COVID-19 Pandemic in Malegaon: SUTRA over the Three Waves.

Over the past two years, the COVID-19 pandemic has seen multiple waves with high morbidity and mortality. Lockdowns and other prompt responses helped India's situation become less severe. Although Malegaon in the Indian state of Maharashtra has a high population density, poor hygienic standards, and oppositional local community views toward national pandemic addressing measures, it is nevertheless reasonably safe. To understand the possible reasons serosurvey was conducted to estimate the anti-SARS-CoV-2 neutralizing antibody levels in the Malegaon population. Also, we did SUTRA mathematical modeling to the Malegaon daily data on COVID-19 attributable events and compared it with the National and state level. The case fatality rate (CFR) in Malegaon city for the first, second, and third waves was 3.25%, 2.25%, and 0.39%, respectively. The crude death rate (CDR) for Maharashtra ranked first for the initial two waves and India for the third wave. Malegaon, meanwhile, finished second in the first two waves but fared best in the third. The Vaccination coverage for the first dose before the second wave was only 0.34% but had risen to 64.46% by 12 Oct 2022. By then, the second and booster dose coverage was 27.55% and 2.38%, respectively. Serosurvey did between 12 and 18 Jan 2022 showed a 93.93% anti-SARS-CoV-2 neutralizing antibody presence. SUTRA modeling elucidated the high levels of antibodies due to the pandemic-reach over 102% by the third wave. The serosurvey and the model explain why the pandemic severity in terms of duration and CFR during the subsequent waves, especially third wave, was milder compared to the first wave in spite of low vaccination rates. Supplementary Information: The online version contains supplementary material available at 10.1007/s12088-023-01096-3.

Modelling the spread of SARS-CoV-2 pandemic - Impact of lockdowns & interventions.

BACKGROUND & OBJECTIVES: To handle the current COVID-19 pandemic in India, multiple strategies have been applied and implemented to slow down the virus transmission. These included clinical management of active cases, rapid development of treatment strategies, vaccines computational modelling and statistical tools to name a few. This article presents a mathematical model for a time series prediction and analyzes the impact of the lockdown. METHODS: Several existing mathematical models were not able to account for asymptomatic patients, with limited testing capability at onset and no data on serosurveillance. In this study, a new model was used which was developed on lines of susceptible-asymptomatic-infected-recovered (SAIR) to assess the impact of the lockdown and make predictions on its future course. Four parameters were used, namely ß, γ, η and ε. ß measures the likelihood of the susceptible person getting infected, and γ denotes recovery rate of patients. The ratio ß/γ is denoted by R0 (basic reproduction number). RESULTS: The disease spread was reduced due to initial lockdown. An increase in γ reflects healthcare and hospital services, medications and protocols put in place. In Delhi, the predictions from the model were corroborated with July and September serosurveys, which showed antibodies in 23.5 and 33 per cent population, respectively. INTERPRETATION & CONCLUSIONS: The SAIR model has helped understand the disease better. If the model is correct, we may have reached herd immunity with about 380 million people already infected. However, personal protective measures remain crucial. If there was no lockdown, the number of active infections would have peaked at close to 14.7 million, resulted in more than 2.6 million deaths, and the peak would have arrived by June 2020. The number of deaths with the current trends may be less than 0.2 million.

Bootstrapping variables in algebraic circuits.

We show that for the blackbox polynomial identity testing (PIT) problem it suffices to study circuits that depend only on the first extremely few variables. One needs only to consider size-s degree-s circuits that depend on the first [Formula: see text] variables (where c is a constant and composes a logarithm with itself c times). Thus, the hitting-set generator (hsg) manifests a bootstrapping behavior-a partial hsg against very few variables can be efficiently grown to a complete hsg. A Boolean analog, or a pseudorandom generator property of this type, is unheard of. Our idea is to use the partial hsg and its annihilator polynomial to efficiently bootstrap the hsg exponentially w.r.t. variables. This is repeated c times in an efficient way. Pushing the envelope further we show that (i) a quadratic-time blackbox PIT for 6,913-variate degree-s size-s polynomials will lead to a "near"-complete derandomization of PIT and (ii) a blackbox PIT for n-variate degree-s size-s circuits in [Formula: see text] time, for [Formula: see text], will lead to a near-complete derandomization of PIT (in contrast, [Formula: see text] time is trivial). Our second idea is to study depth-4 circuits that depend on constantly many variables. We show that a polynomial-time computable, [Formula: see text]-degree hsg for trivariate depth-4 circuits bootstraps to a quasipolynomial time hsg for general polydegree circuits and implies a lower bound that is a bit stronger than that of Kabanets and Impagliazzo [Kabanets V, Impagliazzo R (2003) Proceedings of the Thirty-Fifth Annual ACM Symposium on Theory of Computing STOC '03].