Modeling the invasion and spread of contagious disease in heterogeneous populations

The evolution of disease requires a firm understanding of hetero-geneity among pathogen strains and hosts with regard to the processes oftransmission, movement, recovery, and pathobiology. In this chapter, we buildon the basic methodologies outlined in the previous chapter to address thequestion of how to model the invasion and spread of diseases in heterogeneousenvironments, without making an explicit link to natural selection—the topicof other chapters in this volume. After a general introdution in Section 1, thematerial is organized into three sections (Sections 2–4). Section 2 covers het-erogeneous populations structured into homogeneous subgroups, with applica-tion to modeling TB and HIV epidemics. Section 3 reviews a new approach toanalyzing epidemics in well-mixed populations in which individual-level vari-ation in infectiousness is represented by a distributed reproductive number[51]—in particular, the expected number of secondary cases due to each in-dividual is drawn from a gamma distribution, yielding a negative binomialoffspring distribution after stochasticity in transmission is taken into account.In Section 3, we discuss ideas relating to superspreading events, as well as thebest way to characterize the heterogeneity associated with transmission in realepidemics, including SARS, measles, and various pox viruses. Section 4 dealswith individual-based approaches to modeling the spread of disease in finitepopulations with group structure, focusing on several issues including interac-tions among movement, transmission, and demographic time-scales, the effectsof network connectivity on the spread of disease, and the spread of disease ininvading or colonizing hosts. The applications in Section 5 focus on bovine TB(BTB) in an African buffalo population and the potential for BTB to invadea colonizing Persian fallow deer populations