Understanding Spatial Heterogeneity of COVID-19 Pandemic Using Shape Analysis of Growth Rate Curves

Mathematical modeling of SARS-CoV-2 variant substitutions in European countries: transmission dynamics and epidemiological insights

Background

Countries across Europe have faced similar evolutions of SARS-CoV-2 variants of concern, including the Alpha, Delta, and Omicron variants.

Materials and methods

We used data from GISAID and applied a robust, automated mathematical substitution model to study the dynamics of COVID-19 variants in Europe over a period of more than 2 years, from late 2020 to early 2023. This model identifies variant substitution patterns and distinguishes between residual and dominant behavior. We used weekly sequencing data from 19 European countries to estimate the increase in transmissibility  ( Δ β )   between consecutive SARS-CoV-2 variants. In addition, we focused on large countries with separate regional outbreaks and complex scenarios of multiple competing variants.

Results

Our model accurately reproduced the observed substitution patterns between the Alpha, Delta, and Omicron major variants. We estimated the daily variant prevalence and calculated Δ β between variants, revealing that: ( i ) Δ β increased progressively from the Alpha to the Omicron variant; ( i i ) Δ β showed a high degree of variability within Omicron variants; ( i i i ) a higher Δ β was associated with a later emergence of the variant within a country; ( i v ) a higher degree of immunization of the population against previous variants was associated with a higher Δ β for the Delta variant; ( v ) larger countries exhibited smaller Δ β ,  suggesting regionally diverse outbreaks within the same country; and finally ( v i ) the model reliably captures the dynamics of competing variants, even in complex scenarios.

Conclusion

The use of mathematical models allows for precise and reliable estimation of daily cases of each variant. By quantifying Δ β ,  we have tracked the spread of the different variants across Europe, highlighting a robust increase in transmissibility trend from Alpha to Omicron. Additionally, we have shown that the geographical characteristics of a country, as well as the timing of new variant entrances, can explain some of the observed differences in variant substitution dynamics across countries.

Data-driven analysis and predictive modeling on COVID-19

The coronavirus (COVID-19) started in China in 2019, has spread rapidly in every single country and has spread in millions of cases worldwide. This paper presents a proposed approach that involves identifying the relative impact of COVID-19 on a specific gender, the mortality rate in specific age, investigating different safety measures adopted by each country and their impact on the virus growth rate. Our study proposes data-driven analysis and prediction modeling by investigating three aspects of the pandemic (gender of patients, global growth rate, and social distancing). Several machine learning and ensemble models have been used and compared to obtain the best accuracy. Experiments have been demonstrated on three large public datasets. The motivation of this study is to propose an analytical machine learning based model to explore three significant aspects of COVID-19 pandemic as gender, global growth rate, and social distancing. The proposed analytical model includes classic classifiers, distinctive ensemble methods such as bagging, feature based ensemble, voting and stacking. The results show a superior prediction performance comparing with the related approaches.

Persistent cross-species SARS-CoV-2 variant infectivity predicted via comparative molecular dynamics simulation

Widespread human transmission of SARS-CoV-2 highlights the substantial public health, economic and societal consequences of virus spillover from wildlife and also presents a repeated risk of reverse spillovers back to naive wildlife populations. We employ comparative statistical analyses of a large set of short-term molecular dynamic (MD) simulations to investigate the potential human-to-bat (genus Rhinolophus) cross-species infectivity allowed by the binding of SARS-CoV-2 receptor-binding domain (RBD) to angiotensin-converting enzyme 2 (ACE2) across the bat progenitor strain and emerging human strain variants of concern (VOC). We statistically compare the dampening of atom motion across protein sites upon the formation of the RBD/ACE2 binding interface using various bat versus human target receptors (i.e. bACE2 and hACE2). We report that while the bat progenitor viral strain RaTG13 shows some pre-adaption binding to hACE2, it also exhibits stronger affinity to bACE2. While early emergent human strains and later VOCs exhibit robust binding to both hACE2 and bACE2, the delta and omicron variants exhibit evolutionary adaption of binding to hACE2. However, we conclude there is a still significant risk of mammalian cross-species infectivity of human VOCs during upcoming waves of infection as COVID-19 transitions from a pandemic to endemic status.

Heterogeneity of the COVID-19 Pandemic in the United States of America: A Geo-Epidemiological Perspective

The spread of the COVID-19 pandemic has shown great heterogeneity between regions of countries, e. g., in the United States of America (USA). With the growing of the worldwide COVID-19 pandemic, there is a need to better highlight the variability in the trajectory of this disease in different worldwide geographic areas. Indeed, the epidemic trends across areas can display completely different evolution at a given time. Geo-epidemiological analyses using data, that are publicly available, could be a major topic to help governments and public administrations to implement health policies. Geo-epidemiological analyses could provide a basis for the implementation of relevant public health policies. With the COVID-19 pandemic, geo-epidemiological analyses can be readily utilized by policy interventions and USA public health authorities to highlight geographic areas of particular concern and enhance the allocation of resources.

A review of mathematical model-based scenario analysis and interventions for COVID-19

Mathematical model-based analysis has proven its potential as a critical tool in the battle against COVID-19 by enabling better understanding of the disease transmission dynamics, deeper analysis of the cost-effectiveness of various scenarios, and more accurate forecast of the trends with and without interventions. However, due to the outpouring of information and disparity between reported mathematical models, there exists a need for a more concise and unified discussion pertaining to the mathematical modeling of COVID-19 to overcome related skepticism. Towards this goal, this paper presents a review of mathematical model-based scenario analysis and interventions for COVID-19 with the main objectives of (1) including a brief overview of the existing reviews on mathematical models, (2) providing an integrated framework to unify models, (3) investigating various mitigation strategies and model parameters that reflect the effect of interventions, (4) discussing different mathematical models used to conduct scenario-based analysis, and (5) surveying active control methods used to combat COVID-19.

A unifying nonlinear probabilistic epidemic model in space and time

Covid-19 epidemic dramatically relaunched the importance of mathematical modelling in supporting governments decisions to slow down the disease propagation. On the other hand, it remains a challenging task for mathematical modelling. The interplay between different models could be a key element in the modelling strategies. Here we propose a continuous space-time non-linear probabilistic model from which we can derive many of the existing models both deterministic and stochastic as for example SI, SIR, SIR stochastic, continuous-time stochastic models, discrete stochastic models, Fisher-Kolmogorov model. A partial analogy with the statistical interpretation of quantum mechanics provides an interpretation of the model. Epidemic forecasting is one of its possible applications; in principle, the model can be used in order to locate those regions of space where the infection probability is going to increase. The connection between non-linear probabilistic and non-linear deterministic models is analyzed. In particular, it is shown that the Fisher-Kolmogorov equation is connected to linear probabilistic models. On the other hand, a generalized version of the Fisher-Kolmogorov equation is derived from the non-linear probabilistic model and is shown to be characterized by a non-homogeneous time-dependent diffusion coefficient (anomalous diffusion) which encodes information about the non-linearity of the probabilistic model.

Toward Achieving a Vaccine-Derived Herd Immunity Threshold for COVID-19 in the U.S

A novel coronavirus emerged in December of 2019 (COVID-19), causing a pandemic that inflicted unprecedented public health and economic burden in all nooks and corners of the world. Although the control of COVID-19 largely focused on the use of basic public health measures (primarily based on using non-pharmaceutical interventions, such as quarantine, isolation, social-distancing, face mask usage, and community lockdowns) initially, three safe and highly-effective vaccines (by AstraZeneca Inc., Moderna Inc., and Pfizer Inc.), were approved for use in humans in December 2020. We present a new mathematical model for assessing the population-level impact of these vaccines on curtailing the burden of COVID-19. The model stratifies the total population into two subgroups, based on whether or not they habitually wear face mask in public. The resulting multigroup model, which takes the form of a deterministic system of nonlinear differential equations, is fitted and parameterized using COVID-19 cumulative mortality data for the third wave of the COVID-19 pandemic in the United States. Conditions for the asymptotic stability of the associated disease-free equilibrium, as well as an expression for the vaccine-derived herd immunity threshold, are rigorously derived. Numerical simulations of the model show that the size of the initial proportion of individuals in the mask-wearing group, together with positive change in behavior from the non-mask wearing group (as well as those in the mask-wearing group, who do not abandon their mask-wearing habit) play a crucial role in effectively curtailing the COVID-19 pandemic in the United States. This study further shows that the prospect of achieving vaccine-derived herd immunity (required for COVID-19 elimination) in the U.S., using the Pfizer or Moderna vaccine, is quite promising. In particular, our study shows that herd immunity can be achieved in the U.S. if at least 60% of the population are fully vaccinated. Furthermore, the prospect of eliminating the pandemic in the U.S. in the year 2021 is significantly enhanced if the vaccination program is complemented with non-pharmaceutical interventions at moderate increased levels of compliance (in relation to their baseline compliance). The study further suggests that, while the waning of natural and vaccine-derived immunity against COVID-19 induces only a marginal increase in the burden and projected time-to-elimination of the pandemic, adding the impacts of therapeutic benefits of the vaccines into the model resulted in a dramatic reduction in the burden and time-to-elimination of the pandemic.