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One of the reasons for the large investment the scientific community has made in the study of social networks is their connection with the spread of disease. Diseases spread over networks of contacts between individuals: airborne diseases like influenza or tuberculosis are communicated when two people breathe the air in the same room; contagious diseases and parasites can be communicated when people touch; HIV and other sexually transmitted diseases are communicated when people have sex. The patterns of such contacts can be represented as networks and a good deal of effort has been devoted to empirical studies of these networks' structure. This chapter looks at the connections between network structure and disease dynamics and at mathematical theories that allow us to understand and predict the outcomes of epidemics. Exercises are provided at the end of the chapter.

This chapter defines a stochastic counterpart to the homogeneous deterministic epidemic model introduced in Chapter 1. The model considers a homogeneous community of individuals that mix uniformly, meaning that there is no social structure in the community. The word “mix” is used in the sense of engaging in a type of contact that may possibly lead to transmission; what mixing is will therefore depend on characteristics of the infectious agent and the host. The randomness in the model stems from the latency and infectious periods being random (i.e., typically different for different individuals), and also from the contact process: infectious contacts of infected individuals occur randomly in time and with randomly selected individuals in a finite population. The chapter highlights two special cases, called the “general” epidemic and the Reed–Frost epidemic in the literature.

This chapter discusses the obstacles to HIV vaccine development and reviews vaccine strategies currently under development. It discusses HIV epidemic control models as health policy tools. These models can be used to design vaccination strategies to eliminate HIV and to assess the epidemiological impact of behavioral changes that occur with a mass vaccination campaign against HIV.

This chapter describes methods for making inferences about key epidemiological parameters from available data. The chapter presents the powerful statistical method called maximum-likelihood (ML) which is illustrated in the context of a simple transmission model for intensive care units (ICU). This is further developed to derive estimators for the parameter length of stay in an ICU. The chapter then returns to the prototype stochastic epidemic model of Chapter 3 and derives inference methods for key parameters of this model, both for the situation where the epidemic is observed continuously and the situation where only the final size of the outbreak is observed. Finally, the chapter returns to the ICU situation, but now considers a model with transmission leading to dependencies. Model parameters are again estimated by ML-inference with the aid of counting processes.

Chapters 5, 13 and 14 presented methods for making inference about infectious diseases from available data. This is of course one of the main motivations for modeling: learning about important features, such as R₀, the initial growth rate, potential outbreak sizes and what effect different control measures might have in the context of specific infections. The models considered in these chapters have all been simple enough to obtain more or less explicit estimates of just a few relevant parameters. In more complicated and parameter-rich models, and/or when analyzing large data sets, it is usually impossible to estimate key model parameters explicitly. In such situations there are (at least) two ways to proceed. One uses Bayesian statistical inference by means of Markov chain Monte Carlo methods (MCMC), and the other uses large scale simulations along with numerical optimization to fit parameters to data. This chapter mainly describes Bayesian inference using MCMC and only briefly some large simulation methods.

This chapter discusses how information should flow in an organization. There are only two ways in which information can exist in any location — either it was created there, or it was transferred there from somewhere else. It is often assumed that information is transferred from a single source as a complete package, a finished innovation. However, rather than a complete package delivered from a single source, bits of information are much more likely to be transferred, and an innovation is a contribution to yet more innovation. The Epidemic Model of Diffusion further explains the flow of information: sent information is not likely to arrive in parts from multiple sources. What is transmitted is what arrives, and all that is required to be known about its transfer can be known from the location and timing of its further incidence.

This chapter explores the key statistical issues that emerge in the design and analysis of HIV prevention studies. It focuses on the strengths and limitations of various study designs including randomized trials, natural experiments, and observational studies. The trends of HIV/AID surveillance data and uses of associated epidemic modeling are also discussed. The chapter concludes by emphasizing careful consideration of the unit of analysis for evaluating HIV prevention programs.

This chapter elaborates on the special case of age structure. Especially in the context of infectious diseases among humans, “age” is often used to characterize individuals. Partly this reflects our system of public health administration (and, perhaps, our preoccupation with age). There is, however, a more “mechanistic” reason to incorporate age structure: patterns of human social behavior and sexual activity correlate with age. In addition, the effect that the infective agent has on the host sometimes depends heavily on the age of the host (e.g., in polio) or it may depend on another aspect of the host, such as pregnancy, which correlates with age (e.g., in rubella). The chapter also discusses vaccination strategies as one of the major applied issues of age-structured epidemic models.