Erratum: Publisher Correction: Relevant mathematical modelling efforts for understanding COVID-19 dynamics: an educational challenge.

[This corrects the article DOI: 10.1007/s11858-022-01447-2.].

Relevant mathematical modelling efforts for understanding COVID-19 dynamics: an educational challenge.

The purpose of the work described in this paper is to emphasize the importance of using mathematical models and mathematical modelling in order to be able to understand and to learn possible behaviours in epidemic situations such as that of the COVID-19 pandemic, besides suggesting modelling techniques with which to evaluate certain sanitary decisions and policies which do, in fact, affect society as a whole. The mathematical tools that are used derive from nonlinear systems of difference equations (possibly viable at a high school level, using spreadsheets or adequate software) as well as nonlinear systems of ordinary differential equations (therefore using mathematical tools and software well within the reach of undergraduate students of many courses). This purpose is accomplished by motivating students and learners to study existing SIR-type models and modifying them in order to have a fully understandable translation of dynamics for infectious diseases such as COVID-19 in several different realistic scenarios, that is to say, situations that consider social distancing policies, widespread vaccination programmes, as well as possible and even probable results when in the presence of negationist postures and attitudes. Several modelling choices referring to real-life situations are shown and explored. These models are analysed and discussed, implicitly proposing similar attitudes and evaluations in learning environments. Conclusions are drawn, stimulating further work using the described mathematical tools and resources. Supplementary Information: The online version contains supplementary material available at 10.1007/s11858-022-01447-2.

Soil temperature and diapause maintenance in eggs of the spittlebug, Deois flavopicta (Hemiptera: Cercopidae)

Diapausing eggs of the neotropical pasture pest, Deois flavopicta (Stal) (Hemiptera: Cercopidae), were exposed to low overnight temperatures that simulated field conditions during the dry season (23/12, 23/15 and 23/18ºC day/night), for different periods (0-60 days). After treatment, eggs were kept at 28ºC and contact water (100 percent humidity) until hatching. A group of diapausing eggs were kept all the time under this last condition as a control treatment. Time for hatching (in degree-days) was reduced with decrease in low overnight temperature and increase of exposure time to these cold shocks, although there was no interaction between the factors. Regression of exposure time to cold shock influencing the expected mean hatching time produced independent equations for temperatures below 18ºC and 15ºC. We constructed a model that simulates the expected proportion of the population hatching after the beginning of rainy season based on regression equations to mean hatching time and associated standard deviation. The simulation generated for the model correlated significantly with nymphal population observed in the field. These results showed that overnight soil temperatures below 18ºC, as occurs in Central and South-eastern Brazil between May and August, shorten the period of diapause, increase quiescent eggs in the soil, and may synchronize the population hatching