On the role of financial support programs in mitigating the SARS-CoV-2 spread in Brazil.

BACKGROUND: During 2020, there were no effective treatments or vaccines against SARS-CoV-2. The most common disease contention measures were social distance (social isolation), the use of face masks and lockdowns. In the beginning, numerous countries have succeeded to control and reduce COVID-19 infections at a high economic cost. Thus, to alleviate such side effects, many countries have implemented socioeconomic programs to fund individuals that lost their jobs and to help endangered businesses to survive. METHODS: We assess the role of a socioeconomic program, so-called "Auxilio Emergencial" (AE), during 2020 as a measure to mitigate the Coronavirus Disease 2019 (COVID-19) outbreak in Brazil. For each Brazilian State, we estimate the time-dependent reproduction number from daily reports of COVID-19 infections and deaths using a Susceptible-Exposed-Infected-Recovered-like (SEIR-like) model. Then, we analyse the correlations between the reproduction number, the amount of individuals receiving governmental aid, and the index of social isolation based on mobile phone information. RESULTS: We observed significant positive correlation values between the average values by the AE and median values of an index accounting for individual mobility. We also observed significantly negative correlation values between the reproduction number and this index on individual mobility. Using the simulations of a susceptible-exposed-infected-removed-like model, if the AE was not operational during the first wave of COVID-19 infections, the accumulated number of infections and deaths could be 6.5 (90% CI: 1.3-21) and 7.9 (90% CI: 1.5-23) times higher, respectively, in comparison with the actual implementation of AE. CONCLUSIONS: Our results suggest that the AE implemented in Brazil had a significant influence on social isolation by allowing those in need to stay at home, which would reduce the expected numbers of infections and deaths.

A singularly perturbed HIV model with treatment and antigenic variation.

We study the long term dynamics and the multiscale aspects of a within-host HIV model that takes into account both mutation and treatment with enzyme inhibitors. This model generalizes a number of other models that have been extensively used to describe the HIV dynamics. Since the free virus dynamics occur on a much faster time-scale than cell dynamics, the model has two intrinsic time scales and should be viewed as a singularly perturbed system. Using Tikhonov's theorem we prove that the model can be approximated by a lower dimensional nonlinear model. Furthermore, we show that this reduced system is globally asymptotically stable by using Lyapunov's stability theory.