The reinfection threshold regulates pathogen diversity: the case of influenza

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 outcom

Humans use different statistics for sequence analysis depending on the task

Despite its long history (Luce, 1986) the study of sequential effects has mostly been confined to simple binary tasks such as two-alternative forced choice tasks (2AFC). Here we present experimental results from a choice task with three rather than two alternatives (3AFC) as well as a novel model that can explain them. We find that humans change the statistics they use to analyse a sequence depending on the task constraints, relying on first-order transition probabilities in a 2AFC but event relative frequencies (i.e., zeroth-order transition probabilities) in a 3AFC.Dinis Gökaydin, Anna Ma-Wyatt, Daniel Navarro, Amy Perfor

Genetic Diversity in the SIR Model of Pathogen Evolution

We introduce a model for assessing the levels and patterns of genetic diversity in pathogen populations, whose epidemiology follows a susceptible-infected-recovered model (SIR). We model the population of pathogens as a metapopulation composed of subpopulations (infected hosts), where pathogens replicate and mutate. Hosts transmit pathogens to uninfected hosts. We show that the level of pathogen variation is well predicted by analytical expressions, such that pathogen neutral molecular variation is bounded by the level of infection and increases with the duration of infection. We then introduce selection in the model and study the invasion probability of a new pathogenic strain whose fitness (R0(1+s)) is higher than the fitness of the resident strain (R0). We show that this invasion probability is given by the relative increment in R0 of the new pathogen (s). By analyzing the patterns of genetic diversity in this framework, we identify the molecular signatures during the replacement and compare these with those observed in sequences of influenza A

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

Understanding how immunity shapes the dynamics of multistrain pathogens is essential in determining the selective pressures imposed by vaccines. There is currently much interest in elucidating the strain dynamics of rotavirus to determine whether vaccination may lead to the replacement of vaccine-type strains. In developed countries, G1P[8] strains constitute the majority of rotavirus infections most years, but occasionally other genotypes dominate for reasons that are not well understood. We developed a mathematical model to examine the interaction of five common rotavirus genotypes. We explored a range of estimates for the relative strength of homotypic vs. heterotypic immunity and compared model predictions against observed genotype patterns from six countries. We then incorporated vaccination in the model to examine its impact on rotavirus incidence and the distribution of strains. Our model can explain the coexistence and cyclical pattern in the distribution of genotypes observed in most developed countries. The predicted frequency of cycling depends on the relative strength of homotypic vs. heterotypic immunity. Vaccination that provides strong protection against G1 and weaker protection against other strains will likely lead to an increase in the relative prevalence of non-G1 strains, whereas a vaccine that provides equally strong immunity against all strains may promote the continued predominance of G1. Overall, however, disease incidence is expected to be substantially reduced under both scenarios and remain below prevaccination levels despite the possible emergence of new strains. Better understanding of homotypic vs. heterotypic immunity, both natural and vaccine-induced, will be critical in predicting the impact of vaccination