Super- and Coinfection: The Two Extremes

As is well known, the “conventional wisdom” that successful parasites have to become benign is not based on exact evolutionary analysis. Rather than minimizing virulence, selection works to maximize a parasite’s reproduction ratio (see Box 9.1). If the rate of transmission is linked to virulence (defined here as increased mortality due to infection), then selection may in some circumstances lead to intermediate levels of virulence, or even to ever-increasing virulence (see Anderson and May 1991; Diekmann et al. 1990, and the references cited there). A variety of mathematical models has been developed to explore theoretical aspects of the evolution of virulence (see, for instance, Chapters 2, 3, 11, and 16). Most of these models exclude the possibility that an already infected host can be infected by another parasite strain. They assume that infection by a given strain entails immunity against competing strains. However, many pathogens allow for multiple infections, as shown in Chapters 6, 12, and 25. The (by now classic) results on optimization of the basic reproduction ratio cannot be applied in these cases. The mathematical modeling of multiple infections is of recent origin, and currently booming. Levin and Pimentel (1981) and Levin (1983a, 1983b) analyzed two-strain models in which the more virulent strain can take over a host infected by the less virulent strain. They found conditions for coexistence between the two strains. Bremermann and Pickering (1983) looked at competition between parasite strains within a host, and concluded that selection always favors the most virulent strain. Frank (1992a) analyzed a model for the evolutionarily stable level of virulence if there is a trade-off between virulence and infectivity, and if infection occurs with an ensemble of related parasite strains. In Adler and Brunet (1991), Van Baalen and Sabelis (1995a), Andreasen and Pugliese (1995), Lipsitch et al. (1995a), and Claessen and de Roos (1995), further aspects of multiple infection are discussed. In this chapter, following Nowak and May (1994) and May and Nowak (1994, 1995), we deal with two opposite extreme instances of multiple infection by several strains of a parasite. These simplified extreme cases, which are at least partly amenable to analytical understanding, seem to “bracket” the more general situation. The first case deals with superinfection. This approach assumes a competitive hierarchy among the different parasite strains, such that a more virulent parasite