The reinfection threshold regulates pathogen diversity: the case of influenza

Abstract

The awareness that pathogens can adapt and evolve over relatively short time-scales is changing our view of infectious disease epidemiology and control. Research on the transmission dynamics of antigenically diverse pathogens is progressing and there is increasing recognition for the need of new concepts and theories. Mathematical models have been developed considering the modelling unit in two extreme scales: either diversity is not explicitly represented or diversity is represented at the finest scale of single variants. Here, we use an intermediate approach and construct a model at the scale of clusters of variants. The model captures essential properties of more detailed systems and is much more amenable to mathematical treatment. Specificities of pathogen clusters and the overall potential for transmission determine the reinfection rates. These are, in turn, important regulators of cluster dynamics. Ultimately, we detect a reinfection threshold (RT) that separates different behaviours along the transmissibility axis: below RT, levels of infection are low and cluster substitutions are probable; while above RT, levels of infection are high and multiple cluster coexistence is the most probable outcome.

Modeling rotavirus strain dynamics in developed countries to understand the potential impact of vaccination on genotype distributions

“…mathematical modeling | transmission dynamics | strain replacement D ifferences in the strength of immunity and cross-immunity among strains are thought to play an important role in shaping the epidemiological and evolutionary patterns of infectious diseases (1). Models for the transmission dynamics of multistrain pathogens have helped elucidate the mechanisms behind empirical patterns, including multiannual oscillations in the incidence of influenza (2-4) and dengue cases (5-10), antigenic drift within influenza subtypes (11)(12)(13)(14), and cyclical patterns in the predominance of different strains of influenza (3,15), respiratory syncytial virus (16), dengue (5-10), malaria (17), and cholera (18). Vaccines that elicit a stronger immune response to specific strains may impact the distribution of genotypes in unforeseen ways, which in turn may affect overall disease incidence.…”

Localized contacts between hosts reduce pathogen diversity

“…A homogeneously mixed stochastic version of model (1) was considered by Gökaydin et al (2005) for population sizes between 10 6 and 10 8 , and, as expected, stochasticity was found to favour strain replacement and extinction both for similar and dissimilar strains. This effect may be, however, greatly enhanced in more realistic descriptions of the host population where the homogeneously mixed assumption is relaxed.…”

“…The spreading of multiple strains may be investigated by means of mathematical models, and four studies have recently uncovered the role of a 'reinfection threshold' in regulating pathogen diversity (Gomes et al 2002;Boni et al 2004;Abu-Raddad & Ferguson 2004;Gökaydin et al 2005). In spite of the significant differences in model formulations, assumptions, and propositions, there is a striking convergence at the level of the underlying mechanisms and results: levels of infection increase abruptly as a certain threshold is crossed, increasing the potential for pathogen diversity.…”

“…For the invasion by a pathogen strain of a homogeneously mixed population where another strain circulates, it was recently found that strain replacement is favoured when the transmissibility is below the reinfection threshold, while coexistence is favoured above (Gökaydin et al 2005). Here we consider a model of contact structure in the host population to describe the underlying network for disease transmission, and investigate how this impacts on the outcome of an invasion by a new strain, that starts by infecting a very small fraction of the population.…”

A New Mathematical Model of Syphilis

“…al. later applied these models to tuberculosis [9] and influenza [12] with an emphasis on reinfection [10,11].…”