ABSTRACT This work addresses the COVID-19 pandemic on two fronts: proposing a system of ordinary differential equations to model it and fitting this model to Brazilian and Portuguese data. It presents estimations to important parameters for the infection dynamics, such as the percentage of asymptomatic individuals, and it stresses out that non-biological human aspects, for example, cultural, social, and economic, are not only impacted by the pandemic but also impact the pandemic dynamics itself. We state that, despite significant variations in the parameters, due to those human elements present in the contemporary pandemic, and despite the strong nonlinearities of the problem, wise human intervention is possible and able to minimize human losses. We show that the mortality rate does not behave as one would expect for a biological problem, independent of cultural aspects, and we also point to possible dates for the peaks of infection in both countries depending on the control of the transmissibility.

Foram expostos ovos diapáusicos da praga de pastagens na região neotropical, Deois flavopicta (Stal) (Hemiptera: Cercopidae), a baixas temperaturas noturnas, simulando condições de campo durante a estação seca (23/12, 23/15 e 23/18ºC dia/noite), por diferentes períodos (0, 15, 30, 40, 50 e 60 dias). Após o tratamento térmico, os ovos foram mantidos a 28ºC e em água de contato (100% de umidade), até a eclosão das ninfas. Um grupo-controle de ovos diapáusicos foi mantido por todo o período experimental em altas temperaturas e umidade. O tempo para eclosão (em graus/dia) foi reduzido devido ao efeito das baixas temperaturas noturnas e ao aumento no período de exposição ao choque frio, embora não tenha sido observada interação significativa entre esses fatores. A regressão do efeito do período de choque frio no tempo médio para eclosão das ninfas provenientes de ovos diapáusicos produziu equações independentes para as temperaturas abaixo de 18ºC e 15ºC. Com base nas equações de regressão do tempo médio e no desvio-padrão associado, construímos um modelo que simula a proporção esperada da população que eclodirá após o início da estação chuvosa. A simulação gerada pelo modelo correlacionou-se significativamente à população de ninfas observada no campo. Estes resultados mostram que temperaturas noturnas abaixo de 18ºC, como ocorre no Centro-Sul do Brasil entre maio e agosto, abreviam o período da diapausa, acumulam ovos quiescentes no solo e podem sincronizar a eclosão da população.

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% 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.