Emergence of Cooperation in Heterogeneous Population: A Discrete-Time Replicator Dynamics Analysis

The emergence of cooperation is analyzed in heterogeneous populations where individuals can be classified in two groups according to their phenotypic appearance. Phenotype recognition is assumed for all individuals: individuals are able to identify the type of every other individual, but fail to recognize their own type, and thus behave under partial information conditions. The interactions between individuals are described by 2 × 2 symmetric games where individuals can either cooperate or defect. The evolution of such populations is studied in the framework of evolutionary game by means of the replicator dynamics. Overlapping generations are considered, so the replicator equations are formulated in discrete-time form. The well-posedness conditions of the system are derived. Depending on the parameters of the game, a restriction may exist for the generation length. The stability analysis of the dynamical system is carried out and a detailed description of the behavior of trajectories starting from the interior of the state-space is given. We find that, provided the conditions of well-posedness are verified, the linear stability of monomorphic states in the discrete-time replicator coincides with the one of the continuous case. Specific from the discrete-time case, a relaxed restriction for the generation length is derived, for which larger time-steps can be used without compromising the well-posedness of the replicator system.

Social, economic, and health impact of the respiratory syncytial virus: a systematic search

Background: Bronchiolitis caused by the respiratory syncytial virus (RSV) and its related complications are common in infants born prematurely, with severe congenital heart disease, or bronchopulmonary dysplasia, as well as in immunosuppressed infants. There is a rich literature on the different aspects of RSV infection with a focus, for the most part, on specific risk populations. However, there is a need for a systematic global analysis of the impact of RSV infection in terms of use of resources and health impact on both children and adults. With this aim, we performed a systematic search of scientific evidence on the social, economic, and health impact of RSV infection. Methods: A systematic search of the following databases was performed: MEDLINE, EMBASE, Spanish Medical Index, MEDES-MEDicina in Spanish, Cochrane Plus Library, and Google without time limits. We selected 421 abstracts based on the 6,598 articles identified. From these abstracts, 4 RSV experts selected the most relevant articles. They selected 65 articles. After reading the full articles, 23 of their references were also selected. Finally, one more article found through a literature information alert system was included. Results: The information collected was summarized and organized into the following topics: 1. Impact on health (infections and respiratory complications, mid-to long-term lung function decline, recurrent wheezing, asthma, other complications such as otitis and rhino-conjunctivitis, and mortality; 2. Impact on resources (visits to primary care and specialists offices, emergency room visits, hospital admissions, ICU admissions, diagnostic tests, and treatments); 3. Impact on costs (direct and indirect costs); 4. Impact on quality of life; and 5. Strategies to reduce the impact (interventions on social and hygienic factors and prophylactic treatments). Conclusions: We concluded that 1. The health impact of RSV infection is relevant and goes beyond the acute episode phase; 2. The health impact of RSV infection on children is much better documented than the impact on adults; 3. Further research is needed on mid-and long-term impact of RSV infection on the adult population, especially those at high-risk; 4. There is a need for interventions aimed at reducing the impact of RSV infection by targeting health education, information, and prophylaxis in high-risk populations.