Epidemiological models are used to inform health policy on issues such as target vaccination levels, comparing quarantine options and estimating the eventual size of an epidemic. Models that incorporate some elements of the social network structure are used for diseases where close contact is required for transmission. The motivation of this research is to extend epidemic models to include the relationship with a broader set of relevant real world network properties. The impact of degree distribution by itself is reasonably well understood, but studies with assortativity or clustering are limited and none examine their interaction. To evaluate the impact of these properties, I simulate epidemics on networks with a range of property values. However, a suitable algorithm to generate the networks is not available in the literature. There are thus two research aspects: generating networks with relevant properties, and estimating the impact of social network structure on epidemic behaviour. Firstly, I introduce a flexible network generation algorithm that can independently control degree distribution, clustering coefficient and degree assortativity. Results show that the algorithm is able to generate networks with properties that are close to those targeted. Secondly, I fit models that account for the relationship between network properties and epidemic behaviour. Using results from a large number of epidemic simulations over networks with a range of properties, regression models are fitted to estimate the separate and joint effect of the identified social network properties on the probability of an epidemic occurring and the basic reproduction ratio. The latter is a key epidemic parameter that represents the number of people infected by a typical initial infected person in a population. Results show that social network properties have a significant influence on epidemic behaviour within the property space investigated. Ignoring the differences between social networks can lead to substantial errors when estimating the basic reproduction ratio from an epidemic and then applying the estimate to a different social network. In turn, these errors could lead to failure in public health programs that rely on such estimates.

In this thesis we discuss deterministic compartmental epidemic models. We study the asymp- totic stability of the disease-free solution of models with pulse vaccination campaigns. The main contributions of this thesis are to extend the literature of pulse vaccination models with delay. We take results for ordinary differential equation models and extend them to models with delay differential equations. Model generalizations include the use of a general incidence term as an upper bound for the actual incidence, and the use of switch parameters to approximate time-varying parameters. In particular, we look at contact rate parameters which are piecewise constant or time-varying. We extend literature results for non-delay general incidence models to find uniform asymptotic stability of the disease-free solution which helps us to add delay. We find an upper bound for the susceptible population under pulse vaccination and use this bound to tighten results for eradication thresholds: that is, we use this upper bound to find sufficient conditions for the uniform asymptotic stability of the disease-free solution of delayed pulse vaccination models. We extend literature results for constant contact rate bilinear incidence delay models to models with periodic time-varying contact rate, and determine conditions under which the disease-free solution is uniformly asymptotically stable for small delay. We also find conditions for disease permanence in the corresponding non-delay, time-varying-parameter pulse vaccination model. For piecewise- constant contact rate bilinear incidence models we again find thresholds which guarantee uniform asymptotic stability under small delay. We additionally discuss the effects of time-varying total population on our results, through a change of variables to population fractions. The total population is commonly held constant in the literature, for analytical simplicity, so we survey the methods for time-varying total population and the effects of such variation on the pulse vaccination schemes. We retain thresholds for eradication by considering the compartment populations as fractions of the total, instead of population numbers. The result is also applied to constant-population delay systems. When changing from standard incidence to bilinear incidence in delay systems, we discuss a way to estimate the effect of time-varying N. We support our theory with simulation results.

In this thesis we discuss deterministic compartmental epidemic models. We study the asymp- totic stability of the disease-free solution of models with pulse vaccination campaigns. The main contributions of this thesis are to extend the literature of pulse vaccination models with delay. We take results for ordinary differential equation models and extend them to models with delay differential equations. Model generalizations include the use of a general incidence term as an upper bound for the actual incidence, and the use of switch parameters to approximate time-varying parameters. In particular, we look at contact rate parameters which are piecewise constant or time-varying. We extend literature results for non-delay general incidence models to find uniform asymptotic stability of the disease-free solution which helps us to add delay. We find an upper bound for the susceptible population under pulse vaccination and use this bound to tighten results for eradication thresholds: that is, we use this upper bound to find sufficient conditions for the uniform asymptotic stability of the disease-free solution of delayed pulse vaccination models. We extend literature results for constant contact rate bilinear incidence delay models to models with periodic time-varying contact rate, and determine conditions under which the disease-free solution is uniformly asymptotically stable for small delay. We also find conditions for disease permanence in the corresponding non-delay, time-varying-parameter pulse vaccination model. For piecewise- constant contact rate bilinear incidence models we again find thresholds which guarantee uniform asymptotic stability under small delay. We additionally discuss the effects of time-varying total population on our results, through a change of variables to population fractions. The total population is commonly held constant in the literature, for analytical simplicity, so we survey the methods for time-varying total population and the effects of such variation on the pulse vaccination schemes. We retain thresholds for eradication by considering the compartment populations as fractions of the total, instead of population numbers. The result is also applied to constant-population delay systems. When changing from standard incidence to bilinear incidence in delay systems, we discuss a way to estimate the effect of time-varying N. We support our theory with simulation results.

Segundo a OMS as gastroenterites agudas são a segunda maior causa de morte de crianças no mundo. Este cenário é mais grave em países em desenvolvimento. Presume-se que a grande maioria das hospitalizações e mortes por gastroenterites agudas são causadas pela rotavirose. No ano de 2009 a OMS recomendou a vacinação internacional de crianças de 0-5 anos devido ao sucesso das campanhas de vacinação em países que adotaram esta política pública. Atualmente há uma variedade de vacinas para o rotavírus, tornando a avaliação do custobenefício destas vacinas desejável. O objetivo deste trabalho é adaptar um modelo da dinâmica da transmissão que possa contribuir com estas avaliações de custo-benefício. Para tanto foi adotada a abordagem ampla com ênfase na análise quantitativa da dinâmica da doença. O método consistiu em adaptar um modelo compartimental de referência da literatura internacional sobre modelagem de doenças com protocolo de vacinação. Este modelo de referência foi estudado e simulado para diferentes valores para posteriormente se imputar os parâmetros do modelo com os valores estimados para a rotavirose no Estado de São Paulo. Os resultados foram comparados com os valores obtidos dos dados do Datasus. Como resultado foram estimados alguns parâmetros da infecção e de seu comportamento dinâmico com informações da literatura. Conclui-se que são necessários mais estudos que possam caracterizar melhor a infecção no Estado de São Paulo, para que com isto se possa estimar melhor a infecção / According to WHO, acute gastroenteritis is the second leading cause of death for children in the world. This scenario is more serious in developing countries. It is assumed that the vast majority of hospitalizations and deaths from acute gastroenteritis are caused by rotavirus. In 2009, WHO recommended the international vaccination of children aged 0-5 due to the success of vaccination campaigns in countries that adopted this public policy. Currently, there are a variety of rotavirus vaccines, making the cost-benefit assessment of these vaccines desirable. The purpose of this paper is to contribute to these cost-benefit assessments. For that, a broad approach was adopted with emphasis on the quantitative analysis of the dynamics of the disease. The method consisted of adopting a compartmental model of the international literature on disease modelling. This reference model was studied, simulated for different values to later assign the parameters of the model to the estimated values for rotavirus in the State of São Paulo. The results were compared with the data obtained from Datasus. As a result of this work, some parameters of the infection have been estimated and it was studied the dynamic behaviour of the disease using the information available in the literature. It is concluded that further studies are needed to better characterize the infection in the State of São Paulo so that it is possible to better estimate the infection

The importance of modelling the spreading of infectious diseases as part of a public health strategy has been highlighted by the ongoing coronavirus pandemic. This includes identifying the geographical areas or travel routes most likely to contribute to the spreading of an outbreak. These areas and routes can then be monitored as part of an early warning system, be part of intervention strategies, e.g. lockdowns, aiming to mitigate the spreading of the disease or be a focus of vaccination campaigns.  This thesis focus on developing a network-based infection model between the municipalities of Sweden in order to identify the areas most likely to contribute to an epidemic. First, a human mobility model is constructed based on the well-known radiation model. Then a network-based SEIR compartmental model is employed to simulate epidemic outbreaks with various parameters. Finally, the adoption of the influence maximization problem known in network science to identify the municipalities having the largest impact on the spreading of infectious diseases.  The resulting super-spreading municipalities point towards confirmation of the known fact that central highly populated regions in highly populated areas carry a greater risk than their neighbours initially. However, once these areas are targeted, the other resulting nodes show a greater variety in geographical location than expected. Furthermore, a correlation can be seen between increased infections time and greater variety, although more empirical data is required to support this claim.   For further evaluation of the model, the mobility network was studied due to its central role in creating data for the model parameters. Commuting data in the Gothenburg region were compared to the estimations, showing an overall good accuracy with major deviations in few cases.

Recent developments in nanotechnology have enabled the fabrication of nanomachines with very limited sensing, computation, communication, and action capabilities. The network of communicating nanomachines is envisaged as nanonetworks that are designed to accomplish complex tasks such as drug delivery and health monitoring. For the realization of future nanonetworks, it is essential to develop novel and efficient communication and networking paradigms. In this thesis, the first step towards designing a mobile ad hoc molecular nanonetwork (MAMNET) with electrochemical communication is taken. MAMNET consists of mobile nanomachines and infostations that share nanoscale information using electrochemical communication whenever they have a physical contact with each other. In MAMNET, the intermittent connectivity introduced by the mobility of nanomachines and infostations is a critical issue to be addressed. In this thesis, an analytical framework that incorporates the effect of mobility into the performance of electrochemical communication among nanomachines is presented. Using the analytical model, numerical analysis for the performance evaluation of MAMNET is obtained. Results reveal that MAMNET achieves adequately high throughput performance to enable frontier nanonetwork applications with sufficiently low communication delay.

Classical Continuous System Simulation (CSS) is restricted to modelling continuous flows, and therefore, cannot correctly realise a conceptual model with discrete objects. The development of Full Potential CSS solves this problem by (1) handling discrete quantities as discrete and continuous matter as continuous, (2) preserving the sojourn time distribution of a stage, (3) implementing attributes correctly, and (4) describing different types of uncertainties in a proper way. In order to apply Full Potential CSS a new software, StochSD, has been developed. This thesis evaluates StochSD's ability to model Full Potential CSS, where the points 1-4 above are included. As a test model a well-defined conceptual epidemic model, which includes all aspects of Full Potential CSS, was chosen. The study was performed by starting with a classical SIR model and then stepwise add the different aspects of the Conceptual Model. The effects of each step were demonstrated in terms of size and duration of the epidemic. Finally, the conceptual model was also realised as an Agent Based Model (ABM). The results from 10 000 replications each of the CSS and ABM models were compared and no statistical differences could be confirmed. The conclusion is that StochSD passed the evaluation.

Antibiotic resistant pathogens, such as methicillin-resistant Staphylococcus aureus (MRSA), and vancomycin-resistant enterococci (VRE), are an increasing burden on healthcare systems. Hospital acquired infections with these organisms leads to higher morbidity and mortality compared with the sensitive strains of the same species and both VRE and MRSA are on the rise worldwide including in Australian hospitals. Emerging community infectious diseases are also having an impact on hospitals. The Severe Acute Respiratory Syndrome virus (SARS Co-V) was noted for its propensity to spread throughout hospitals, and was contained largely through social distancing interventions including hospital isolation. A detailed understanding of the transmission of these and other emerging pathogens is crucial for their containment. The statistical inference and mathematical models used in this thesis aim to improve understanding of pathogen transmission by estimating the transmission rates of contagions and predicting the impact of interventions. Datasets used for these studies come from the Princess Alexandra Hospital in Brisbane, Australia and Shanxi province, mainland China. Epidemiological data on infection outbreaks are challenging to analyse due to the censored nature of infection transmission events. Most datasets record the time on symptom onset, but the transmission time is not observable. There are many ways of managing censored data, in this study we use Bayesian inference, with transmission times incorporated into the augmented dataset as latent variables. Hospital infection surveillance data is often much less detailed that data collected for epidemiological studies, often consisting of serial incidence or prevalence of patient colonisation with a resistant pathogen without individual patient event histories. Despite the lack of detailed data, transmission characteristics can be inferred from such a dataset using structured HiddenMarkovModels (HMMs). Each new transmission in an epidemic increases the infection pressure on those remaining susceptible, hence infection outbreak data are serially dependent. Statistical methods that assume independence of infection events are misleading and prone to over-estimating the impact of infection control interventions. Structured mathematical models that include transmission pressure are essential. Mathematical models can also give insights into the potential impact of interventions. The complex interaction of different infection control strategies, and their likely impact on transmission can be predicted using mathematical models. This dissertation uses modified or novel mathematical models that are specific to the pathogen and dataset being analysed. The first study estimates MRSA transmission in an Intensive Care Unit, using a structured four compartment model, Bayesian inference and a piecewise hazard methods. The model predicts the impact of interventions, such as changes to staff/patient ratios, ward size and decolonisation. A comparison of results of the stochastic and deterministic model is made and reason for differences given. The second study constructs a Hidden Markov Model to describe longitudinal data on weekly VRE prevalence. Transmission is assumed to be either from patient to patient cross-transmission or sporadic (independent of cross-transmission) and parameters for each mode of acquisition are estimated from the data. The third study develops a new model with a compartment representing an environmental reservoir. Parameters for the model are gathered from literature sources and the implications of the environmental reservoir are explored. The fourth study uses a modified Susceptible-Exposed-Infectious-Removed (SEIR) model to analyse data from a SARS outbreak in Shanxi province, China. Infectivity is determined before and after interventions as well as separately for hospitalised and community symptomatic SARS cases. Model diagnostics including sensitivity analysis, model comparison and bootstrapping are implemented.