At the date, Europe and part of North America face the second wave of COVID-19, causing more than 1 300 000 deaths worldwide. Humanity lacks successful treatments, and a sustainable solution is an effective vaccine. Pfizer and the Russian Gamaleya Institute report that its vaccines reach more than 90 % efficacy in a recent press release. If third stage trial results favorable, pharmaceutical firms estimate big scale production of its vaccine candidates around the first 2021 quarter and the World Health organization fix as objective, vaccinate 20 % of the whole population at the final of 2021. However, since COVID-19 is new to our knowledge, vaccine efficacy and induced-immunity responses remain poorly understood. There are great expectations, but few think the first vaccines will be fully protective. Instead, they may reduce the severity of illness, reducing hospitalization and death cases. Further, logistic supply, economic and political implications impose a set of grand challenges to develop vaccination policies. For this reason, health decision-makers require tools to evaluate hypothetical scenarios and evaluate admissible responses. Our contribution answers questions in this direction. According to the WHO Strategic Advisory Group of Experts on Immunization Working Group on COVID-19 Vaccines, we formulate an optimal controlled model to describe vaccination policies that minimize the burden of COVID-19 quantified by the number of disability-adjusted years of life lost. Additionally, we analyze the reproductive vaccination number according to vaccination profiles depending on coverage, efficacy, horizon time, and vaccination rate. We explore scenarios regarding efficacy, coverage, vaccine-induced immunity, and natural immunity via numerical simulation. Our results suggest that response regarding vaccine-induced immunity and natural immunity would play a dominant role in the vaccination policy design. Likewise, the vaccine efficacy would influence the time of intensifying the number of doses in the vaccination policy.

Diseases transmitted by vectors in crops represent a severe risk to the farmer, causing low production and lower quality, which results in a drastic reduction in crop yield. Here we study a stochastic plant-vector-host epidemic model with direct transmission. Perturbing with Brownian motion plant replanting and vector fumigation rates, we formulate an Ito stochastic differential equations that capture the uncertainty of the controls. We derive conditions to assure extinction and persistence of disease using two different stochastic versions of the so-called basic reproductive number. Finally, we verify and illustrate our theory by numerical experiments. Our simulations suggest that uncertainty could drive dramatic stability changes. Because in practice, to confirm an infected plant via laboratory tests is not necessarily feasible, replanting and fumigation strategies suffer considerable uncertainty. Here, we quantify and study the impact and consequences of this uncertainty. We conclude that environmental noise promotes dramatic stability changes.