Virus infection speeds: theory versus experiment

In order to explain the speed of Vesicular Stomatitis Virus VSV infections, we develop a simple model that improves previous approaches to the propagation of virus infections. For VSV infections, we find that the delay time elapsed between the adsorption of a viral particle into a cell and the release of its progeny has a very important effect. Moreover, this delay time makes the adsorption rate essentially irrelevant in order to predict VSV infection speeds. Numerical simulations are in agreement with the analytical results. Our model satisfactorily explains the experimentally measured speeds of VSV infections

Epidemiological Models of Directly Transmitted Diseases: An Approach via Fuzzy Sets Theory

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Optimal control and numerical optimization applied to epidemiological models

A relação entre a epidemiologia, a modelação matemática e as ferramentas computacionais permite construir e testar teorias sobre o desenvolvimento e combate de uma doença. Esta tese tem como motivação o estudo de modelos epidemiológicos aplicados a doenças infeciosas numa perspetiva de Controlo Ótimo, dando particular relevância ao Dengue. Sendo uma doença tropical e subtropical transmitida por mosquitos, afecta cerca de 100 milhões de pessoas por ano, e é considerada pela Organização Mundial de Saúde como uma grande preocupação para a saúde pública. Os modelos matemáticos desenvolvidos e testados neste trabalho, baseiam-se em equações diferenciais ordinárias que descrevem a dinâmica subjacente à doença nomeadamente a interação entre humanos e mosquitos. É feito um estudo analítico dos mesmos relativamente aos pontos de equilíbrio, sua estabilidade e número básico de reprodução. A propagação do Dengue pode ser atenuada através de medidas de controlo do vetor transmissor, tais como o uso de inseticidas específicos e campanhas educacionais. Como o desenvolvimento de uma potencial vacina tem sido uma aposta mundial recente, são propostos modelos baseados na simulação de um hipotético processo de vacinação numa população. Tendo por base a teoria de Controlo Ótimo, são analisadas as estratégias ótimas para o uso destes controlos e respetivas repercussões na redução/erradicação da doença aquando de um surto na população, considerando uma abordagem bioeconómica. Os problemas formulados são resolvidos numericamente usando métodos diretos e indiretos. Os primeiros discretizam o problema reformulando-o num problema de optimização não linear. Os métodos indiretos usam o Princípio do Máximo de Pontryagin como condição necessária para encontrar a curva ótima para o respetivo controlo. Nestas duas estratégias utilizam-se vários pacotes de software numérico. Ao longo deste trabalho, houve sempre um compromisso entre o realismo dos modelos epidemiológicos e a sua tratabilidade em termos matemáticos.

Quantifying urbanisation as a risk factor for non-communicable disease

Aim of this study was to investigate the poorly understood relationship between the process of urbanization and non-communicable diseases (NCDs) in Sri Lanka using a multi-component, quantitative measure of urbanicity.

NCD prevalence data were taken from the Sri Lankan Diabetes and Cardiovascular Study comprising a representative sample of people from seven of the nine provinces in Sri Lanka (n=4,485/5,000; response rate=89.7%). We constructed a measure of the urban environment for seven areas using a seven-item scale based on data from study clusters to develop an ―urbanicity” scale. The items were population size, population density, and access to markets, transportation, communications/media, economic factors, environment/sanitation, health, education, and housing quality. Linear and logistic regression models were constructed to examine the relationship between urbanicity and chronic disease risk factors.

Among men, urbanicity was positively associated with physical inactivity (OR: 3.22; 2.27 – 4.57), high body mass index (OR: 2.45; 95% CI: 1.88 – 3.20) and diabetes mellitus (OR: 2.44; 95% CI: 1.66 – 3.57). Among women, too, urbanicity was positively associated with physical inactivity (OR: 2.29; 95% CI: 1.64 – 3.21), high body mass index (OR: 2.92;95% CI: 2.41 – 3.55) and diabetes mellitus (OR: 2.10; 95% CI: 1.58 – 2.80).

There is a clear relationship between urbanicity and common modifiable risk factors for chronic disease in a representative sample of Sri Lankan adults.

Stability and sensitivity analysis of Be-CoDiS, an epidemiological model to predict the spread of human diseases between countries. Validation with data from the 2014-16 West African Ebola Virus Disease epidemic.

Ebola virus disease is a lethal human and primate disease that requires a particular attention from the international health authorities due to important recent outbreaks in some Western African countries and isolated cases in European and North-America continents. Regarding the emergency of this situation, various decision tools, such as mathematical models, were developed to assist the authorities to focus their efforts in important factors to eradicate Ebola. In a previous work, we have proposed an original deterministic spatial-temporal model, called Be-CoDiS (Between-Countries Disease Spread), to study the evolution of human diseases within and between countries by taking into consideration the movement of people between geographical areas. This model was validated by considering numerical experiments regarding the 2014-16 West African Ebola Virus Disease epidemic. In this article, we propose to perform a stability analysis of Be-CoDiS. Our first objective is to study the equilibrium states of simplified versions of this model, limited to the cases of one an two countries, and to determine their basic reproduction ratios. Then, in order to give some recommendations for the allocation of resources used to control the disease, we perform a sensitivity analysis of those basic reproduction ratios regarding the model parameters. Finally, we validate the obtained results by considering numerical experiments based on data from the 2014-16 West African Ebola Virus Disease epidemic.

Modern mathematical methods and models; a book of experimental text materials.

v. 1. Multicomponent methods.--v. 2. Mathematical models.

Rules and regulations of the Iowa State Department of Health relating to communicable and other reportable diseases : with suggestions for their prevention or control, 1938

Includes reports, information, rules and regulations on communicable diseases. Describes individually many of these diseases and how to manage them.

A generative design system based on evolutionary and mathematical functions

Previous work by Professor John Frazer on Evolutionary Architecture provides a basis for the development of a system evolving architectural envelopes in a generic and abstract manner. Recent research by the authors has focused on the implementation of a virtual environment for the automatic generation and exploration of complex forms and architectural envelopes based on solid modelling techniques and the integration of evolutionary algorithms, enhanced computational and mathematical models. Abstract data types are introduced for genotypes in a genetic algorithm order to develop complex models using generative and evolutionary computing techniques. Multi-objective optimisation techniques are employed for defining the fitness function in the evaluation process.

A review on reliability models with covariates

Modern Engineering Asset Management (EAM) requires the accurate assessment of current and the prediction of future asset health condition. Suitable mathematical models that are capable of predicting Time-to-Failure (TTF) and the probability of failure in future time are essential. In traditional reliability models, the lifetime of assets is estimated using failure time data. However, in most real-life situations and industry applications, the lifetime of assets is influenced by different risk factors, which are called covariates. The fundamental notion in reliability theory is the failure time of a system and its covariates. These covariates change stochastically and may influence and/or indicate the failure time. Research shows that many statistical models have been developed to estimate the hazard of assets or individuals with covariates. An extensive amount of literature on hazard models with covariates (also termed covariate models), including theory and practical applications, has emerged. This paper is a state-of-the-art review of the existing literature on these covariate models in both the reliability and biomedical fields. One of the major purposes of this expository paper is to synthesise these models from both industrial reliability and biomedical fields and then contextually group them into non-parametric and semi-parametric models. Comments on their merits and limitations are also presented. Another main purpose of this paper is to comprehensively review and summarise the current research on the development of the covariate models so as to facilitate the application of more covariate modelling techniques into prognostics and asset health management.

Disease prevention and control

Globally, the main contributors to morbidity and mortality are chronic diseases, including cardiovascular disease and diabetes. Chronic diseases are costly and partially avoidable, with around sixty percent of deaths and nearly fifty percent of the global disease burden attributable to these conditions. By 2020, chronic illnesses will likely be the leading cause of disability worldwide. Existing health care systems, both national and international, that focus on acute episodic health conditions, cannot address the worldwide transition to chronic illness; nor are they appropriate for the ongoing care and management of those already afflicted with chronic diseases. International and Australian strategic planning documents articulate similar elements to manage chronic disease; including the need for aligning sectoral policies for health, forming partnerships and engaging communities in decision-making. The Australian National Chronic Disease Strategy focuses on four core areas for managing chronic disease; prevention across the continuum, early detection and treatment, integrated and coordinated care, and self-management. Such a comprehensive approach incorporates the entire population continuum, from the ‘healthy’, to those with risk factors, through to people suffering from chronic conditions and their sequelae. This chapter examines comprehensive approach to the prevention, management and care of the population with non-communicable, chronic diseases and communicable diseases. It analyses models of care in the context of need, service delivery options and the potential to prevent or manage early intervention for chronic and communicable diseases. Approaches to chronic diseases require integrated approaches that incorporate interventions targeted at both individuals and populations, and emphasise the shared risk factors of different conditions. Communicable diseases are a common and significant contributor to ill health throughout the world. In many countries, this impact has been minimised by the combined efforts of preventative health measures and improved treatment of infectious diseases. However in underdeveloped nations, communicable diseases continue to contribute significantly to the burden of disease. The aim of this chapter is to outline the impact that chronic and communicable diseases have on the health of the community, the public health strategies that are used to reduce the burden of those diseases and the old and emerging risks to public health from infectious diseases.

Density variation of different shaped food particulates in fluid bed drying : empirical models

Three particular geometrical shapes of parallelepiped, cylindrical and spheres were selected from potatoes (aspect ratio = 1:1, 2:1, 3:1), cut beans (length:diameter = 1:1, 2:1, 3:1) and peas respectively. The density variation of food particulates was studied in a batch fluidised bed dryer connected to a heat pump dehumidifier system. Apparent density and bulk density were evaluated with non-dimensional moisture at three different drying temperatures of 30, 40 and 50 o C. Relative humidity of hot air was kept at 15% in all drying temperatures. Several empirical relationships were developed for the determination of changes in densities with the moisture content. Simple mathematical models were obtained to relate apparent density and bulk density with moisture content.