(1) Background: The coronavirus 2019 (COVID-19) pandemic has caused multiple waves of cases and deaths in the United States (US). The wild strain, the Alpha variant (B.1.1.7) and the Delta variant (B.1.617.2) of severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) were the principal culprits behind these waves. To mitigate the pandemic, the vaccination campaign was started in January 2021. While the vaccine efficacy is less than 1, breakthrough infections were reported. This work aims to examine the effects of the vaccination across 50 US states and the District of Columbia. (2) Methods: Based on the classic Susceptible—Exposed—Infectious–Recovered (SEIR) model, we add a delay class between infectious and death, a death class and a vaccinated class. We compare two special cases of our new model to simulate the effects of the vaccination. The first case expounds the vaccinated individuals with full protection or not, compared to the second case where all vaccinated individuals have the same level of protection. (3) Results: Through fitting the two approaches to reported COVID-19 deaths in all 50 US states and the District of Columbia, we found that these two approaches are equivalent. We calculate that the death toll could be 1.67–3.33 fold in most states if the vaccine was not available. The median and mean infection fatality ratio are estimated to be approximately 0.6 and 0.7%. (4) Conclusions: The two approaches we compared were equivalent in evaluating the effectiveness of the vaccination campaign in the US. In addition, the effect of the vaccination campaign was significant, with a large number of deaths averted.

In the context of infectious disease transmission, high heterogeneity in individual infectiousness indicates that a few index cases can generate large numbers of secondary cases, a phenomenon commonly known as superspreading. The potential of disease superspreading can be characterized by describing the distribution of secondary cases (of each seed case) as a negative binomial (NB) distribution with the dispersion parameter, k. Based on the feature of NB distribution, there must be a proportion of individuals with individual reproduction number of almost 0, which appears restricted and unrealistic. To overcome this limitation, we generalized the compound structure of a Poisson rate and included an additional parameter, and divided the reproduction number into independent and additive fixed and variable components. Then, the secondary cases followed a Delaporte distribution. We demonstrated that the Delaporte distribution was important for understanding the characteristics of disease transmission, which generated new insights distinct from the NB model. By using real-world dataset, the Delaporte distribution provides improvements in describing the distributions of COVID-19 and SARS cases compared to the NB distribution. The model selection yielded increasing statistical power with larger sample sizes as well as conservative type I error in detecting the improvement in fitting with the likelihood ratio (LR) test. Numerical simulation revealed that the control strategy-making process may benefit from monitoring the transmission characteristics under the Delaporte framework. Our findings highlighted that for the COVID-19 pandemic, population-wide interventions may control disease transmission on a general scale before recommending the high-risk-specific control strategies.

Background The ongoing coronavirus 2019 (COVID-19) pandemic has emerged and caused multiple pandemic waves in the following six countries: India, Indonesia, Nepal, Malaysia, Bangladesh and Myanmar. Some of the countries have been much less studied in this devastating pandemic. This study aims to assess the impact of the Omicron variant in these six countries and estimate the infection fatality rate (IFR) and the reproduction number $${R}_{0}$$ R 0 in these six South Asia, Southeast Asia and Oceania countries. Methods We propose a Susceptible-Vaccinated-Exposed-Infectious-Hospitalized-Death-Recovered model with a time-varying transmission rate $$\beta (t)$$ β ( t ) to fit the multiple waves of the COVID-19 pandemic and to estimate the IFR and $${R}_{0}(t)$$ R 0 ( t ) in the aforementioned six countries. The level of immune evasion and the intrinsic transmissibility advantage of the Omicron variant are also considered in this model. Results We fit our model to the reported deaths well. We estimate the IFR (in the range of 0.016 to 0.136%) and the reproduction number $${R}_{0}(t)$$ R 0 ( t ) (in the range of 0 to 9) in the six countries. Multiple pandemic waves in each country were observed in our simulation results. Conclusions The invasion of the Omicron variant caused the new pandemic waves in the six countries. The higher $${R}_{0}(t)$$ R 0 ( t ) suggests the intrinsic transmissibility advantage of the Omicron variant. Our model simulation forecast implies that the Omicron pandemic wave may be mitigated due to the increasing immunized population and vaccine coverage.

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<abstract> <sec><title>Backgrounds</title><p>Brazil has suffered two waves of Coronavirus Disease 2019 (COVID-19). The second wave, coinciding with the spread of the Gamma variant, was more severe than the first wave. Studies have not yet reached a conclusion on some issues including the extent of reinfection, the infection fatality rate (IFR), the infection attack rate (IAR) and the effects of the vaccination campaign in Brazil, though it was reported that confirmed reinfection was at a low level.</p> </sec> <sec><title>Methods</title><p>We modify the classical Susceptible-Exposed-Infectious-Recovered (SEIR) model with additional class for severe cases, vaccination and time-varying transmission rates. We fit the model to the severe acute respiratory infection (SARI) deaths, which is a proxy of the COVID-19 deaths, in 20 Brazilian cities with the large number of death tolls. We evaluate the vaccination effect by a contrast of "with" vaccination actual scenario and "without" vaccination in a counterfactual scenario. We evaluate the model performance when the reinfection is absent in the model.</p> </sec> <sec><title>Results</title><p>In the 20 Brazilian cities, the model simulated death matched the reported deaths reasonably well. The effect of the vaccination varies across cities. The estimated median IFR is around 1.2%.</p> </sec> <sec><title>Conclusion</title><p>Overall, through this modeling exercise, we conclude that the effects of vaccination campaigns vary across cites and the reinfection is not crucial for the second wave. The relatively high IFR could be due to the breakdown of medical system in many cities.</p> </sec> </abstract>