Estimating the date at which an epidemic started in a country and the date at which it can end depending on interventions intensity are important to guide public health responses. Both are potentially shaped by similar factors including stochasticity (due to small population sizes), superspreading events, and memory effects (the fact that the occurrence of some events, e.g. recovering from an infection, depend on the past, e.g. the number of days since the infection). Focusing on COVID-19 epidemics, we develop and analyse mathematical models to explore how these three factors may affect early and final epidemic dynamics. Regarding the date of origin, we find limited effects on the mean estimates, but strong effects on their variances. Regarding the date of extinction following lockdown onset, mean values decrease with stochasticity or with the presence of superspreading events. These results underline the importance of accounting for heterogeneity in infection history and transmission patterns to accurately capture early and late epidemic dynamics.

Background: An initial epidemiological study carried out 18 years ago in Marseilles indicated that the air quality in schools was poor and that there was an association between the level of fine particulates and the occurrence of asthma in children. The aim of the present study was to evaluate the change in the prevalence of childhood asthma and allergic diseases and their link with the levels of air pollutants and other factors of potential risk. Methods: In 2016, using a questionnaire identical to the one used for the 1st survey in 1998-1999, we collected information regarding the symptoms, the diagnosis, and the potential confounding factors. We measured the main indoor and outdoor pollutants at the schools. Results: Overall, the prevalence of asthma and of allergic diseases exhibited an increasing trend in the time interval between the two studies, significant only for dry cough and pollen allergy. The level of air pollutants decreased significantly indoors. In spite of this, we found a correlation and a dose-effect relationship between the level of PM 2.5 and the prevalence of asthma. A family history of asthma and allergies, the insalubrity of the place of residence, and a non-Mediterranean diet were also associated with the risk of these diseases. Conclusion: In the time interval between the two studies, which were 18 years apart, despite a reduction in the level of air pollutants in classrooms, asthma was still related to PM 2.5. Other potentially causative or contributing environmental factors were also related to asthma and allergies.

Disassortative mating is a rare form of mate preference that promotes the persistence of polymorphism. While the evolution of assortative mating, and its consequences on trait variation and speciation have been extensively studied, the conditions enabling the evolution of disassortative mating are still poorly understood. Mate preferences increase the risk of missing mating opportunities, a cost that can be compensated by a greater fitness of offspring. Heterozygote advantage should therefore promote the evolution of disassortative mating, which maximizes the number of heterozygous offspring. From the analysis of a two-locus diploid model, with one locus controlling the mating cue under viability selection and the other locus coding for the level of disassortative preference, we show that heterozygote advantage and negative frequency-dependent viability selection acting at the cue locus promote the evolution of disassortative preferences. We predict conditions of evolution of disassortative mating coherent with selection regimes acting on traits observed in the wild. We also show that disassortative mating generates sexual selection which disadvantages heterozygotes at the cue locus, limiting the evolution of disassortative preferences. Altogether our results partially explain why this behavior is rare in natural populations. 2