Modeling the invasion and spread of contagious diseases in heterogeneous populations

The evolution of disease requires a firm understanding of heterogeneity among pathogen strains and hosts with regard to the processes of transmission, movement, recovery, and pathobiology. In this chapter, we build on the basic methodologies outlined in the previous chapter to address the question of how to model the invasion and spread of diseases in heterogeneous environments, without making an explicit link to natural selection—the topic of other chapters in this volume. After a general introdution in Section 1, the material is organized into three sections (Sections 2–4). Section 2 covers heterogeneous populations structured into homogeneous subgroups, with application to modeling TB and HIV epidemics. Section 3 reviews a new approach to analyzing epidemics in well-mixed populations in which individual-level variation in infectiousness is represented by a distributed reproductive number [51]—in particular, the expected number of secondary cases due to each individual is drawn from a gamma distribution, yielding a negative binomial offspring distribution after stochasticity in transmission is taken into account. In Section 3, we discuss ideas relating to superspreading events, as well as the best way to characterize the heterogeneity associated with transmission in real epidemics, including SARS, measles, and various pox viruses. Section 4 deals with individual-based approaches to modeling the spread of disease in finite populations with group structure, focusing on several issues including interactions among movement, transmission, and demographic time-scales, the effects of network connectivity on the spread of disease, and the spread of disease in invading or colonizing hosts. The applications in Section 5 focus on bovine TB (BTB) in an African buffalo population and the potential for BTB to invade a colonizing Persian fallow deer populations.