oor MIV/VIGS beskikbaar. Derhalwe moet daar van modelle gebruik gemaak word. Dit is weens hierdie feit noodsaaklik om die moontlikhede en beperkings van modelle goed te verstaan. In hierdie werk word ´n eenvoudige model voorgelˆe en dit word dan uitgebrei deur insluiting van aspekte soos stadiums van MIV outwikkeling, tydvertraging by VIGS-sterftes en risikogroepe in bevolkings. Die analise is beklemtoon nie die wiskundage vorme nie en ook nie die data nie. Dit is eerder ´n verkennende studie waarin beide wiskundige metodes en numeriese simula˙sie behandel word. Daar is bevind dat insluiting van stadiums op korttermyn tot ho¨er voorkoms vlakke aanleiding gee. Die gevolgtrekking is dat die primˆere stadium die siekte dryf. Verder is gevind dat die insluiting van tydvestraging wel die kurwe van sterfbegevalle sterk be¨ınvloed, maar dit het min invloed op die verhouding van aangestekte persone. Daar word getoon dat die kenmerkende gedrag van die meeste epidemi¨e, naamlik `n aanvanklike styging, `n piek en dan `n afname, in die geval van VIGS slegs voorkom as die bevolking dele bevat met lae risiko. Die algehele gevolgtrekking word gemaak dat vir goeie vooruitskattings met sinvolle parameters, op grond van wiskundige modelle, die insluiting van stadiums, risikogroepe en vertragings benodig word.

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Orientador: Cláudia Pio Ferreira / Banca: Fernanado Luiz Pio dos Santos / Banca: Suani Tavares Rubim de Pinho / Resumo: Apresenta-se um modelo de equações diferenciais ordinárias que descreve a transmissão de dengue em uma população humana e de mosquitos quando há circulação de dois sorotipos de vírus. Resultados analíticos e numéricos para os pontos de equilíbrio deste modelo, e o estudo da estabilidade dos mesmos são obtidos. Faz-se uma aproximação de estado quase-estacionário para a população de mosquito, com o objetivo de estudar e comparar a dinâmica da transmissão da dengue em redes de diferentes topologias. O modelo de transmissão através de redes complexas considera diferentes graus de conectividade entre os indivíduos da população e por isso representa melhor as interações sociais. Observa-se que a dinâmica da transmissão da dengue depende fortemente da topologia da rede e do número médio de conexões, portanto medidas de controle da doença devem ter um impacto diferente dada a diversidade das conexões entre os indivíduos de uma população / Abstract: We present a model of ordinary differential equations to describe the dengue transmission in a human and a mosquito populations when there are two serotypes of circulating virus. Analytic and numeric results to the equilibruim points of this model, and the study of the stability of this points were obtained. We assume the quasi-steady state approach to the mosquito population, in order to study and compare the dynamics of transmission of two serotypes of dengue virus in networks with different topologies. We consider the transmission model through complex networks with different degrees of conectivity among the individuals and, thus, it provides a better representation of the social interations. We observe that the transmission dynamics of dengue depends strongly on the network topology and the mean number of conections, thus the control measures must have a different impact given the diversity of conections among the individuals on the population / Mestre

Epidemiologists engage in the study of the distribution and determinants of health-related states or events in human populations. Eventually, they will apply that study to prevent and control problems and contingencies associated with the health of the population. Due to the spread of new pathogens and the emergence of new bio-terrorism threats, it has become imperative to develop new and expand existing techniques to equip public health providers with robust tools to predict and control health-related crises. In this dissertation, I explore the effects caused in the disease dynamics by the differences in individuals’ physiology and social/behavioral characteristics. Multiple computational and mathematical models were developed to quantify the effect of those factors on spatial and temporal variations of the disease epidemics. I developed statistical methods to measure the effects caused in the outbreak dynamics by the incorporation of heterogeneous demographics and social interactions to the individuals of the population. Specifically, I studied the relationship between demographics and the physiological characteristics of an individual when preparing for an infectious disease epidemic.

Gyrodactylus salaris Malmberg, 1957, is a notifiable freshwater ecto-parasite that infects both wild and farmed populations of Atlantic salmon (Salmo salar, L.). It has caused catastrophic damage to wild salmon stocks in Norway since its accidental introduction in 1975, reducing salmon density in some rivers by 98% over a period of five years. It is estimated that G. salaris has cost the Norwegian salmon industry more than 500 million EUR. Currently the UK has G. salaris free status under EU law, however, it is believed that if G. salaris emerged in the UK the impact would be similar to that witnessed in Norway. The aim of this thesis is to develop mathematical models that describe the salmon-G. salaris system in order to gain a greater understanding of the possible long-term impact the parasite may have on wild populations of Atlantic salmon in G. salaris-free territories such as the UK. Mathematical models, including deterministic, Leslie matrix and individual based models, were used to investigate the impact of G. salaris on Atlantic salmon at the individual and population level. It is known that the Atlantic strain of Atlantic salmon, examples of which occur naturally in Norway and the UK, does not have any resistance to G. salaris infections and the parasite population is able to quickly grow to epidemic levels. In contrast, the Baltic strain of Atlantic salmon, examples of which occur naturally in Sweden and Russia, exhibits some form of resistance and the parasite is unable to persist. Thus, baseline models were extended to include immunity to infection, a trade-off on salmon reproductive rate, and finally, to consider interactions between populations of G. salaris and multiple strains of salmon exhibiting varying levels of immunity from fully susceptible to resistant. The models proposed predict that in the absence of host resistance or an immune response infections by G. salaris will result in an epidemic followed by the extinction of the salmon host population. Models also predict that if salmon are able to increase their resistance to G. salaris infections through mutations, salmon population recovery after the epidemic is indeed possible within 10-15 years post introduction with low level parasite coexistence. Finally, models also highlight areas where additional information is needed in order to improve predictions and enable the estimation of important parameter values. Model predictions will ultimately be used to assist in future contingency planning against G. salaris outbreaks in the UK and possibly as a basis for future models describing other fish/ecto-parasite systems.

Internet technology has affected humans' lives in many disciplines. The search engine is one of the most important Internet tools in that it allows people to search for what they want. Search queries entered in a web search engine can be used to predict dengue incidence. This vector borne disease causes severe illness and kills a large number of people every year. This dissertation utilizes the capabilities of search queries related to dengue and climate to forecast the number of dengue cases. Several machine learning techniques are applied for data analysis, including Multiple Linear Regression, Artificial Neural Networks, and the Seasonal Autoregressive Integrated Moving Average. Predictive models produced from these machine learning methods are measured for their performance to find which technique generates the best model for dengue prediction. The results of experiments presented in this dissertation indicate that search query data related to dengue and climate can be used to forecast the number of dengue cases. The performance measurement of predictive models shows that Artificial Neural Networks outperform the others. These results will help public health officials in planning to deal with the outbreaks.

Abstract Probabilistic reasoning under uncertainty suits well to analysis of disease dynamics. The stochastic nature of disease progression is modeled by applying the principles of Bayesian learning. Bayesian learning predicts the disease progression, including prevalence and incidence, for a geographic region and demographic composition. Public health resources, prioritized by the order of risk levels of the population, will efficiently minimize the disease spread and curtail the epidemic at the earliest. A Bayesian network representing the outbreak of influenza and pneumonia in a geographic region is ported to a newer region with different demographic composition. Upon analysis for the newer region, the corresponding prevalence of influenza and pneumonia among the different demographic subgroups is inferred for the newer region. Bayesian reasoning coupled with disease timeline is used to reverse engineer an influenza outbreak for a given geographic and demographic setting. The temporal flow of the epidemic among the different sections of the population is analyzed to identify the corresponding risk levels. In comparison to spread vaccination, prioritizing the limited vaccination resources to the higher risk groups results in relatively lower influenza prevalence. HIV incidence in Texas from 1989-2002 is analyzed using demographic based epidemic curves. Dynamic Bayesian networks are integrated with probability distributions of HIV surveillance data coupled with the census population data to estimate the proportion of HIV incidence among the different demographic subgroups. Demographic based risk analysis lends to observation of varied spectrum of HIV risk among the different demographic subgroups. A methodology using hidden Markov models is introduced that enables to investigate the impact of social behavioral interactions in the incidence and prevalence of infectious diseases. The methodology is presented in the context of simulated disease outbreak data for influenza. Probabilistic reasoning analysis enhances the understanding of disease progression in order to identify the critical points of surveillance, control and prevention. Public health resources, prioritized by the order of risk levels of the population, will efficiently minimize the disease spread and curtail the epidemic at the earliest.

With a growing concern of an infectious diseases spreading in a population, epidemiology is becoming more important for the future of public health. In the past epidemiologist used existing data of an outbreak to help them determine how an infectious disease might spread in the future. Now with computational models, they able to analysis data produced by these models to help with prevention and intervention plans. This paper looks at the design, implementation, and analysis of a computational model based on the interactions of the population between individuals. The design of the working contact model looks closely at the SEIR model used as the foundation and the two timelines of a disease. The implementation of the contact model is reviewed while looking closely at data structures. The analysis of the experiments provide evidence this contact model can be used to help epidemiologist study the spread of an infectious disease based on the contact rate of individuals.

Orientador: Luiz Koodi Hotta / Dissertação (mestrado) - Universidade Estadual de Campinas, Instituto de Matemática Estatística e Computação Científica / Made available in DSpace on 2018-08-24T12:49:57Z (GMT). No. of bitstreams: 1 MercadoLondono_SergioLuis_M.pdf: 1311356 bytes, checksum: 23c15e842c02af3c1dc7de3a2a46a5df (MD5) Previous issue date: 2014 / Resumo: Uma das quantidades mais importante definida na epidemiologia é o número de reprodução basal, ou básico, associado com a pandemia e denotado por $R_0$. Ele proporciona uma medida da intensidade das intervenções necessárias para o controle da epidemia. Ao mesmo tempo, os modelos epidemiológicos compartimentais SIR, SEIR, tanto no enfoque enfoque determinístico quanto no estocástico, têm sido de grande ajuda para a compreensão dos mecanismos de transmissão de doenças infecciosas em todo o mundo. Esta dissertação apresenta alguns métodos para estimar esta quantidade através da utilização dos modelos epidemiológicos compartimentais. São considerados os quatro métodos apresentados por Chowell et al. (Mathematical Biosciences, 2007, v. 208, p. 571-589). O primeiro método é baseado na taxa de crescimento (inicial) exponencial da epidemia. Dada a taxa de crescimento exponencial e o modelo subjacente temos uma estimativa de $R_{0}$. No caso dos métodos 2 e 3 o processo de estimação do $R_0$ baseia-se nos modelos compartimentais, modelos SIR e SEIR no método 2, e em um modelo SEIR estendido no método 3. O método 4 utiliza uma abordagem bayesiana do modelo SIR estocástico. O objetivo da dissertação é estudar as propriedades dos estimadores baseados nos métodos 1, 2 e 4. Através de simulações são estimados os vícios, os erros quadráticos médios, as cobertura e as larguras dos intervalos de confiança. Os métodos são estudados quando os verdadeiros processos geradores de dados são os modelos SIR ou SEIR estocásticos. Inicialmente foram estudados os métodos, como apresentados por Chowell et al. (2007), e depois apresentadas modificações para melhorar o desempenho dos estimadores. A dissertação está organizada da seguinte forma: o Capítulo 2 consiste na apresentação dos modelos compartimentais, SIR e SEIR para análise das doenças infecciosas; tanto na abordagem determinística quanto estocástica. Este capítulo apresenta também o número de reprodução basal. O Capítulo 3 apresenta os quatro métodos de estimação apresentados em Chowell et al. (2007) para estimação do número de reprodução basal. O Capítulo 4 apresenta uma comparação de três dos quatro métodos através de simulação, quando o processo gerador de dados é um modelo SIR ou SEIR estocásticos. Neste capítulo também são apresentadas as modificações dos métodos. A conclusão final e as sugestões de trabalhos futuros são apresentadas no Capítulo 5 / Abstract: The basic reproduction number, usually denoted by $R_0$, is one of the most important quantities defined in epidemiology and is associated with the potential of an infectious disease to spread through a population. It provides a measure of the intensity needed to control the epidemic interventions. At the same time, the compartmental epidemiological models SIR and SEIR , both in the deterministic and in the stochastic approach, have been very helpful for understanding the mechanisms of infectious diseases transmission. This paper considers the four methods presented by Chowell et al. (Mathematical Biosciences, 2007, v. 208, p. 571-589) to estimate $R_0$. All methods are based on compartmental epidemiological models. The first method is based on the epidemic (initial) exponential growth rate. Given an estimate of the exponential growth rate and an underlying compartmental model we have an estimate of $R_{0}$. The second method is based on fitting SIR or SEIR compartmental models, and the third method in fitting an extended SEIR model. The fourth method uses a Bayesian approach to a stochastic SIR model. The aim of this work is to study the properties of estimators based on methods 1, 2 and 4. The bias, the mean squared errors, the coverage and the widths of the confidence intervals are estimated through simulation. The methods are studied when the true data generating processes are the stochastic SIR or SEIR models. Initially the methods, as presented by Chowell et al. (2007), were studied and then presented modifications to improve the performance of the estimators. The dissertation is organized as follows: Chapter 2 consists of the presentation of compartmental SIR and SEIR models, the deterministic and stochastic approaches for analysis of infectious diseases. This chapter also presents the basic reproduction number. Chapter 3 explains the four estimation methods presented in Chowell et al. (2007) to estimate the basic reproduction number. Chapter 4 discusses and compares three of the four methods by simulation when the data generating process is a SIR or SEIR model. In this chapter the modifications of the methods are also considered. The final conclusion and suggestions for future work are presented in Chapter 5 / Mestrado / Estatistica / Mestre em Estatística

The dengue virus has become widespread worldwide in recent decades. It has no specific treatment and affects more than 40% of the entire population in the world. In Thailand, dengue has been a health concern for more than half a century. The highest number of cases in one year was 174,285 in 1987, leading to 1,007 deaths. In the present day, dengue is distributed throughout the entire country. Therefore, dengue has become a major challenge for public health in terms of both prevention and control of outbreaks. Different methodologies and ways of dealing with dengue outbreaks have been put forward by researchers. Computational models and simulations play an important role, as they have the ability to help researchers and officers in public health gain a greater understanding of the virus's epidemic activities. In this context, this dissertation presents a new framework, Modified Agent-Based Modeling (mABM), a hybrid platform between a mathematical model and a computational model, to simulate a dengue outbreak in human and mosquito populations. This framework improves on the realism of former models by utilizing the reported data from several Thai government organizations, such as the Thai Ministry of Public Health (MoPH), the National Statistical Office, and others. Additionally, its implementation takes into account the geography of Thailand, as well as synthetic mosquito and synthetic human populations. mABM can be used to represent human behavior in a large population across variant distances by specifying demographic factors and assigning mobility patterns for weekdays, weekends, and holidays for the synthetic human population. The mosquito dynamic population model (MDP), which is a component of the mABM framework, is used for representing the synthetic mosquito population dynamic and their ecology by integrating the regional model to capture the effect of dengue outbreak. The two synthetic populations can be linked to each other for the purpose of presenting their interactions, and the Local Stochastic Contact Model for Dengue (LSCM-DEN) is utilized. For validation, the number of cases from the experiment is compared to reported cases from the Thailand Vector Borne Disease Bureau for the selected years. This framework facilitates model configuration for sensitivity analysis by changing parameters, such as travel routes and seasonal temperatures. The effects of these parameters were studied and analyzed for an improved understanding of dengue outbreak dynamics.